Abstract
A monopolist sells a product at home and remote places. There is a cost to ship the product to the remote place or, alternatively, to build a second factory there. In Model 2A, a monopolist with one factory sells its product only at the home place. In Model 2B (localization), the firm also supplies the remote place from the same factory. In Model 2C (no localization), the firm builds a second factory at the remote place and serves customers at each place from their own factory. Model 2D considers a monopolist choosing whether to build one factory or two. Where the number of customers is sufficiently large—which in turn may require that the two places be sufficiently close together—there will be at least one factory and it will be located at the place with the larger demand. If the unit shipping cost is sufficiently low, there will be localization (i.e., one factory serves both places), and soap will be priced differently at the two places (partial freight absorption). Model 2E shows how one might think about entry deterrence at the remote place. If unit shipping cost is sufficiently high, and the smaller place has enough customers, the firm builds a second factory there and prices will be the same at the two places. In this chapter, localization and prices (one for each place) are joint outcomes of profit-maximizing behavior.
(Greenhut–Manne Problem)
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Notes
- 1.
The amount by which a firm’s revenue for a period exceeds its costs inclusive of a normal return on any unpriced factors such as owner equity or management skill. Also known as excess profit.
- 2.
A feature of a model wherein geography plays no role. Typically, shipping cost and/or commuting costs are assumed zero or are otherwise ignored.
- 3.
A market sufficiently small in area that we can ignore shipping costs on shipments of the good within that market.
- 4.
For this good, local producers and demanders transact in this and only this market. No one else transacts product there: e.g., no one purchases there for the purpose of reselling elsewhere or resells there a good purchased elsewhere.
- 5.
Ritter (1995, p. 134–135) describes the emergence of paper (fiat) money economies in the twentieth century and its relationship to seigniorage (the profit earned by a government on the difference between the nominal value of a coin and the cost of minting it). I assume here that the paper money supply is maintained by an authority (central bank) to ensure that the currency is a good store of value (or, equivalently, that the level of inflation is low).
- 6.
Economists might prefer to measure capital physically (e.g., number of machines) rather than in dollars. Capital—measured in dollars—is a given physical amount of capital times the price per unit of capital. In turn, the price of a unit of capital can be thought to be determined in a market for plant and equipment where suppliers of capital commodities interact with demanders including our firm. A problem with using dollars, as done here, is that a change the price of a capital asset will have no direct effect on the amount of output that can be produced, say daily, from a given physical amount of capital. However, such productivity concerns are not relevant in this model since, as I comment below, the model assumes an unlimited wellspring of production once the factory is built.
- 7.
The return on the best alternative investment opportunity available to the firm at a similar level of risk.
- 8.
A caveat is in order here. Later in the chapter, I argue that the market clears. Depending on the nature of the production technology, that might be difficult to ensure if the period were very short, say one second to the next.
- 9.
A cost incurred by the firm for a period of operation that does not depend on the quantity of output produced.
- 10.
An attribute of a production process such that production cannot be replicated at a smaller scale with the same efficiency.
- 11.
A schedule showing the marginal (additional) cost incurred by the firm (usually over the short run wherein capital invested is held constant) as a function of the quantity to be supplied.
- 12.
The profit attributable to an unpriced factor of production such as entrepreneurial skill or owner equity.
- 13.
A production technology characterized by the fact that each unit of output produced requires exactly the same amount of an input regardless of the relative prices of inputs. In other words, there is no substitutability among inputs in production. Put differently, a doubling of output requires a doubling of each and every input used in production. It is named after Wassily Leontief, an American Economist and Nobel Laureate (1973), whose main area of research was input–output analysis.
- 14.
As used here, a condition of a production function wherein, if as firm expenditure (output) is increased by a fixed proportion holding prices of inputs constant, the efficient firm purchases the same proportion more of each input.
- 15.
The amount of output that can be produced by a given factory over a stated period of time. In a simple case, we imagine that the unit variable cost of production is fixed per unit for any quantity up to capacity (marginal cost of production is a horizontal line up to capacity). To allow for the concept that no quantity greater than capacity is possible, we typically assume the marginal cost curve then becomes vertical. In other words, no matter how much the firm might want to further increase quantity, it cannot produce a quantity in excess of capacity.
- 16.
In effect, rK is akin to a lump-sum licensing fee paid annually by the firm that gives it authority to produce as much of the commodity as it wants during that period.
- 17.
The increment to the firm’s total cost incurred by the last unit produced.
- 18.
A condition under which a market participant (supplier or demander) is unable to affect the price they receive or pay for a unit of the product by varying the quantity that they supply or demand. The supplier (demander) sees the demand (supply) for its product as horizontal: i.e., infinitely elastic at the given market price.
- 19.
For a firm, the sum of variable and fixed costs of production inclusive of any unpriced resources such as entrepreneurial talent.
