Societal Outcomes: Predicting Food Market Prices and Quantities

Abstract

This chapter explains how societal outcomes can be seen as the result of individuals interacting with each other. Markets are physical places or online environments where interactions occur, as people exchange goods and services in pursuit of their individual goals, given their own production possibilities, income or wealth, and their own preferences for consumption. To explain and predict observed prices and total quantities, we proceed graphically in two dimensions to derive supply curves from production possibilities, derive demand curves from incomes and preferences, and then show how interactions among many sellers and buyers lead to observed outcomes for each group of people with and without the possibility of trade with others. We explain how supply, demand and trade diagrams provide qualitative explanations and predictions, and show how a population’s food consumption response to policy or other changes can be measured using elasticities of demand with respect to price and income. Measuring change in elasticity terms allows us to classify goods as more or less responsive to policy intervention, and discuss factors that influence the supply or demand response of different populations to interventions for each kind of food.

3.1 Market Equilibrium with Perfectly Competitive Interactions

3.1.1 Motivation and Guiding Questions

The previous chapter described how individual behavior is influenced by prices, but where do prices come from? Why are some foods expensive while others are cheap, and how do prices relate to quantities produced or consumed?

To answer these questions and predict how prices and quantities might change in response to different government policies or other circumstances, we derive analytical diagrams that provide qualitative insights, offering simplified models to explain the direction and relative magnitude of differences or changes in price and quantity. A wide range of theories about prices and quantities have been tested by successive generations of economists, leading to the causal framework described here. These diagrams guide how prices and quantities are measured and interpreted. Testing hypotheses about predicted outcomes under different circumstances leads to further refinement of the models, altering their focus to capture the most important aspects of behavior for each situation.

Our focus is on interactions between people in what economists call a market, meaning any in-person or electronic environment in which people exchange things. In most markets, whether transactions occur online or in physical places, people exchange things for money and we track prices paid or received as well as the quantities bought and sold. The same analytical models can also be used for nonmarket transactions such as volunteering and use of donated things, for example to explain, predict and assess services provided in food pantries or meal services.

The market diagrams in this chapter use lines and curves to identify a market equilibrium. This is one of many instances where terminology in economics can be confusing. Economists use the word ‘equilibrium’ to mean any predictable outcome of interactions between people. In everyday usage, an equilibrium is a stable or desirable condition, but the balance between economic forces that predict market outcomes can lead to terrible outcomes such as price spikes, hunger and deprivation. Predicting these outcomes as an equilibrium between forces allows economists to identify how changing policies or technologies might lead to different outcomes.

The conditions under which transactions occur is known as market structure. For example, some markets involve interactions only within a community, while other markets are open to trade with people elsewhere. This section of our first chapter on market equilibrium concerns the simplest kind of market, in which a community of people has many buyers and sellers exchanging a uniform product at a single price. Markets of this type are perfectly competitive. Like any kind of perfection, a market with entirely perfect competition cannot exist in reality, but the resulting model provides a useful benchmark against which to compare outcomes from various kinds of market failures addressed in later chapters such as monopoly power, externalities and lack of information about product quality. Food markets are often subject to market failures, but can also be shaped by policy and technology to have more buyers and sellers, fewer externalities and greater transparency about product quality, thereby reducing imperfections and moving towards the benchmark model of perfect competition introduced in this chapter.

The toolkit of analytical diagrams in this and later chapters uses different market structures to predict different outcomes, all following the same economic principles. In the previous chapter, we explained individual behavior as each person’s choice from their limited options, drawn as points of tangency between a line and a curve. In this chapter, we explain societal outcomes as an interaction between individuals, drawn as a point of intersection between two curves. For individuals, the optimal choice may be the least bad of their options, and for societies even a perfectly competitive equilibrium can be very undesirable. The toolkit of economics allows us to build market models tailored to observed conditions and identify how changes in policies and technologies could lead to market outcomes with greater sustainability, equity and health for the populations we serve.

By the end of this section, you will be able to:

• 1. Derive supply curves from PPFs and revenue lines;

• 2. Derive demand curves from indifference curves and budget lines;

• 3. Describe how movements along supply and demand curves differ from shifts in those curves, and lead to observed outcomes; and

• 4. Identify predicted prices and quantities produced and consumed in markets with imports, exports or without trade, in settings with many buyers and sellers for a standard product of known quality.

3.1.2 Analytical Tools

The models for societal outcomes used in this book are all derived from the theory of individual choice developed in the previous chapter. Like those individual-choice diagrams, market models are drawn by first defining the variables on each axis, and then tracing lines and curves that show a particular relationship between those two variables. The definition of each line or curve leads to its position and shape, and the predicted outcome is the point of intersection between two of the lines. As always, each diagram corresponds to a specific scenario with a given level of all other variables.

Every market model refers to a specific community, adding up the choices of all individuals in that community. Market models refer to a specific set of people, often all of the residents of a city, state or the world as a whole, and may also distinguish between subpopulations especially regarding equity between groups. The horizontal X axis always shows the total quantity of a good or service, added up over a specific period of time, while the vertical Y axis shows its price or cost per unit at that time. Quantities are measured in weight or volume which might add up to millions of liters or tons per year, while prices are those facing each individual such as cost per serving.

For quantitative research, market models would correspond to actual data published by someone, such as the price and quantity of all apples each year in the U.S. which is estimated by the USDA based on surveys of apple growers and distributors. In this book we use diagrams only for qualitative analysis, to see causal relationships and relative magnitudes based on geometric relationships. This allows us to make diagrams about something for which quantitative information is not available, such as the cost and quantity of home-made bread produced and consumed in a neighborhood each month. We could try to estimate that, but we can also obtain useful insights through qualitative analysis.

To build our market models we begin with production, deriving a community’s supply curve from the production possibility frontiers (PPFs) and price lines faced by each individual farmer or food producer. We then derive that same community’s food demand curve from each individual consumer’s budget lines and indifference curves, and explain outcomes as the interaction between people in the benchmark case of a perfectly competitive market, with many sellers and buyers who face a single price for a uniform product. We draw each market diagram first for a community in isolation, leading to a single quantity produced and consumed, and then for a community that might also export or import the product by trading with other people. The resulting predictions can be surprising and provide useful insights about the real world, even before we explore market failures and policy interventions in later chapters.

3.1.2.1 The Supply Curve

Total production in any community is the sum of each person’s quantity produced. Here we show how that level of supply is derived from each individual’s production possibilities, moving along their PPF towards additional output of things whose price has increased. For simplicity we derive the community’s supply curve from each individual’s production possibilities at a fixed level of all input used, but similar decisions underlie choices based on input response and input substitution curves. Because individuals have moved to points where each curve’s slope just equals the relative price received, the price received always equals the marginal cost of additional production.

The relationship between substitution among outputs along a PPF and the marginal opportunity cost of production is shown for an individual producer with example numbers in Fig. 3.1.

Fig. 3.1

We can derive an individual producer’s supply curve from their PPF

The diagram in Fig. 3.1 uses concrete numbers between 1 and 4, allowing you to verify each calculation in the transformation of individual choices on the left to a supply curve on the right. As shown in the previous chapter, each individual will try to produce at a point of tangency between their PPF and a price line, so in this case they might produce one unit at a price of 1/3, three units at a price of 1 and four units at a price of 3. We use pesos as the name of the monetary unit in this diagram only because it is a short and familiar word for money in several countries. More generally we would use whatever currency can be exchanged for the set of all other goods along the vertical axis of the right panel, which can be imagined as a vertical stack of all other things measured in monetary terms. To simplify comparison between the two panels, they are drawn to scale so you could verify these slopes using a ruler.

The data in Fig. 3.1 are shown with example numbers of kilograms and pesos for a single person. That allows you to check unit conversions and thereby build your intuition about how the variables on each axis relate to each other. Even without numbers you can use the name of each measurement unit to see how individual choices underlie the supply curve. Once we see the quantity of all other things along the vertical axis of the PPF as a vertical stack of money, in this case pesos, so the rise-over-run slope of the frontier is measured in pesos per kilogram. The slope of each price line used to identify producers’ choices along their PPF is also measured in pesos/kg, and that price is also the unit of measure for the supply curve’s vertical axis.

Verifying unit conversions, with or without concrete numbers, can be extremely helpful to confirm that abstract concepts like price and quantity are being used as intended in each situation. The structure of models like Fig. 3.1 can be explained in words and mathematical symbols, and then you can check how the variables relate to each other by replacing each variable name with its unit of measure. For example you can replace price with P in pesos/kg, and replace quantity with Q in kg, to verify that P times Q would be measured in pesos. Every variable in our models has an implicit unit of measure, and making those units explicit can be very helpful to check the validity and meaning of the model. In the case of Fig. 3.1, the units are specified as pesos and kg for one individual person, but there is no mention of time or location. Models used in practical applications should be labeled with the time, place and other identifying information.

Each producer’s PPF and supply curves reflect their individual circumstances and are drawn on our analytical diagrams in the simplest form needed to show the qualitative direction of effect. The individual supply curve in Fig. 3.1 happened to be bowed upwards but that was an accident driven by the arbitrary numbers used for ease of calculation. For visual clarity it is easiest to draw supply curves as straight lines, and we can imagine a variety of similar individual producers in a community whose market supply curve is shown in Fig. 3.2.

