Using Price Incentives to Increase the Consumption of Fruits and Vegetables Among a Low-Income Population

Key Points

• 1. Low socio-economic households eat fewer servings of fruits and vegetables a day and have a higher incidence of dietary related chronic diseases such as diabetes, cancer, and heart disease.

• 2. A price subsidy for fruits and vegetables for SNAP beneficiaries would lower their relative price, thereby encouraging healthier eating, and that may lower the rate of dietary related diseases among this high-risk population.

• 3. Price incentives have previously been used successfully to reduce the rate of tobacco use and alcohol consumption and provide a model for price incentives for healthier eating.

• 4. A price subsidy for SNAP beneficiaries would be justified from a budgetary perspective if greater fruit and vegetable consumption lowers Medicaid and Medicare expenditures on chronic diseases for people who participate in these programs.

• 5. A 25% price subsidy is estimated to increase net fruit and vegetable consumption by 6.9%, with the largest percentage increases for fruit, and deep yellow vegetables, and the smallest percentage increases for starchy vegetables.

• 6. A 40% price subsidy is estimated to increase net fruit and vegetable consumption by 11.1%.

• 7. The subsidy program is estimated to cost between $$1.745 billion and $$2.941 billion a year; ­however, the per person per month costs are only estimated to be $$8.45 under the 25% subsidy and $$14.25 under the 40% subsidy.

• 8. Total benefits will depend upon how changes in consumption affect the incidence of chronic ­disease and public expenditure on Medicaid and Medicare.

Appendices

Appendix

The market model used to estimate the response by SNAP consumers to the price subsidy, and the final direct public cost of the program is described below. This model contains separate equations for the retail market, trade, a marketing sector that combines the farm and marketing inputs for the final market, and the farm and marketing input markets.

Final Market Demand Equations

The quantity demanded, Y, for fruit or vegetable commodity j by consumption group k, depends upon its own-price P _j , the price of other commodities, P _-j , and an exogenous demand shifter ϕ that represents the price subsidy for fruits and vegetables (9.1)

$$ {Y}_{jk}={d}_{jk}\left({P}_{1},\mathrm{...},{P}_{J};{f}_{jk}\right). $$

(9.1)

Total demand for commodity j is the sum of demand for each consumption group k (9.2)

$$ {Y}_{j}^{D}={\displaystyle \sum _{k}{Y}_{jk}}.$$

(9.2)

Final Market Supply Equations

The US market supply, ${Y}^{S}$, of commodity j comes from production, Q, by the marketing sector in region i, where i is California or the rest of the United States and from net trade, T, with other countries (9.3). Net trade is equal to total imports less total exports. If T is positive, the United States imported more than it exported. If T is negative, the United States exported more than it imported.

$$ {Y}_{j}^{S}={\displaystyle \sum _{i}{Q}_{ji}+}{T}_{j}.$$

(9.3)

In equilibrium total quantity demanded has to equal total quantity supplied (9.4).

$$ {Y}_{j}^{D}={Y}_{j}^{S}$$

(9.4)

Trade in commodity j depends on its US market price (9.5). As US prices increase, the amount of commodity j that goes to the US market also increases.

$$ {T}_{j}={t}_{j}\left({P}_{j}\right)$$

(9.5)

Marketing Sector

The marketing sector takes the farm product and either packs it fresh for delivery to markets, or processes it to sell as juiced, canned, frozen or dried products. Marketing inputs such as labor, ­transportation, packing materials, machinery in processing plants, etc., are used to bring fruits and vegetables to market. The total cost of the marketing inputs is ${w}_{m}$. The price received by growers of fruits and vegetables, ${w}_{g}$, will change as the quantity demanded for fruits and vegetables changes in response to the price subsidy for SNAP beneficiaries. The retail price depends upon the cost of the farm and marketing inputs in each region i (9.6).

$$ {P}_{j}={C}_{ji}\left({w}_{jgi},{w}_{jmi}\right)$$

(9.6)

The marketing sector receives the farm commodity from growers and the marketing inputs from other suppliers. As demand for the final output changes, demand for the farm commodity and non-farm inputs changes. Using Shepard’s Lemma, the derived demand for the farm commodity, ${x}_{jgi}$, (9.7) by the marketing sector in each region is

$$ {x}_{jgi}=\partial {C}_{ji}\left({w}_{jgi},{w}_{jm};{Q}_{ji}\right)/\partial {w}_{jgi}.$$

(9.7)

Again using Shepard’s Lemma, the derived demand for the marketing input, ${x}_{jmi}$, (9.8) in each region is

$$ {x}_{jmi}=\partial {C}_{ji}\left({w}_{jgi},{w}_{jm};{Q}_{ji}\right)/\partial {w}_{jm}.$$

(9.8)

The supply for the marketing input and grower inputs depends on the price for those inputs so that

$$ {x}_{jgi}={x}_{jgi}({w}_{jgi})\text{and}$$

(9.9)

$$ {x}_{jmi}={x}_{jmi}({w}_{jmi}).$$

(9.10)

Total quantity supplied for the marketing input by each region is the sum of quantity supplied by •each region (9.11).

$$ {X}_{jm}={\displaystyle \sum _{i}{x}_{jmi}}$$

(9.11)