- 20.
For a firm, total cost divided by the amount produced.
- 21.
An efficient firm (1) incurs the least possible cost in achieving its desired output and (2) seeks the maximum revenue possible from that output. It adopts an organizational structure than enables it to be efficient. It has a production function which shows, for each combination of inputs, the maximum possible output that can be produced with those inputs. The firm also has a cost function which shows, for each level of output (Q), the minimum possible cost of achieving that Q. Finally, the firm knows the demand for its product and exploits that information along with the knowledge of its cost and production functions to maximize its own profit.
- 22.
See (2.1.3). A demand function is generally expressed as a schedule of quantity demanded (Q) at various prices (P): i.e., \(Q\,=\,f[ P ]\). An inverse demand function rearranges this as the price consumers are willing to pay as a function of the quantity supplied to the market: that is, \(P\,=\,f^{-1} [ Q ]\).
- 23.
A commodity would be a store of value if it was nonperishable and could be readily resold in the future: i.e., either converted back to cash at a low transaction cost or offer the possibility of capital gains.
- 24.
Economists in general moved away the notion of diminishing marginal utility of commodities because it was seen to be based on a cardinal measurement of utility. Instead, the ordinal assumption of a diminishing marginal rate of substitution between commodities was invoked. In this book, I retain the use of diminishing marginal utility because students find it helpful. Where it becomes problematic (e.g., in Chapter 9), I will discuss the matter further.
- 25.
A skeptical reader here might well ask how a firm can know the demand curve of its customer when in fact it can, at best, try varying the price it charges to see how much of the good is demanded. This raises more generally the problem of whether economic agents ever have the full information about the market that is presumed by economists in these models. For an important paper on this topic, see Alchian (1950, pp. 220–221) on the famous adoption-versus-adaptation argument.
- 26.
In a linear inverse demand curve, maximum price is the Y-intercept: the price at and above which the quantity demanded is zero.
- 27.
An attribute of consumer demand for a product such that there is a price above which the consumer demands none of it. The opposite of an expendable good is an indispensable good: i.e., a good which must be consumed in some quantity, however small, even when its price is high.
- 28.
The lowest price at which a profit-maximizing firm would participate in the market. Revenue just covers the variable cost of production. Minimum price is not sustainable over the longer run because fixed costs of production are not covered.
- 29.
In a region, this is the demand for a product by consumers for local consumption and firms for local production. Specifically, local demand does not include demand by arbitrageurs for resale in another region. Marshall (1907, p. 112) invokes a similar notion when he refers to those who buy for their own consumption, and not for the purposes of trade. Larch (2007) uses a similar approach to local demand in international trade theory. In practice, there is no generally accepted standard in Economics for measuring local demand. In empirical practice, local demand is often taken to mean simply that the quantity demanded varies from one location to the next: see, for example, Megdal (1984) and Justman (1994).
- 30.
The addition to the firm’s total revenue created by the last unit supplied by the firm to the market. If the firm’s demand curve is horizontal, it is a price taker (i.e., in a perfectly competitive market) and therefore its marginal revenue is simply the price. On the other hand, if the firm’s demand curve is downward sloping, marginal revenue is the price of the last unit sold minus the revenue lost on all other units sold because the market price has now been reduced because of the marginal unit of product supplied.
- 31.
See (2.1.5). For ease of exposition throughout this book, I do not discuss the second-order conditions for profit maximization.
- 32.
For a firm, revenue minus variable cost. In this book, variable cost includes both production and shipment. The firm’s net revenue (profit) is semi-net revenue minus fixed cost.
- 33.
Throughout this book, I use the convention that variables (algebraic labels), equations, and expressions are italicized while other figure labels (representing points, lines, and areas) are not. All figures are labeled by their vertexes, and I indicate a polygon by repeating the first vertex again at the end of the label.
- 34.
Revenue of the firm in excess of all costs, including normal profit on unpriced inputs like the firm’s capital and entrepreneurial skill.
- 35.
See (2.1.6) and (2.1.7) and the corresponding excess profit (2.1.8). For those readers whose microeconomics is rusty, to the left of Q in Fig. 2.1, the firm finds that increasing Q also increases semi-net revenue. To the right of Q, semi-net revenue falls if we further increase Q.
- 36.
An excess profit that arises because of an asset or market situation unique to a firm that prevents competitors from entering the market and/or earning the same profit.
- 37.
In a demand model, “no money illusion” means that price is relative to the units in which other money variables are measured. Put differently, if money quantities were all to double, quantity demanded would be unchanged.
- 38.
See (2.1.15).
- 39.
A cost incurred by the firm for a period of operation that varies with the quantity of output produced.
- 40.