Fig. 3.2

Definition of the supply curve

Market supply in Fig. 3.2 is shown with numbers along the axes to illustrate how the quantities from each individual are added up to obtain the whole community’s supply curve at each price. In this case we use the abbreviated dollar sign for monetary price per kilogram ($/kg) along the vertical axis, and to show large quantities over a long period time the horizontal axis is in metric tons per year (mt/yr).

Supply curves are drawn as straight lines here and throughout this book partly for visual clarity, and also to differentiate supply curves from the indifference curves, PPFs, IRCs or ISCs each of which has a specific curvature. Using a set of straight lines reveals how the horizontal sum of quantities at each price has a flatter slope than each individual line. That qualitative insight would remain true for supply curves of different shapes. When supply curves are estimated statistically they take a variety of mathematical forms, but in all cases the definition of supply is the quantity produced at each price, or equivalently the price required for each quantity produced. Price always equals marginal cost, so supply curves can always be labeled S = MC.

Models like Fig. 3.2 help us distinguish clearly between supply, meaning the entire curve of quantities produced at each price, and production which is a particular quantity produced along the curve. A larger community or changes in circumstances would bring shifts in supply, to a different quantity at the same price. Those would be caused by external factors not shown in this diagram, sometimes called exogenous changes originating outside the model. In contrast, a change in price from people moving along their supply curves is endogenous to the model. Those terms use the Latin prefixes exo- and endo- to mean outside or inside, and -genous to mean where the change comes from. Exogenous changes are sometimes called ‘shocks’ to the model, whether or not they happen suddenly because they come from outside, whereas endogenous changes are results that the diagram aims to explain and predict. Some examples are shown in Fig. 3.3.

Fig. 3.3

Price change leads producers to move along their supply curve, which can shift

The points in Fig. 3.3 show six different quantities produced, from around 12 to over 40 mt/yr. Initial observations might be either of the two solid black dots, at a low or high price, but then resource depletion might shift supply leftward leading to the gray dashed line, or technological innovation might shift supply rightward leading to the gray solid line. Actually estimating any of these lines would require advanced techniques for data collection and analysis. The qualitative model in each diagram provides helpful vocabulary, tells us what to look for and generates hypotheses that could be tested to distinguish among possible causal mechanisms behind the outcomes we see.

The changes shown in Fig. 3.3 use linear supply curves only for simplicity. The only attribute of all supply curves is that they never slope down. Where available technologies offer increasing returns to size or scale, producers might switch up to larger operations at higher prices and shut down entirely to produce zero when prices are below a minimum threshold. Available technologies might also allow expansion at constant returns and hence horizontal supply curves until some limiting factor is reached, beyond which producers face diminishing returns and upward sloping supply.

Drawing supply curves yields remarkable insights about production, showing how people’s choices select from all possible options in systematic ways. Due to human selection, the range of things we might actually observe in any situation is only a subset of potential outcomes. Economic principles reveal qualitative similarities in what might be observed, point to the subject-matter knowledge we would need for empirical work in specific situations, and suggest causal mechanisms that might explain, predict and allow improvement in observed results. For example, in Fig. 3.3, there are two possible points on each supply curves. What explains which point we might observe? For that we need additional information, starting with consumer demand.

3.1.2.2 The Demand Curve

Like supply, we can derive demand using each person’s choices from their available options. Just as supply was defined as the quantity produced at each price, derived from producers choosing among production possibilities based on price received, demand is defined as the quantity consumed at each price and is derived from consumers choosing along budget lines to reach their highest level of wellbeing.

The derivation of an individual’s demand curve from their budget lines and indifference curves is illustrated in Fig. 3.4.

Fig. 3.4

We can derive an individual’s demand curve from their indifference curve and budget line

The left and right panels of Fig. 3.4 show how demand curves relate to each person’s subjective wellbeing, reflecting their individual goals and constraints. The left panel shows how a higher price for the product of interest, for example shifting from one to two pesos per kilogram, might reduce their quantity consumed. The consumer’s choices along their budget lines lead to level of wellbeing where the price paid for something just equals the slope of their indifference curve for it, meaning the additional quantity of all other things they would accept for one more unit of it. The right panel shows that price as the consumer’s willingness to pay (WTP) at each quantity, or equivalently the quantity that they would be willing and able to consume at each price paid.

In the same way that production choices traced out a curve labeled S = MC, demand curves can be labeled D = WTP. In that notation, the S = MS and D = WTP both refer to a price along the vertical axis, for the quantity shown on the horizontal axis. Some sources refer to these as inverse supply and inverse demand curves, when referring to equations where quantity is a function of price. In practice, however, price and quantity are determined simultaneously so the two curves can simply be called supply and demand.

The individual’s demand curve in Fig. 3.4 is shown as a straight line only for visual clarity, joining the solid black dot and the dashed gray dot in the simplest possible way. That simplification makes the demand curve on the right look superficially like the budget line on the left, but their definitions and interpretation are completely different. The budget line is always drawn linearly to show the price paid for additional units, just as the indifference curve is always bowed-in to show the degree of diminishing marginal benefits or rates of substitution in consumption of things. Meanwhile the demand curve could take any shape, and is usually shown as a straight line only to make each market diagram easier to interpret.

As shown by the two panels of Fig. 3.4, higher prices generally lead to lower quantities consumed. That is the net result of two changes, the loss of purchasing power and lower real income shown by the lower indifference level, and a substitution effect along each indifference curve. The combination of income and substitution effects is such that moving from solid black to dashed gray almost always reduces quantity consumed along the horizontal axis, so demand curves almost always slope down.

The unusual cases where demand curves might sometimes slope up are so rare that they are named after the researchers who first described them. In the 1890s, at the same time as Alfred Marshall’s Principles of Economics popularized the use of demand curves to explain consumption, the British statistician Robert Giffen described how the poorest people in Britain were sometimes forced by rising price of the cheapest foods such as potatoes to buy even more of them, because higher costs left them able to afford even less of their preferred but more expensive foods such as milk or vegetables. Soon thereafter, in 1899 the American sociologist Thorstein Veblen noted that richer people in the U.S. were buying expensive things as a signal of wealth and taste, thereby creating both high prices and high quantity for some items. We will return to both Giffen goods and Veblen goods later in this book, but both are relatively rare and limited to a subset of the population. In general for entire societies, the ‘Marshallian’ demand curve for each good slopes down.

As with supply, a community’s demand curve is the horizontal sum of each person’s quantity at each price. For demand we add up the community’s consumption, tracing quantity consumed at each price, or equivalently the price that consumers would be willing to pay for each quantity as shown in Fig. 3.5.

Fig. 3.5

Definition of the demand curve

Each community’s demand curve, like their supply curve, reveals how movements along the curve involve variation in both price and quantity under a given set of circumstances, while shifts in the curve represent a change in circumstances. For the supply curve, shifts are caused by changes in the natural environment or available technology, whereas demand curve shifts are caused by changes in population size, income or preferences. For production, the two kinds of shift go in opposite directions: changes in environmental conditions typically reduce supply, while new technologies that are adopted typically increase supply. For consumption, income and preferences can shift demand in either direction, as illustrated in Fig. 3.6.

Fig. 3.6

Price change leads consumers to move along their demand curve, which can shift

Food demand curves generally shift to the right over time due to growth in the size of each population, expanding quantities demanded at each price. Another factor that often shifts demand to the right is income growth per person, but richer people do not always have higher willingness to pay at each quantity. For some foods, known as inferior goods for the population of interest, higher income shifts demand down and to the left. Changes in preferences and other factors can also shift demand in either direction, to the left or to the right.

In recent decades there have been large changes in global food consumption known as the dietary transition, typically towards more packaged and processed food as well as food consumed away from home. Some of these changes could be due to movements along the demand curve for each type of food, but observed price changes have been insufficient to explain the magnitude, direction and timing of quantity changes discussed in Section 10.2 of this book. Beyond price-induced movements along each curve, some of the dietary transition must have been caused by shifts in the curves as shown in Fig. 3.6.

The extent of movements along and shifts in demand curves for different foods in different places has been difficult to measure precisely, but analytical diagrams like Fig. 3.6 suggest what to look for and how to interpret observed data. Some shifts in demand curves at each price have been associated with changes in employment, urbanization and preferences about time use. Other shifts in demand could be caused by changes in how foods are produced and marketed, as well as changes in public perceptions and news coverage that influence the attractiveness of different foods.

To begin seeing how we might distinguish among the possible causes of change in consumption, we need to describe how producers and consumers interact. When we put supply and demand together, we will see that some markets are for products that are exchanged only within the community of interest, while others involve trade with other people outside the community. These interactions determine the prices we observe and quantities produced or consumed.

In later chapters of this book we will look beyond price and quantity to address other kinds of market outcomes and different market structures. For example, in the next chapter we will address inequity and social welfare, using the example of a market composed of distinct individuals. Then Chapter 5 addresses market power, and the ways in which a monopoly business might influence outcomes. To start, we use the benchmark case of a perfectly competitive market in which there is a very large number of similar buyers and sellers as described below.

