The U.S. government spends over $33 billion on its Food Stamp Program to provide millions of Americans with the means to purchase food. These stamps are redeemable for food at over 160,000 store locations throughout the nation, and they cannot be sold for cash or used to purchase nonfood items. The average food stamp benefit is about $284 per month. Suppose that, in the absence of food stamps, the average consumer must divide $600 in monthly income between food and “all other goods” such that the following budget constraint holds: $600 = $12A + $4F, where A is the quantity of “all other goods” and F is the quantity of food purchased. Using the graph below, draw the consumer’s budget line in the absence of the Food Stamp Program. On the same graph, show the budget line with the Food Stamp Program.

Instruction: If the budget line has any kinks, be sure to plot all the points where the kinks occur in addition to the points where the line crosses the intercepts. Graph both budget sets from where Food = 0 to where they cross the X-axis.

The food stamp is worth 71 units of food (=284/4). Therefore with the food stamp, each household can consume upto 71 units of food for free. This means that there is a straight line at A=50 since each household can spend its entire income on all other goods and still be able to consume upto 71 units of food. Then the budget constraint kicks in.

Now if a household spends all its income on food it can consume 221 units of food[=(600+284)/4 = 884/4=221]

What is the market rate of substitution between food and “all other goods” for the budget line without the Food Stamp Program?

Instruction: Round your answer to two decimal places.
The market rate of substitution is given by the ratio of market prices of each good. For every unit of food bought, a household has to spend $4 which alternatively implies 1/3rd unit of all other goods have to be given up.

With the Food Stamp Program in place, would this consumer benefit from illegally exchanging food stamps for cash?

Yes – illegally exchanging food stamps for cash will definitely make him/her better off.   Once the household exchanges food stamps for cash, the food stamp becomes in effect an income transfer. Doing so shifts the budget line parallel outward by $284, i.e. there is no kink unlike in the case without illegal exchange for cash. Thus with the income transfer, it can consume more of both goods and hence is strictly better off.
Possibly – depending on his/her preferences.
No – he/she cannot benefit from illegal exchange of food stamps.

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