A comparison of outcomes (endogenous values) predicted by a model when a given (exogenous variable or parameter) is changed by a small amount. Some models describe market equilibrium; here comparative statics details the changes in equilibrium when a given is changed by a small amount. In other cases, models describe optimal outcomes; here comparative statics details changes in optimal outcome when a given is changed.
- 41.
See, for example, Hsu and Tan (1999).
- 42.
In assuming sx fixed, I ignore the possibility of congestion on transportation networks that might cause sx to vary with the level of shipments. In this book, except where otherwise noted, I also ignore the idea that unit shipping cost might somehow vary directly with price: see Azar (2008) for a model where consumers perceive unit shipping cost to be relative to price.
- 43.
Firm sets price for good delivered to customer; consumer does not pay a separate shipping charge.
- 44.
A pricing scheme used by a monopolist to enhance profit that results in different prices for different markets or submarkets, it is sometimes called third-degree price discrimination.
- 45.
Depending on local price elasticities, there is even the possibility that the firm could set a price in the remote market that is lower than the price in the home market.
- 46.
See (2.3.4) and (2.3.5).
- 47.
See (2.3.14).
- 48.
A market outcome in which the prices at which a monopolist sells the same good in two markets differ by half the difference in shipping costs of shipping to the two markets. In general, this arises when consumers in the two markets are identical and have linear demand curves.
- 49.
See (2.3.7).
- 50.
For an expendable good sold at an f.o.b. price, the distance at which shipping cost is sufficiently high to cause demand to drop to zero.
- 51.
The starting point for this book is the firm producing a good or service. The book therefore ignores firms whose business is the construction of a network. De Fraja and Manenti (2003) study the extension of local telephone calling areas—within which long distance charges do not apply—as a strategic variable chosen to maximize the carrier’s profit.
- 52.
An expendable good is such that there is a price above which the consumer demands none of it. The opposite of an expendable good is an indispensable good: i.e., a good which must be consumed in some quantity, however small, even when its price is high.
- 53.
A similar point is made in McChesney, Shughart, and Haddock (2004).
- 54.
To me, a market for identical, or similar, commodities is said to be formed of submarkets when prices in the submarkets differ but are linked in some respect. In a strong version of submarkets, the price in one submarket is a fixed premium on the price in another submarket. In a weak version, a rise in price in one submarket causes the price in the other submarket to change, but there is no fixed premium.
- 55.
See Furlong and Slotsve (1983).
- 56.
Classic works in this field include Smithies (1942), Stigler (1949), and Machlup (1949). See also DeCanio (1984), Deutsch (1965), Faminow and Benson (1990), Gilligan (1992), Haddock (1982), Hughes and Barbezat (1996), Levy and Reitzes (1993), Lord and Farr (2003), Needham (1964), Soper, Norman, Greenhut, and Benson (1991), and Thisse and Vives (1992).
- 57.
Among papers making the same argument, see Gee (1985).
- 58.
See, for example, Ohta, Lin, and Naito (2005).
- 59.
Also, in this chapter, I assume that all consumers are the same. Suppose however that consumers at Place 2 differed in that some regularly visited Place 1 and could stock up on the good, while others did not. The firm might then be able to use this information to better price discriminate between the two markets. See Anderson and Ginsberg (1999).
- 60.
Because the model assumes no uncertainty, the firm does not need to think about the possibility of a breakdown, strike, or temporary reduction in the flow of inputs at one of its plants. If it did have such uncertainties, the firm might well ship output from one place to the other.
- 61.
A feature of shipping rates such that the cost of shipping a unit of product from Place i to Place j is the same as the cost of shipping a unit from j to i.
- 62.
In fact, if \(sx\,=\,0\), the firm is indifferent between having its factory at Place 1 and Place 2 even if \(N_1 \ne N_2\).
- 63.
Backhaus (2002) makes a similar point about the importance of opportunity costs in location theory.
- 64.
The topic of tariff jumping appears to have begun with Brander and Spencer (1987), Motta (1992), and Neven and Slotis (1996). See also Belderbos (1997), Belderbos and Sleuwaegen (1998), Horn and Persson (2001), Hwang and Mai (2002), Neary (2002), and Norback and Persson (2004).
- 65.
See Penfold (2002).
- 66.
For related work in this area, see Aguirre, Espinosa, and Macho-Stadler (1998), Eaton and Lipsey (1979), Hohenbalken and West (1986), Schmitt (1993), Serra and ReVelle (1994), West (1981), and Ziss (1993).
- 67.
See Baumol, Panzar, and Willig (1982).
- 68.
Any behavior of a firm such that it does not foresee any reaction by its competitors to its choices: e.g., with respect to price, range, or quality of commodities sold, or geographic location.
- 69.
See (2.7.7)
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Miron, J.R. (2010). The Firm at Home and Abroad. In: The Geography of Competition. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5626-2_2
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