3.1.2.3 Interaction in Markets Between Local Producers, Local Consumers and Trade with Others

Market models use supply and demand curves to explain and predict changes in price and quantity. Each curve traces all possible points that producers and consumers might have chosen, so only the intersection of two curves is a point that could be sustained by interaction between producers, consumers and other people. Those intersections are a potential market equilibrium that might be observed, if it persists long enough to be measured before the next shift in supply or demand leads to a different equilibrium.

Readers of this book can use market models directly, just by following the definition of each line to each point of intersection. Geometry will lead us to the logical outcome of each scenario. But it is easy to misinterpret one or more elements of the diagrams, and thereby draw incorrect conclusions. Building your own understanding of the diagrams, by sketching them yourself and explaining them in your own words, is the only way to be sure that you have used each element as intended. Practicing economists sketch these diagrams repeatedly, over and over again, with slight variations to see how the elements interact and build intuition about the logic.

For some readers, many or all of the logical steps using each diagram will seem familiar, and the results will be intuitively plausible. Some of the most valuable moments, however, will be when a sequence of plausible steps leads to an unexpected conclusion, with results that seem completely implausible. That’s helpful when it prompts readers to retrace their steps, which might reveal an error and improve understanding of how economic models work. But the best moments of all are when retracing each step confirms that the story is correct, and leads to a new understanding of the world itself. Readers might go from bored to puzzled, or from ‘duh’ to ‘huh?’, with the goal being to reach those elusive ‘aha!’ moments of unexpected insight.

If you have not yet encountered a surprising aspect of economics, you are likely to find one by working through the logic of market interactions shown in Fig. 3.7.

Fig. 3.7

Interactions between supply, demand and trade

The three market diagrams in Fig. 3.7 are drawn around real-life examples with which many students might be familiar. All three diagrams refer to the entire population of Massachusetts in a recent year. In the left panel is the state’s market for hot pizza, sold in every community around the state in restaurants or for home delivery. In the middle is the market for cranberries, a fruit grown for centuries in coastal wetlands, and on the right is the market for apples, a fruit that grows in many temperate environments. To be clear that we are talking about real things consumed by actual people, the units of measure shown are slices of pizza, pounds (lbs) of cranberries and bushels (bu) of apples, and it turns out that Massachusetts has about 7 million people, served by about 2000 registered pizzerias, about 375 cranberry growers and roughly 400 apple growers. The state’s demand and supply curves could be estimated empirically, but for this textbook we focus on qualitative insights about how people would respond to change.

Starting with the supply of pizza, cranberries and apples, every potential seller will produce along their own production possibilities, building new facilities and hiring the staff needed to sell each quantity. For pizza the first units along the state’s supply curve might be sold from low-rent storefronts with low-cost ingredients by low-wage workers, and building more pizzerias would require bidding for additional space and workers with other options. The pizza supply curve might actually be horizontal if the pizza sector has scale economies that reach lower or constant costs at greater quantities sold, but at some point expansion would encounter diminishing returns and the supply curve would slope up. A similar logic applies to the supply curve for cranberries, which are grown on suitable wetlands in coastal areas that might also be used for recreation and other purposes, as well as the supply curve for apples that are grown in orchards all around the state. All of the supply curves could be horizontal or upward sloping, and are drawn as straight lines for simplicity.

Switching to the demand for pizza, cranberries and apples, we can trace downward sloping demand curves for each food as consumers with the greatest willingness and ability to pay for the items buy the first units, and successive consumers enter to buy each additional quantity if sold at a lower price. We could have a very enjoyable discussion of what determines those quantities consumed at each price, including product quality and convenience as well as cultural and historical factors, healthiness and so forth, but the demand curves would still almost always slope down, drawn straight for simplicity.

Turning to the predicted outcome for each product, the definition of a perfectly competitive equilibrium is the price and quantity that follows if many buyers and sellers can easily find each other and exchange a known product of uniform quality. Perfect competition implies that producers move along their supply curve until they run out of willing buyers, and consumers move along their demand curve until they run out of willing sellers.

The model’s prediction about pizza is our first main result. It may seem intuitively plausible that supply equals demand, but this diagram is supposed to illustrate all production and consumption for the entire state, so that the entire state’s lowest willingness to pay for one additional unit just equals the entire state’s highest marginal cost of production. In fact Massachusetts extends almost 190 miles in length, and the feasible distance for pizza delivery or pickup might be up to 5 or 10 miles, so there cannot be competition between all producers for delivery to all consumers. It would be more realistic to draw separate supply and demand curves for each place, leading to the possibility that prices differ by location. There might also be separate supply and demand curves for pizza of different qualities, and many other refinements.

The model’s prediction about cranberries is also surprising. One might think that supply equals demand, but Massachusetts ships most of its production out of state. Generic processed cranberries can readily be put on a truck or train and shipped thousands of miles at very low transport costs, and products from each region are of similar quality, so there is in effect a national market and a single U.S. price for that product at any one time. Massachusetts producers can sell to any buyer so move along their supply curve up to that price paid for shipments out of state, and Massachusetts consumers find nothing to buy below that price, so the horizontal price line from the U.S. as a whole dictates both production and consumption. Within Massachusetts, demand and supply do not meet, and local prices come from the supply-demand balance in the entire U.S.

The model’s predictions about apples is the mirror image of cranberries. While Massachusetts was once an exporter of apples to other states, other regions of U.S. now produce much larger volumes at prevailing prices, and Massachusetts is a net importer. Again, the result of relatively low shipping costs is that local prices come from the balance of supply and demand to and from all other locations. Consumption in Massachusetts can extend along its demand curve all the way down to that price, while production in Massachusetts extends along its supply curve only up to that cost. In fact a few additional apples may be sold at a premium for being locally grown, but that would be drawn as separate markets for apples of different types.

Despite the limitations of these three simple models, the central insight of Fig. 3.7 is that the perfectly competitive benchmark provides a useful starting point, revealing that only local services such as pizza delivery in each town have markets where local production equals local consumption. For products that can transported at low cost relative to product value, prices are set over the whole market area such as the entire U.S., and each community is likely to be either exporting or importing to other regions.

The purpose of each market diagram is to provide qualitative insights that explain and predict responses to change. It is helpful to draw a separate set of diagrams for service such as hot pizza in each neighborhood where supply equals demand, in contrast to products such as cranberries or apples that can be traded with people elsewhere. We start with the nontraded services for which each location is said to be in autarky, from the Greek word for self-sufficiency. In this context, autarky and self-sufficiency refer only to the absence of trade in this specific product, and does not imply autonomy or self-reliance in general. As we will see, being self-sufficient in one thing may come at a cost in terms of vulnerability and limited access to other things, so can reduce a community’s degree of overall autonomy and self-reliance. That question is addressed in the next chapter when we address social welfare. For now we focus on how price and quantity respond to change as shown in Fig. 3.8.

Fig. 3.8

Supply and demand shifts in a market without trade

The left side of Fig. 3.8 reveals how shifts in supply trace out the market's demand curve, while the right side shows how shifts in demand trace out the market’s supply curve. This figure also introduces a new aspect of our analytical diagrams, which is to use the prime (‘) and double-prime (“) symbols to denote different scenarios. On the left panel drawing shifts in supply, the initial price and quantity observed in this market are P and Q at supply curve S, and then when supply improves the new outcome is P’ and Q’ at S’, or when supply worsens the outcome becomes P” and Q” and S”. A similar trio of scenarios is shown in the right panel, with the initial price and quantity, then a prime and a double-prime.

In each case, only one of the curves shifts and the other doesn’t. Movements along the curve that stays in place are endogenous changes generated inside the model, while shifts in the other curve are exogenous events arising from other variables. Example scenarios might be a supply-enhancing innovation that causes the shift from S to S’, or damage to the environment that shifts supply to S”, each of which is drawn as an exogenous shock which the model predicts would cause endogenous demand response through consumers’ movement along the demand curve.

Behavioral responses within the simplified model of Fig. 3.8 are all drawn as straight lines with similar slopes for visual clarity, but supply may in fact be quite horizontal due to expansion at roughly constant costs, while demand may be quite steep due to consumer preferences. The role of differences in slope will be addressed in the following section, where slope is measured as the elasticities of supply and demand.

For market diagrams about products in communities that are traded with people elsewhere, shifts in local supply and demand affect only local production and consumption. Price is set in the larger market outside of any given community. With trade, local production does not equal local consumption but the difference is the quantity traded and not a ‘surplus’ or ‘shortage’. Market structure depends not just on characteristics of the item but also the community whose producers and consumers are shown in the diagram. For example, Massachusetts is an importer of apples from elsewhere, but the U.S. as a whole is an exporter of apples to other countries. Whether importing or exporting, trade ensures that shifts in demand and supply affect only one side of the market, because price is set elsewhere as shown in Figs. 3.9 and 3.10.

Fig. 3.9

Response to shifts in demand for products that are traded with others

Fig. 3.10

Response to shifts in supply for products that are traded with others

The consequences of shifts in demand for a traded product are shown in Fig. 3.9. In these markets, when foreign buyers offer higher prices than our community would have in self-sufficiency, our sellers choose to export (as shown for cranberries on the left panels), or when foreign sellers offer lower prices, so our buyers choose to import (as shown for apples on the right panels). In either case, shifts in demand affect only consumption and the quantity traded, which adjusts to the price set in the rest of the world.

