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ARE 2260 Food Policy

Healthy Food Subsidy Calculation

The example below projects costs of a city-level subsidy to encourage fruit and vegetable purchases by SNAP-participating households. You would follow similar steps when estimating costs of any consumer subsidy and for any population.

Assume you are hired to estimate the cost of a 30% subsidy on purchases of fruit and vegetables by SNAP-participating households in the city of Seattle, WA. You will need the following inputs to complete your calculation. I will give these inputs to you for your exam/ homework calculation, but also explain below how you would go about finding them in real life:

- Number of people/consumers – For the total population, we can use the US Census data for a relevant city/county/state. For a subset of the population, such as SNAP-participating households, we can find data from the USDA. To get the number of customers in a certain market, we would want to know % of “users” or individuals buying a product of interest – this is often determined using household surveys or proprietary data from marketing companies.

- Per capita consumption/purchases – It measures how much of a certain product that a typical consumer buys and/or consumes over a certain period. Note that we could assume that consumption is equal to purchases for simplicity, but there is often quite a lot of waste. The data on purchases or consumption could be purchased from a marketing company or found in a household survey, National Health and Nutrition Examination Survey (NHANES)

- Average pre-subsidy price – It is an average price across all types of products and retailers; data could be acquired from marketing companies or collected on your own from price audits in a small location/market to study.

- Price elasticity of demand – It is based on published studies, such as a systematic review of literature on price effects. For fruit and vegetables, published reviews suggest a range of the own-price elasticity of demand at -0.6 to -0.80. This means that a 10% decrease in fruit and vegetable prices would increase demand/purchases by 6% to 8% (inelastic demand).

or

Assume there are 3 million people living in Seattle, of which 10% are SNAP participants that would be eligible for the subsidy. Average monthly purchases of fruit and vegetables before the subsidy are 10 pounds (lb) per SNAP participant. Average price is $1.5 per lb and the price elasticity of demand for fruit and vegetables among SNAP participants is -0.7. In other words:

- Number of people getting the subsidy = 3,000,000 * 10% = 300,000

- Per capita consumption of fruit and vegetables among the subsidized population before getting the subsidized price = 10 lb per month

- Average price per lb of fruit and vegetables without a subsidy = $1.5/lb

- Own price elasticity of demand for fruit and vegetables = -0.7

- Subsidy of 30% means %∆P = -30% (it is a negative number showing a price reduction due to a subsidy)

Step-by-step calculation.

1. Start by determining %∆P (for a subsidy, it is always a negative number); in this example %∆P = -30% as the proposed subsidy.

2. Calculate %∆Q or % increase in purchases (also known as quantity demanded or ∆Q) based on the price elasticity formula when you know %∆P and the price elasticity of , so %∆Q = %∆P x Elasticity of demand.

In our example, %∆P = -30% and price elasticity=-0.7, so %∆Q = (-30%)*(-0.7) = 21% (it is positive as demand or Q increases due to the price reduction).

3. Calculate the post-subsidy purchases of fruit and vegetables per SNAP participant. We show in step 2 that the subsidy increases demand by 21%. In other words, pre-subsidy Q (10lb in our example) will go up by 21%, so mathematically:

Q after subsidy = pre-subsidy Q * (100%+%∆Q) = 10lb * (100%+21%) = 10lb *121% = 10lb * 1.21 = 12.1lb per SNAP participant

4. Calculate the dollar cost of this subsidy per SNAP participant. Remember that the government pays only 30% of the price per pound of fruit and vegetables, so:

a) A subsidy cost per 1lb is 30%* $1.5 = $0.45 - this is the subsidy amount for 1lb of fruit and vegetables;

b) A subsidy cost per monthly purchases by one SNAP participant = $0.45 * 12.1lb = $5.445 – Here we use a new subsidized amount of fruit and vegetables of 12.1lb that we calculated in step 3.

5. The last step is to calculate the total monthly cost for all SNAP participants getting the subsidy for fruit and vegetables in Seattle. Use the number of SNAP participants times the cost of each subsidy per SNAP participant from step 4b.

Monthly $ subsidy: 300,000 * $5.445 = $1,633,500. All set.