Model in Log-Linear Specification

The log-differential is taken of the system of equations specified above, and parameters converted into elasticities, and demand, supply and cost shares. The final simulation model, expanded for each equation, is:

$$ d\mathrm{ln}{Y}_{j}^{fsh}={\eta }_{jj}^{L}d\mathrm{ln}P+{\displaystyle \sum _{-j}{\eta }_{j-j}^{L}d\mathrm{ln}}{P}_{-j}+{\eta }_{jj}^{L}d\mathrm{ln}{\varphi }_{j}$$

(9.1)

$$ d\mathrm{ln}{Y}_{j}^{fsa}={\eta }_{jj}^{L}d\mathrm{ln}{P}_{j}+{\displaystyle \sum _{-j}{\eta }_{j-j}^{L}d\mathrm{ln}{P}_{-j}}$$

(9.2)

$$ d\mathrm{ln}{Y}_{j}^{lt1.3}={\eta }_{jj}^{L}d\mathrm{ln}{P}_{j}+{\displaystyle \sum _{-j}{\eta }_{j-j}^{L}d\mathrm{ln}{P}_{-j}}$$

(9.3)

$$ d\mathrm{ln}{Y}_{j}^{gt1.3}={\eta }_{jj}^{H}d\mathrm{ln}{P}_{j}+{\displaystyle \sum _{-j}{\eta }_{j-j}^{H}d\mathrm{ln}{P}_{-j}}$$

(9.4)

$$ d\mathrm{ln}{Y}_{j}={\displaystyle \sum _{k}{\gamma }_{k}}d\mathrm{ln}{Y}_{jk}$$

(9.5)

$$ d\mathrm{ln}{Y}_{j}={\lambda }_{jC}d\mathrm{ln}{Q}_{jC}+{\lambda }_{jR}d\mathrm{ln}{Q}_{jR}+{\lambda }_{jT}d\mathrm{ln}{T}_{j}$$

(9.6)

$$ d\mathrm{ln}{T}_{j}={\epsilon }_{jT}d\mathrm{ln}{P}_{j}$$

(9.7)

$$ d\mathrm{ln}{P}_{j}={\alpha }_{jgC}d\mathrm{ln}{w}_{jgC}+{\alpha }_{jmC}d\mathrm{ln}{w}_{jmC}.$$

(9.8)

$$ d\mathrm{ln}{P}_{j}={\alpha }_{jgR}d\mathrm{ln}{w}_{jgR}+{\alpha }_{jmR}d\mathrm{ln}{w}_{jmR}.$$

(9.9)

$$ d\mathrm{ln}{x}_{jgC}=-{\alpha }_{jmC}{\sigma }_{jgmC}d\mathrm{ln}{w}_{jgC}+{\alpha }_{jmC}{\sigma }_{jgmC}d\mathrm{ln}{w}_{jm}+d\mathrm{ln}{Q}_{jC}$$

(9.10)

$$ d\mathrm{ln}{x}_{jgR}=-{\alpha }_{jmR}{\sigma }_{jgmR}d\mathrm{ln}{w}_{jgR}+{\alpha }_{jmR}{\sigma }_{jgmR}d\mathrm{ln}{w}_{jm}+d\mathrm{ln}{Q}_{j}$$

(9.11)

$$ d\mathrm{ln}{x}_{jmC}={\alpha }_{jgC}{\sigma }_{jgmC}d\mathrm{ln}{w}_{jgC}-{\alpha }_{jgC}{\sigma }_{jgmC}d\mathrm{ln}{w}_{jm}+d\mathrm{ln}{Q}_{jC}$$

(9.12)

$$ d\mathrm{ln}{x}_{jmR}={\alpha }_{jgR}{\sigma }_{jgmR}d\mathrm{ln}{w}_{jgR}-{\alpha }_{jgR}{\sigma }_{jgmR}d\mathrm{ln}{w}_{jm}+d\mathrm{ln}{Q}_{jR}$$

(9.13)

$$ d\mathrm{ln}{x}_{jgC}={\epsilon }_{jj}d\mathrm{ln}{w}_{jgC}+{\displaystyle \sum _{-j}{\epsilon }_{j-j}d\mathrm{ln}{w}_{-jgC}}$$

(9.14)

$$ d\mathrm{ln}{x}_{jgR}={\epsilon }_{jj}d\mathrm{ln}{w}_{jgR}+{\displaystyle \sum _{-j}{\epsilon }_{j-j}d\mathrm{ln}{w}_{-jgR}}$$

(9.15)

$$ d\mathrm{ln}{x}_{jmc}={\epsilon }_{{x}_{jm}}d\mathrm{ln}{w}_{jmc}$$

(9.16)

$$ d\mathrm{ln}{x}_{jmr}={\epsilon }_{{x}_{jm}}d\mathrm{ln}{w}_{jmr}$$

(9.17)

$$ d\mathrm{ln}{X}_{jm}={\beta }_{jmC}d\mathrm{ln}{x}_{jmC}+{\beta }_{jmR}d\mathrm{ln}{x}_{jmR}$$

(9.18)

where the variables and parameters used in the analysis are defined below (Table 9.5).

Table 9.5 Variable and parameter definitions for market model

The solution to the model is the percentage change in the price and quantity variables and directly estimates the percentage change in fruit and vegetable consumption for SNAP beneficiaries. The direct public cost of the subsidies is estimated from the price and quantity changes from the solution of the model and is calculated as where PD in the amount of the price subsidy, OP is the original price of commodity j, and OY is the original home consumption of commodity j by SNAP beneficiaries