Shifts in demand shown in Fig. 3.9 are mirrored by shifts in supply shown in Fig. 3.10, where exogenous shocks to production conditions affect only quantities grown, and quantities traded adjust to prices set by the rest of the world. In each of these cases, researchers might ask whether the shift in demand or supply shown in each diagram is large enough to affect prices in the entire market elsewhere. That depends on relative sizes of regions where the change occurs, and the elasticities of market response as discussed in the following section.

3.1.3 Conclusion

Market diagrams explain observed outcomes using lines that show quantities chosen at each price, or equivalently the price at which each quantity would be chosen. Each diagram shows production, consumption and all transactions in a given community for a specified product over some period of time. Outcomes that could persist long enough to be observed are at the intersection of two lines, because that is the point where all transactions that people would have chosen already occurred. In each diagram, the points of intersection between two lines are called an equilibrium because they result from a balance of forces. Different outcomes might be better, at least for some people, but further transactions towards a different point would not be chosen unless circumstances change.

For restaurant food and local services such as hot pizza, each unit is consumed near the place and time of production, so market diagrams explain outcomes as the intersection of supply and demand in each neighborhood. For food products like cranberries or apples that can readily be shipped by truck, train or boat, the cost of transportation and storage is typically low enough that prices are set by supply and demand over large areas. Since people in each community can trade with people elsewhere, market outcomes are where supply and demand meet the price observed for trade with others, and each community’s quantity produced differs from its quantity consumed.

Any supply, demand and trade diagram can provide useful insights only to the degree that it reflects the actual decision-making of people in each community. The initial benchmark model shown in this chapter would arise in perfectly competitive situations, with no obstacles to transactions between many buyers and many sellers for a uniform product. Later chapters will introduce models for situations with a variety of market failures and imperfect competition. Economics consists of choosing among models and tailoring them to fit the analyst’s subject-matter knowledge, including magnitudes of response as described in the following section.

3.2 Market Elasticities: Measuring How People Respond to Change

3.2.1 Motivation and Guiding Questions

The previous section showed how to construct analytical diagrams for perfectly competitive markets in any given situation. Those were purely qualitative models, designed to show causal mechanisms behind observed outcomes, but economists often need to estimate quantitative magnitudes of likely response to a change in circumstances. When shifts in supply, demand or trade opportunities occur, how much change will we see in prices and quantities? When governments introduce taxes or regulations, how much change will we see in production and consumption?

Market diagrams can be drawn for transactions using many different units of measure, such as servings per day or tons per year. Prices may be measured in any currency, such as pesos or dollars whose value differs at each place and time. Quantifying how much change to expect calls for subject-matter knowledge, including familiarity with many kinds of data about the factors that influence behavior. To compare findings across settings, it is very helpful to report results as elasticities of change in quantity.

Elasticities of response are the percent change in quantity observed due to a one percent change in something else. Discussing change in terms of elasticity is helpful not only to measure and compare magnitudes of change, but also to make qualitative predictions such as whether an intervention will have any effect at all on buyers or sellers.

So far, we have seen how individual choices lead to societal outcomes within a market. Introducing elasticities of response allows us to begin discussion of other factors that affect outcomes, including government interventions or environmental, technological and other shifts. Later chapters will show data visualizations of how much change has actually occurred and the magnitude of differences observed in populations around the world.

By the end of this section, you will be able to:

• 1. Describe the relationship between price elasticity and supply or demand curves, and between income elasticity and Engel curves;

• 2. Use supply and demand diagrams, with and without trade, to show how price elasticities shape the impact of taxes and regulations on producers and consumers;

• 3. Describe the factors influencing magnitude of price and income elasticities; and

• 4. Describe and use diagrams to show how government trade policies differ from domestic interventions in their effects on producers and consumers.

3.2.2 Analytical Tools

Elasticities are needed to collect and compare results of observed changes for different things in different places, translating the results of our analytical diagrams into magnitudes of response in quantities and prices. Changes in anything can be reported in percentage terms.

In economics, the term ‘elasticity’ always refers to the percentage change in quantity that would follow from each percentage change in something else. Price elasticities are a percent change in quantity for each percent change in price and would be computed for both supply and demand. A product’s price elasticity of supply is always positive (or more precisely it is never negative, because supply curves never slope down), and its price elasticity of demand is almost always negative (and would be positive only for Giffen goods and Veblen goods discussed in the previous section).

For demand we can also calculate income elasticities, which are the percent change in quantity consumed for each percent change in personal or household income of a population. A product’s income elasticity of demand is usually positive but can be negative for inferior goods consumed more at lower incomes. Demand and supply curves can shift due to prices of other things, so economists also refer to the cross-price elasticity for consumption or production of something with respect to the price of something else. When two products are complements typically consumed together, such as tomato sauce and pasta, a rise in the price of tomato sauce might cause a decline in quantity sold of pasta, meaning a negative cross-price elasticity of demand. Most foods are substitutes for each other, leading to positive cross-price demand elasticities.

Elasticities are a ratio between two percentages, providing a unit-free measure that can be measured and compared across different settings. In some situations, analysts use a semi-elasticity, which is the percent change in quantity associated with a specific increment of change in something else. For example, to study soft drink demand, we might report the elasticity of demand for each one percent change in income or price, but the semi-elasticity of demand for each one degree change in temperature.

Using elasticities helps build intuition in applying economic principles to any given situation, by converting the bewildering array of different units into a ratio of percentage changes. Whether elasticities are positive or negative, and greater or less than one, corresponds to qualitative differences in the direction of change for variables of interest that we can discuss verbally and show graphically, even without numerical data.

To see how and why to convert natural units such as pesos and kilograms into elasticities, we start with the mathematical notation that underlies our diagrams. That math could also be used to see how supply and demand elasticities are all interconnected, using algebra in a multivariate system of equations that reflects the world’s multidimensional food system. Readers can also skip the math and go directly to using elasticities for qualitative analysis of how people respond to change.

3.2.2.1 Mathematical Notation and the Definition of Elasticities

In Chapter 2, we showed individual choices along lines and curves whose slopes are always ($\frac{Rise}{Run}$). Price lines have a constant slope, showing the relative cost of one more unit along the X axis ($\frac{-Px}{Py}$), while curves have varying slopes showing the quantity of things along the Y axis given up for each increment along the X axis ($\frac{\Delta Qy}{\Delta Qx}$). Individual-choice diagrams explain each point as having tangency between their lines and curves, meaning that $\frac{-Px}{Py}$ =$\frac{\Delta Qy}{\Delta Qx}$. The slope of a curve on any market diagram, ($\frac{\Delta P}{\Delta Q}$), might vary at different points ($P$, $Q$) and it has very awkward units of measure as explained below. We therefore convert change along each curve to unit-free elasticities, such as the percent change in quantity ($\frac{\Delta Q}{Q}$) for each percent change in price ($\frac{\Delta P}{P}$), expressed as a ratio: ($\frac{\Delta Q}{Q})/(\frac{\Delta P}{P})$.

Why do we need all that notation? To understand any computation we can do analysis of units, in which a variable’s units of measure are treated as if it were itself a number. For example, the price of apples might be measured as dollars per pound ($\frac{\$}{lb}$), and its quantity might be measured in tons per year ($\frac{mt}{yr}$). The slope of its supply or demand curve, ($\frac{\Delta P}{\Delta Q}$), would then be measured in terms that make no sense ($\frac{\$/lb}{mt/yr})$. This unit conversion reveals that the slopes of our diagrams are not interpretable in themselves, but must be converted to unit-free percentage terms:

$$\varepsilon = \frac{percent\;change\;in\;quantity}{{percent\;change\;in\;price}} = \frac{{{ }\Delta Q/Q}}{\Delta P/P} = \frac{{{ }\Delta Q}}{\Delta P} \cdot \frac{{{ }P}}{Q}.$$

(3.1)

Writing the definition of elasticity in mathematical terms confirms that elasticities are related to run-over-rise ($\frac{\Delta Q}{\Delta P}$) which is the inverse of slope, multiplied by ratio of price to quantity ($\frac{P}{Q}$).

3.2.2.2 Elasticities Summarize Complex Interactions in Production and Consumption

Readers can skip over our use of mathematical notation, but seeing it can help everyone recognize that each number is also a variable, that there can be many variables in a model, and that each model specifies just one of the many possible relationships between variables. Elasticities are a two-dimensional relationship within a larger theory of change, summarizing behavioral responses that reflect complex interactions in production and consumption.

The principles of economics, presented graphically and verbally in this or other introductory textbooks, are all derived from more complex models that have evolved over a century of experimentation and practical experience. Each two-dimensional diagram and its resulting elasticities summarize systems of simultaneous equations. For production, the three kinds of curve (PPF, IRC and ISC) represent all kinds of production functions between all inputs and all outputs, from which observed choices come from profit functions that link quantities and prices. Similarly for consumption, the indifference curves and budget lines represent demand systems of interaction between all requisites of wellbeing such as food, housing, education and so forth.

Supply or demand curves and their elasticities are bivariate summaries of deeper multivariate models that can and should consider variation over time, space and other dimensions. Real-life work by professional economists includes the use of two-dimensional models like our diagrams, or multivariate versions of those models that are written in algebraic notation and solved using calculus or other techniques to analyze all possible real numbers. Modern ways of formulating and estimating these models were advanced in the 1980s and 1990s by Angus Deaton, the use of which led to his being awarded the economics Nobel Prize in 2015. The statistical toolkit used to test and estimate economic relationships, known as econometrics, generates estimated elasticities often used in computational models for projections and policy simulations.

In each case, the practical work of economists begins with data in natural units and converts relationships into elasticities for ease of communication. Elasticities show the connection between two variables of a model, but the elasticity itself depends on other factors and could vary when other things change. For food systems one of the most important results of multidimensional models is that elasticities depend on the passage of time. A common finding, named Le Chatelier’s principle after the nineteenth-century scientist who found a similar phenomenon in chemistry, is that quantity change in response to a given shock is often small at first and then rises as more adjustments occur.

Le Chatelier’s principle arises whenever responses happen slowly, and is extremely important for food policies such as soda taxes and agricultural policies such as crop insurance. In many situations, quantity consumed or produced will respond very little at first, but the long-run effect is large. Le Chatelier’s principle can be seen in individuals, if each person responds gradually, and is particularly common for populations where each person responds at a different time. For example soda taxes might have zero effect on some people whose habits are formed, while causing others to cut back as they gradually discover alternatives, and leading future cohorts of people to acquire different habits as they grow through childhood and adolescence. Similarly, crop insurance might lead to no change in just one year followed by experimentation and expansion of riskier activities that are protected by insurance in future years.

Elasticities do not always increase over time, because not all adjustments are costly and slow. In the food system there are often big but temporary jumps in quantity or price that later revert to long-term trends. We often see spikes or dips in quantities of specific things when a news story, price fluctuation, income shock or product introduction lead people to try something new, but then gradually return to their long-term trajectory. For storable products, price elasticities are heavily influenced by stockholding. In normal times inventories may be adequate to absorb shocks, but when inventories are low or shocks are high we see price spikes as consumers, producers, distributors and traders hold on to supplies or build up stocks which they later sell, driving prices back down to long-term levels.

Each elasticity summarizes just one two-dimensional relationship in a dynamic, multidimensional world. Describing relationships in elasticity terms is extremely useful, giving us a clear way to compare responsiveness of quantity to price, income or other factors, but the numerical value of each elasticity is not necessarily fixed. Indeed, an important policy priority may be to increase price elasticities, and thereby make the food system more flexible and resilient.

3.2.2.3 Price Elasticity and Behavioral Responses Along Supply and Demand Curves

We can see the range of price elasticities graphically and compare them to the slopes of supply and demand in Fig. 3.11.

Fig. 3.11

Definition and terminology for price elasticities of demand and supply

Figure 3.11 shows three curves for supply and for demand, illustrating how quantity can be more or less responsive to changes in price. The right side of the figure also lists how elasticities are classified for qualitative analysis. Less response to price means a larger slope and steeper curve, with an elasticity closer to zero.

When describing different levels of elasticity for alternative products in various scenarios, we compare elasticities to each other and also focus on whether the elasticity is above or below zero (0) and one (1). The terms used to compare elasticities describe use their magnitude in absolute value, denoted |ε|. A unit-elastic curve has |ε| = 1, so the percentage changes in quantity and price are equal. With unit-elastic demand, they offset each other and total consumer spending on that product is fixed. For example, a 5% price rise might lead to a 5% quantity decline, and no change in spending. More commonly, we are interested in whether a curve is relatively steep and inelastic, so that |ε| < 1, or relatively flat and elastic, meaning that |ε| > 1. If the curve is perfectly inelastic it would be vertical so |ε| = 0 and quantity remains unchanged when price changes. A curve could also be perfectly elastic and horizontal so |ε| is infinitely large and price remains unchanged even if quantity changes.

The three scenarios in Fig. 3.11 could show adjustment over time, as short-, medium- and long-run demand and supply curves for products such as eggs or liquid milk. Quantities adjust slowly because of how these products are produced and consumed, and also because they are difficult to transport and store. At any given place, a permanent but one-time expansion in supply would cause movement down the demand curve. In the short run, within one or two months, we might see a big price decline along a steep, inelastic demand curve like D. But then in the medium run after one or two years we expect less price change along D’, and in the long run almost all of the shock might be absorbed by increased quantity along D’. Similarly for supply, if there were a permanent but one-time rise in demand, for example building a cake factory that uses a fixed quantity of milk and eggs each month, the initial price change would be large along S, but as farmers respond the price change would be smaller along S’ and then S”.

The three different levels of price elasticity could also correspond to the product category, for example whether the shock affects all dairy products, all kinds of cheese, or just cheddar. For demand, a broader category typically has larger income effects on each consumers’ budget lines and less substitution along indifference curves, leading to differences in the slope of their demand curve. For supply, broader categories generally have fewer substitution possibilities along the producer’s PPF and IRC, and hence more inelastic supply curves. Cheddar is a narrow category with a small share of all spending and close substitutes among other cheeses, so consumers and producers might quickly adjust quantity in response to a shock. In contrast, all dairy is a broad category with larger income effects and fewer substitution possibilities, so quantity would change less quickly and the shock would be absorbed by prices.

The range of elasticities that might be observed in any given situation reveals the need for domain experts with local knowledge about the product and market situation being analyzed. Elasticities are not a fixed characteristic of things, but a behavioral response in each community of interest. To offer just one more example, a population of office workers who receive lunch vouchers worth $10 per day and usually spend that mostly at restaurants near the office would have a close to unit-elastic price elasticity of demand for restaurant lunches, with very price-inelastic demand for all beverages if they usually want one drink with their meal, but highly price-elastic demand for any specific food or beverage as they switch between items on the menu. Those elasticities might not have previously been measured in any empirical study, but a domain expert or qualitative researcher might know what to expect, using the concept of elasticity to explain and predict change.

Elasticity is important for economics because it gives us useful terminology with which to discuss the behavior of individuals and populations, and opportunities to measure whether an external shock is absorbed by change in quantities, prices or some of both. Elasticities are also useful to discuss and measure quantity change in response to other factors, especially income.

3.2.2.4 Income Elasticity, Engel’s Law and Bennett’s Law

Income drives food choice because it sets the level of each consumer’s budget constraint, and incomes of other people influence the food environment around us. Like price response, each person or population’s income elasticity of demand is context-dependent, so the concept offers an extremely useful way of discussing and measuring behavioral responses. The relevant diagrams for individual behavior are presented in Chapter 2, for example Fig. 2.6 that shows how people with different preferences would have different expansion paths of increased consumption for each thing of interest as their income rises. On a market diagram, income changes would be shown as a shift in the demand curve. In each case, the concept of income elasticity converts confusingly jumbled units of measurement into proportional terms, as the percentage change in quantity consumed for each one percent change of income as shown in Fig. 3.12.

Fig. 3.12

Definition and terminology for income elasticities of demand

Income elasticities, denoted e, are classified and discussed in the same way as price elasticities that are denoted ε. In both cases, we can focus on absolute value which is inelastic when close to zero and perfectly inelastic when exactly zero. Income elasticity can never be perfectly elastic because quantities consumed cannot be infinitely large, but income elasticities vary widely and are mostly but not always positive. Important thresholds include e = 1 and e = 0, leading to specific terms used only for income elasticity.

Income elasticity is ‘normal’ when between zero and one (0 < e < 1), meaning that increased income causes a less than proportional increase in quantity consumed. Most goods are almost always normal in this sense, including food. For normal goods, higher incomes lead to a higher level of consumption but a smaller share of total spending, because some of that higher income is spent on other things instead. Those ‘luxury’ goods have an income elasticity above one (e > 1), so that higher-income people spend a larger fraction of their income on luxuries. At the other extreme, some goods for some people are ‘inferior’, meaning a negative income elasticity (e < 0) as higher-income people reduce the quantity consumed.

Figure 3.12 shows how a higher income might shift demand differently for different people, or for different products, causing them to be classified as a normal, luxury or inferior good. For example, the diagram might show how demand shifts in response to a 10% higher income, with no change in price because supply is infinitely elastic, due to ease of expanding production or transport from elsewhere. Some things might be luxuries, so the demand shift to D’ moves to quantity Q’ more than 10% higher, while most are normal so demand at D’ raises quantity Q’ less than 10%, and some things are inferior so demand at D’’ lowers quantity to Q’’.

Whether a product is inferior, normal or a luxury good depends on its context. For many readers of this book, a familiar food that would be classified as inferior in income elasticity is packets of instant noodles. These are commonly consumed as a backstop or fallback meal, so higher incomes lead to lower consumption. But in other settings those same instant noodles might be a normal or even a luxury good, for which higher incomes lead to more consumption or even a larger share of income, because the alternatives are less preferred.

The two main observations about income elasticities of food are known as Engel’s Law and Bennett’s Law. Ernst Engel came first, writing in German in 1857 that ‘the poorer a family, the greater is the share of their total expenditure spent on food’, which he illustrated with data from two different surveys of wage-earning households published in French by others two years earlier. Engel’s law refers to the income elasticity of demand for everything, adding up every type of food or beverage, so that a 10% difference in income causes a less than 10% difference in food spending.

Engel’s law is primarily about the quality of each family’s diet, observing that the switch to or from more expensive items like meat, fish and milk was less than proportional to income. The total quantity of food was already known to vary in a narrow range. Long before in 1776, Adam Smith had written in The Wealth of Nations that ‘the rich man consumes no more food than his poor neighbour’, because both are ‘limited by the narrow capacity of the human stomach’. Adam Smith was referring to quantity in the sense of weight or volume, and shortly thereafter, in the 1780s, Antoine Lavoisier discovered dietary energy could be measured in units of heat. All three ways of measuring quantity (weight, volume or calories) vary with income much less than variation in quality, which was originally measured just as cost per day.

Bennett’s law came later, first observed by Merrill K. Bennett in 1941 from international data compiled during World War II about total quantities of food available in each country. Bennett added up all calories estimated to have been consumed from all foods and from cereal grains like rice or wheat together with starchy roots like potatoes and cassava. Bennett’s estimates suggested that, as of 1935, about half of the world’s population had 80–90% of their calories from the cereals-potato group, while the richest tenth of the world population had only 30–40% of their calories from it. Bennett’s observation concerned just cereal grains plus starchy roots, to which modern observers would add plantain bananas in a category called starchy staples. In other words, Bennett’s law is that the poorer a country, the greater is its share of total calories from starchy staples.

Bennett was writing soon after the discovery of essential nutrients and wrote that ‘the function of the cereal-potato group of foodstuffs in human diets is mainly to provide energy for the body’, while other foods were needed to provide protection from disease ‘in the form of protein, vitamins, and minerals’. That observation led Bennett to write that ‘ratios of cereal-potato calories to total food calories may be regarded as an indicator of relative qualitative adequacy’. Bennett also noted that cereals and potatoes were typically the least expensive source of calories at that time, so shifting to other sources represented a shift to more expensive diets.

Since Bennett’s 1941 study many others have investigated how shifts in spending alter diet quality, and also followed up on Bennett’s observation that starchy staples differ in taste and ease of preparation. For example, Bennett noted that some people ‘regard rice so highly - so greatly enjoy eating it’ that the share of rice in their diet does not decline as income rises. Recent studies have also revisited Bennett’s observation about price per calorie, as the cost of vegetable oils and raw sugar have declined to be about the same as the cheapest starchy staples, and the least expensive calories are now from mixtures of starchy staples with oil and sugar.

Ongoing studies related to Engel’s law focus on all the changes in food spending associated with income, and new work related to Bennett’s law focuses on calorie shares from different kinds of food. Modern terminology refers to these patterns as dietary transition, as higher incomes and associated trends bring different dietary patterns as discussed with data visualizations in Chapter 10. To facilitate that and other discussion of actual data on changes over time and differences among populations, it is helpful to see a schematic illustration of how quantities consumed might vary with income across a wide range of conditions.

The lines shown in Fig. 3.13 trace out two possible expansion paths of spending on each type of food, in response to changes in income. The food categories for which spending is shown on the vertical axis could be defined broadly (such as all kinds of fish) or more narrowly (such as all kinds of rice). The term ‘income’ along the horizontal axis refers to full income, meaning the person or population’s income from all sources, not just labor earnings but also other sources of purchasing power such as income from assets, gifts and program benefits. Full income in this sense is difficult to measure, so in practice the horizontal axis is measured as the sum of total expenditure on all goods and services, while the vertical axis shows a subset of the total.

Fig. 3.13

Visualization of all possible income elasticities along two Engel curves

Figure 3.13 is not an analytical diagram like our previous figures, because each point is an observation without controlling for other factors. The analytical diagrams explained why the observed outcome was chosen instead of other options. When people experience income growth the underlying factors causing that income growth might also affect food consumption. The impact of income as such might not be causal, but the patterns of correlation are nonetheless important for understanding how food consumption varies in the population.

The two Engel curves shown in Fig. 3.13 reveal how consumption of each food category usually begins only after people reach some threshold level of full income. For people moving from A to B along curve 1 and also curve 2, consumption of each kind of food is a luxury in the sense that they take an increasing share of income, even though these things might be basic necessities from the perspective of other people. When moving from B to C, the product shown in curve 1 remains a luxury with an increasing income share, while the product shown in curve 2 has ‘unit-elastic’ demand with a constant share of spending, indicated by a double line that points outward at a constant slope from the origin of zero income and zero consumption. From C to D, the top Engel curve is similarly unit elastic, shown by a double line that is not parallel to the lower double line, but both expand outward at a constant rate from the origin. The Engel curves eventually turn down to become ‘normal’ goods for which spending rises with a declining income share, and the lower curve shows a good for which demand growth with rising income slows to zero, so the Engel curve is ‘perfectly inelastic’ and turns negative for an ‘inferior’ good.

Engel curves like Fig. 3.13 can be drawn with actual data from cross-sectional surveys at one point in time to capture income differences, or a series of observations for the same population year after year to capture income changes over time. Higher or rising income is both cause and consequence of structural changes in society ranging from time use and paid employment to infrastructure and urbanization. Food technology also plays a big role, for example adopting an electric rice cooker to prepare rice unattended or switching from raw to parboiled rice for faster cooking time at home. For all these reasons, observed Engel curves and dietary transitions can be seen as a function of income as shown in Fig. 3.13 but they also trace the passage of time in terms of technological innovation, cultural shifts and many other factors that are correlated with each other over time and space.

Engel’s original observation in 1857 was that richer families spend a smaller share of their total expenditure on all foods and beverages, but their total spending of food and beverages continues to rise as they get richer. Engel’s law continues to hold for almost all populations today, but only if we include spending on restaurants and other food away from home, food delivery, the cost of kitchens and even private chefs for the very wealthy. Much of the variation in spending we observe is for processing, packaging, distribution and other food-related services, even with the same food ingredients. As we will see in later chapters, the dietary transition suggested by Engel’s law is largely about changes in what we will call value added, which is the cost of facilities, labor and other inputs used to transform ingredients before final consumption, along each value chain which is the sequence of steps by which farm products are transformed, transported and ultimately delivered to the consumer.

Bennett’s law refers to the share of calories obtained from starchy staples, noting that it is usually smaller at higher incomes. To show that we would need to redraw Fig. 3.13 for its vertical axis to show the percent of all calories derived from cereal grains, potatoes or other starchy plant roots such as plantain bananas. Bennett’s original observation was a very sharp decline for his cereal-potato grouping from 80–90% on the left to 30–40% on the right, using national averages observed in 1935. A downward slope of that type would still hold for most populations today, but as Bennett noted in 1941, some forms of starchy staples are very attractive especially in processed, precooked and packaged form.

Income elasticities observed historically and today reveal how only some of the rise in food spending involves changing from the least expensive ingredient categories, which are now cereal grains, vegetable oils and sugar, to more expensive food groups such as meat and fish, dairy and eggs, or vegetables and fruits. When we observe Engel’s law today, some of the change is towards more expensive ingredients within food groups, such as a shift from vegetable oil to olive oil, or from sardines and other small fish to large fish consumed without bones, but most of the shift concerns how those foods are processed, packaged and distributed. Elasticities of demand for both raw ingredients and also food transformation and meal preparation have important effects on both health and the environment, and relate closely to the work of food businesses along each value chain towards final consumption as discussed in Section 11.2.

3.2.2.5 Elasticities Determine the Impact of Intervention on Market Outcomes

Economists use elasticities not just to describe observed changes, but because elasticities can tell us how people will respond to interventions. Later in this book we will look more deeply into the interventions themselves, including the very wide range of policies and programs adopted by governments and other institutions. We will describe the economic principles that help explain why the policies and programs we observe are adopted, what factors might help explain changes in those policies and programs, and how policy analysts can help decision-makers improve outcomes.

In this section we describe how market outcomes are altered by interventions, using elasticities to show how people adjust and respond to policy change. Even without numerical estimates of each elasticity, we can use the concept to guide our qualitative understanding of policy impacts, as illustrated for taxes and government restrictions starting with Fig. 3.14.

Fig. 3.14

Elasticities describe response to policy change

Taxes and licenses of the type shown in Fig. 3.14 are some of the oldest, most widely used and important interventions in the food system. Taxes and licenses are used by national governments, local jurisdictions and even non-governmental organizations to influence outcomes in ways that are driven by elasticities in predictable but often surprising ways.

The context for intervention shown in Fig. 3.14 is a market for goods and services that are not traded with people outside the community shown. For example, these diagrams could show taxes or licensing of bars and restaurants in a city or state, as well as products like liquid milk or fresh eggs that are difficult to transport long distances or store over time. Where Amelia lived in Kinshasa, people would carry 10 or more cardboard cartons that held 30 eggs each on their heads for transport which took serious skill. Later we will see how the possibility of trade with other people alters the effect of a policy. As in all our market diagrams, the supply curves show production by people in a given community of interest, for example all of the restaurant operators in your town; the demand curves show consumption by all the people in your town, for example all restaurant customers in your town.

In the left panel we see the example of a tax paid by sellers. For these diagrams, a tax is a payment to the government per unit sold. That tax, labeled t, must be added by each producer to their marginal cost of production before each sale which creates the new market supply, S’ = MC + t. Consumers can no longer buy at the old supply curve, S = MC, but must move along their demand curve to where D meets S’ which is Q’, at which point consumers are paying P_c of which producers receive P_p.

In the middle diagram we see a different policy, which is a tax that must be paid by buyers when they purchase each unit. That tax is the same height, again labeled t, but now it must be paid by each consumer to the government out of their willingness to pay, so the producers receive only the new market demand, D’ = WTP − t. Producers can no longer sell to consumers at D but must now move along their supply curve to where S meets D’ which is Q’, at which point consumers are paying P_c of which producers receive P_p.

It may be surprising that two very different policies point to the same outcome. Whether governments levy the tax on producers or consumers, our analytical diagrams show peoples’ own decisions about how much to produce and consume lead to a shared burden of the tax, with the same quantity sold at a lower price for sellers and a higher price for buyers. Economic principles guide us towards explanations and predictions that take account of people having learned from experience and made their own choices. We represent each person’s complex circumstances using lines and curves that abstract from other factors and focus on how diversity in circumstances leads people to adjust along upward sloping supply and downward sloping demand, resulting in the outcome we see in Fig. 3.14.

The example of restaurant prices shown in Fig. 3.14 was chosen in part because it is familiar to anyone who has traveled between the U.S. and elsewhere. The middle diagram corresponds to restaurants in the U.S., where menu prices are lower than what customers ultimately pay due to taxes and tips that are added to the bill after each meal. The left panel shows restaurants in Europe and other places where menu prices include all taxes and almost all wages for the staff. Visitors to the U.S. may be confused at first, but soon learn how taxes and tips are done and take those costs into account when deciding what to buy. Likewise, travelers from the U.S. to Europe may be surprised by high menu prices, but soon learn that taxes are included and that tips are a smaller fraction of worker earnings than in the U.S., so they can take that into account in their choices.

Redrawing each diagram to tell the story of real people making choices under different conditions often leads to a sequence of discoveries. The first puzzle to solve is how the diagram actually works, and how economic principles are captured by lines and curves that point to each outcome. That takes time and is aided by a second kind of discovery which is how the diagrams relate to personal experiences and observations. The diagrams can be seen as abstract puzzles, but they represent real people, with lines and curves designed to help us take a population’s various interests into account when predicting their behavior. Finally, a third discovery is how to interpret and perhaps modify the diagram for different circumstances. People learn from experience and make their own decisions, but not everyone learns the same way. For example, many Americans traveling abroad tip more than locals, because the use of tips to pay restaurant workers is such a deeply rooted practice in American culture. Different structures for our diagrams may also be needed to capture the real-life market failures discussed later in this book.

Drawing and comparing the first two panels in Fig. 3.14 uses economic principles to guide and build intuition about behavior, showing the qualitative direction in which people will move as they learn from experience. The left and central panels show how people move towards the same outcome in the two cases, whether governments impose taxes on consumers or on producers. That is surprising in part because, until we use supply and demand curves to take account of behavioral responses among diverse people, we might think of policies in terms of the stated intentions of government officials. Policy statements might say that a tax will be paid by producers as in the left panel, or by consumers as in the right panel. The stated goals and specific instruments used by policies and programs are important, but outcomes depend on how people respond.

The right side panel of the diagram shows a third and very different kind of policy, which is a license or quota restriction on the number of meals that can be served. Governments do not control meals directly, but they commonly restrict the size and number of restaurants and regulate them in other ways which limit the number of meals served. If that number is Q’, restaurant operators will be unable to open beyond that number, so they move along their supply curve to rent, maintain and renovate new premises only up to there. Likewise, consumers will be unable to go beyond Q’, so they will move along their demand curve only up to there. Consumers’ D = WTP up to Q’ is above producers’ S = MC at that point, and it is restaurants who set menu prices. They will be able to charge at or near D = WTP, for premises that cost only S = MC to operate and maintain, and they will be willing to pay up to the entire difference between P_c and P_p for the license to open an additional restaurant. Those potential licensing fees are known as a quota rent and can be very large especially in cities that issue relatively few liquor licenses in popular neighborhoods.

The similarity and differences between licenses on the right and taxes at left and center can be investigated at length using Fig. 3.14 and a reader’s contextual knowledge of different market environments. Some readers will have worked or managed restaurants and might even have participated in decisions about where and how to expand or reduce the number of tables, including whether to buy or sell a license to operate. Others will simply have been customers in different towns and cities, and either known or wondered why places differ in terms of the number, size and location of establishments, as well as the quality and pricing of meals and service. Many of those differences are deeply rooted in food culture and other aspects of each place, but visitors can also ask or read about how city and state policies govern restaurant operations. Most often, the impact of taxes and licenses is most visible when they change, and people observe short-run movements along whichever side of the market is more inelastic.

The analysis above reveals how the effects of a tax do not depend very much if at all on how the tax is collected, but depends on relative elasticities as explained below.

3.2.2.6 Price Elasticities and the Incidence of a Tax or Regulation

Elasticities reflect the flexibility of buyers and sellers. When a government introduces a tax or regulation, the more flexible or elastic side of the market can escape to other activities, so a larger share of the cost is borne by those with a lower price elasticity. The incidence of a tax or regulation is the burden paid by each type of participant, which depends on their price elasticities. Each panel of Fig. 3.14 was deliberately drawn so that demand and supply had the same price elasticity, and the burden of each tax or regulation was borne equally by buyers and sellers. The more general case, in which one side of the market pays a larger share, is shown in Fig. 3.15.

Fig. 3.15

Elasticities tell us who pays a tax

In Fig. 3.15 we introduce squares and triangles around the different points of intersection, to emphasize that the same quantity can now have two different prices. The earlier example of a tax was a fixed amount of money (t) per unit sold, added to producers’ cost or subtracted from consumers’ payments the seller, so that the market supply and demand curves (S’ and D’) were parallel to their underlying marginal costs and willingness to pay (S and D). That was done only for visual clarity and simplicity. More commonly, taxes are a fixed percentage of the price for each unit sold, which implies a proportional rotation of the S or D curve.

Our example in Fig. 3.15 is the restaurant tax in Massachusetts, which happens to be 6.5%. In practice that is usually added to the bill after each meal, but because consumers know that it is coming we can draw the diagram as an addition to costs so the new market supply curve (S’) is 6.5% higher than S, to S’ = MC × 1.065. This proportional increase is known as an ad-valorem tax, whereas a fixed amount such as $0.65 per meal is known as a specific tax. Curious readers can verify by sketching the diagram that drawing Fig. 3.15 with a specific tax makes no difference to the results, just as it would make no difference to show the tax as paid by consumers.

In reality, as shown in Fig. 3.15, the group of people who pay the tax is whichever side of the market happens to be more inelastic in response. If consumers can easily go elsewhere or eat at home, the demand curve will be relatively elastic demand curve with a low slope, and sellers will have no choice but to absorb the tax in a lower price received at Q’. In contrast, if consumers insist on going out to eat in this area, the demand curve is steeper so sellers can charge higher prices and quantity sold declines only to Q’.

Elasticities determine who pays taxes, and elasticities also affect how regulation affects prices and quantities. Understanding elasticities can help clarify the policy similarities and differences between taxes and rules, as shown for a place that restricts restaurant supply with licenses as shown in Fig. 3.16.

Fig. 3.16

Elasticities tell us how a quota affects prices paid and received

How rules are implemented makes a big difference to the experience of restaurant operators and their customers, so contextual knowledge plays a big role in policy analysis in any specific setting, but the general economic principles illustrated here show analysts what to look for. As revealed by Fig. 3.16, when regulators allow only Q’ to be provided, sellers and buyers must cut back from Q to that new quantity. Sellers will discover that it is unprofitable to invest beyond where their community’s supply curve reaches Q’ at P_p, and also discover that they can charge consumers along their demand curve D reaches Q’ at P_c.

The qualitative insight here is that, for a given degree of supply response, inelastic demand makes restrictions more costly to consumers. Redrawing Fig. 3.16 with steeper supply curves would show that licensing at Q’ would then cause even greater price gaps, because the quota rent depends on adding up the effects of both elasticities as sellers and buyers interact towards the lower quantity allowed. For government decision-makers who might want to limit quantity at Q’ but also want to keep prices down, an important priority could be to promote greater elasticity of demand in the sense of more different options for consumers.

3.2.2.7 Trade Policy: Tariffs and Quotas on Imports or Exports

In communities that import goods from outsiders, governments often seek to restrict imports. Later we will see the effect of these policies on wellbeing, and how economic principles help explain why governments adopt these and other policy choices in Chapters 4 and 5. That helps explain why import restrictions are among the oldest and most widely used kind of tax, called an import tariff, and how import tariffs are different or similar to restrictions on the quantity imported, known as an import quota.

Our only earlier diagram with imports was Fig. 3.7 in the previous section, showing the market for apples in Massachusetts. Each state in the U.S. cannot restrict imports from other states, so that diagram showed how free trade works: distributors can move apples into Massachusetts where consumers have the option of buying imported apples at prices prevailing in other states, so producers can sell along their supply curve only up to that price in trade. Apple growers in Massachusetts can try to differentiate their apples to sell them at a higher price, and transport or storage costs will lead to small price differences across space and time, but the quantities observed are where supply and demand meet the price prevailing for trade with other places. Unlike individual states within the U.S., national governments can require importers to stop at the border for inspection and compliance with trade rules, and the mechanisms by which tariffs and quotas affect outcomes are both illustrated in Fig. 3.17.

Fig. 3.17

Import restrictions raise domestic prices, reducing quantity consumed

The left panel of Fig. 3.17 shows an import tariff, illustrated as the specific amount t paid to the government of the place shown in the diagram, per unit of the product imported. The right panel shows an import quota, which is a specific quantity q allowed over a specific period of time.

With free trade, distributors can import the product at its prevailing price in trade from elsewhere, P, so consumers can move along their demand curve to where D meets P at Q_c, and producers move along their supply curve to where S meets P at Q_p, so consumption exceeds production by the quantity imported which is Q_c−Q_p. This outcome is a useful benchmark against which to compare the effects of different policies.

When a tariff is charged, distributors who wish to import must pay P for the product plus t for the tariff. Consumers can then move along their demand curve only to Q_c’, where D meets P’ = P + t, and that higher price allows producers to move along supply curve to Q_p’ where S meets P’. There is still separation between production and consumption, but the quantity imported is now Q_c’−Q_p’.

When a quota is imposed, distributors who wish to import can do so only up the fixed limit q, in addition to quantities produced locally along the supply curve. We can find the new predicted outcome by adding q to S which generates a new curve for local supply plus the quota, shown as S’. Consumers can then move along their demand curve only to Q_c’, where D meets S’ = S + q. The price paid where D meets S’ is P’, so producers can sell at that price too and move along supply to Q_p’. The mechanism of adjustment differs, but the quantity imported is again Q_c’−Q_p’.

As with the previous comparison of taxation and licensing, the diagrams are constructed so results are identical, to show how two instruments can lead to the same outcome due to behavioral response by market participants. The difference is that taxes are paid to the government, while licensing creates ‘rents’ paid to people who are allowed by government to do the restricted activity. In Fig. 3.17, those quota rents are the difference between the price obtained, P’, and the price paid for imports, P, over the quantity imported which is Q_c’−Q_p’. The different outcomes are driven by different mechanisms of adjustment. With a tariff, the local price is where D meets the prevailing price of imports, P, so shifts in local supply or demand will alter price only if they cause a change in that price of imports. With a quota, the local price is where D meets S’ = S + q, so shifts in local supply and demand directly alter price, as if this location was in autarky.

Contrasting the two policies highlights the key role of elasticity along demand, supply and trade lines in how policies affect vulnerability or resilience to shocks. With free trade or tariffs, consumers are insulated from fluctuations in local supply, and producers do not experience changes in local demand, because both face the foreign price directly. Shifts in local S and D are absorbed in quantity imported at the import price P for which consumers pay P + t. With quotas, quantity is fixed at q and hence shifts in local S’ = S + q and D are reflected directly in the local price P’. That distinction makes a very big difference in practice, because for most products in most places the rest of the world is larger and more diverse than local own supply and demand. That makes the rest of world a more elastic provider of each product at a more stable price than each location would have in autarky, and a tariff will lead to more stable local prices than import quota.

Trade policy affects local conditions through either imports or exports. The import tariffs and quotas shown in Fig. 3.18 tend to be long-lasting, widely used policies that remain in place for decades. Corresponding restrictions on exports are sometimes long-lasting but are more often responses to a temporary spike in world prices when global stocks are low, or highly targeted efforts to keep supplies within the country. As for imports, our only earlier diagram with exports was Fig. 3.7 showing the market for cranberries in Massachusetts, and now we show the effect of a government policy to restrict such trade as shown in Fig. 3.18.

Fig. 3.18

Export restrictions lower domestic prices, reducing quantity produced

With exports, as with imports, a population that can trade freely with the rest of the world faces the prevailing price in trade, P, so produces at that price along its supply curve at Q_p and consumes at that price along the demand curve at Q_c. The resulting quantity traded is the difference, Q_p−Q_c.

When an export tax (t) is imposed, people in the country seeking to export receive only P’ = P–t. Producers adjust along their supply curve to Q_p’, consumers adjust to Q_c’, and the tax reduces the quantity exported to Q_p’ − Q_c’.

When an export quota (q) is used, people seeking to export can sell only up to a limited quantity. The resulting price can be found by subtracting only that quota from local production, so the restricted market supply is S’ = S −q. Participants in the local market then adjust along S’ and D to P’, the price at which buyers are willing to pay for the quantity that producers can supply, after accounting for the fixed quantity exported.

As with import restrictions, the export taxes and quotas shown in Fig. 3.18 can be drawn to have identical outcomes in terms of peoples’ responses along their supply and demand curves. As before, one difference is that taxes are paid to the government, while licensing creates quota rents paid to whoever is allowed to buy locally at P’ and export at P, over whatever share of the quota is given to them by the government. And as before, another difference concerns instability and adjustment. Export restrictions are usually a temporary policy, imposed during brief periods of world price spikes, unlike the import tariffs and quotas discussed earlier. These interactions between local conditions and trade opportunities greatly influence resilience and response to change, in ways that are especially visible when we go beyond the trade to consider ‘domestic’ policies affecting local producers and consumers.

3.2.2.8 Domestic Policies and Separability Between Supply and Demand

Government interventions within a country’s borders are known as domestic interventions, in contrast to trade policies that operate at the border. We have already seen domestic regulations like restaurant licensing, and now turn to a broader set of policies that might shift supply or demand. As before, once we take account of producer and consumer responses the impact of intervention can be surprising, as shown first for supply shifts supply shown in Fig. 3.19.

Fig. 3.19

Domestic policies affect outcomes differently without and with trade

Production subsidies that increase supply, shown in Fig. 3.19 as a shift from S to S’, could be payments from government to producers or their input providers that reduce the marginal cost of selling one more unit, or equivalently to increase the quantity sold at each level of marginal cost. Examples include low-cost loans and crop insurance, assistance with fuel or machinery and other inputs, or direct payments to farmers in proportion to area or quantity produced. If the government simply provides a cash payment of s per unit sold, then S’ would be S = MC − s, but actual subsidies usually shift supply in other ways.

Many agricultural subsidies do not actually increase supply, in some cases because they are designed explicitly to be ‘decoupled’ from output and help farmers without raising quantity produced. In other cases, payments to farmers may be intended to reduce output, such as a set-aside or buyout program, or they aim to address other concerns such as climate change, biodiversity or animal welfare. Some of these payments might have little effect on supply or shift it to the left, from S’ to S. Examples of supply-reducing payments to farmers include programs for land conservation, tree planting and carbon sequestration, avoidance of water use or less intensive livestock production. Those are payments for services or things other than output, and would be analyzed with other kinds of diagrams.

The purpose of Fig. 3.19 is to show how the left panel, for supply shifts in a market without trade, differs from the same supply shifts in a market with exports or imports. In the market for a nontraded product like fresh eggs or liquid milk, a shift in supply causes movement along the demand curve from Q to Q’, lowering price to P’ and affecting consumers as well as producers. In contrast, for products exported to or imported from a large and diverse rest of the world, the prevailing price in trade at P is often not affected by local events, so a shift in supply from S to S’ does not alter price and does not affect consumers.

The finding that supply shifts affect consumers only where people cannot trade with others is known as separability. Readers can easily sketch a version of Fig. 3.19 in which it is the demand curve that shifts, leading again to separability as demand shifts affect producers only where people cannot trade with others. The reason for separability is that the rest of the world is usually so large and diverse that their prevailing price is almost unaffected by the policy or other shift we are analyzing in a given community of interest.

Trade with others creates the possibility of separation between supply and demand for a whole community, just as our individual diagrams in Chapter 2 showed that exchange with others created separability between consumption and production for an individual farmer who consumes some of what they produce. This reinforces how supply and demand is the sum of all individual choices, reflecting the diversity of individuals within one community and also the differences between one community and the rest of the world.

3.2.3 Conclusion

Analytical diagrams like those presented in this chapter will be used again throughout this book to explain and predict response to policy interventions, environmental shocks, technological innovations and other events. So far we have focused on prices and quantities in places with many buyers and sellers, so that producers move along an upward sloping supply curve and consumers move along a downward sloping demand curve, to the predicted point where no further adjustment would be chosen. Where a community of buyers and sellers can trade with people in the rest of the world, quantities produced and consumed are where supply and demand curves meet that prevailing price.

The diagrams summarize people’s choices among many options as movements along a curve, and we summarize the slopes of those curves using elasticities that convert price and quantity data into percentage changes. The concept of elasticities gives us a clear vocabulary with which to discuss a group’s responsiveness as their percentage change in quantity for each one percent change in price, income or other factor. Elasticities are helpful for measurement and empirical analysis, but we can also use them directly for qualitative analysis based on contextual knowledge of a specific product in a particular community.

A central finding of this chapter is that having larger price elasticities, meaning that people can more freely adjust quantities in response to shocks, can be an important source of resilience to external factors that might otherwise cause large changes in price. One important source of highly elastic response to local shocks is trade with others, as shifts in local supply or demand can be absorbed by changes in quantity exported or imported. Elasticities along each curve of our diagrams, and the model structures through which we predict how people will adjust along those curves, provide useful insights into price and quantity responses. In the next chapter we introduce a measure of social welfare that links prices and quantities, greatly expanding the analytical toolkit to explain and predict policy choices, consider many forms of market failure and analyze the empirical data discussed later in this book.