The U.S. government has a food stamp program for families whose income falls below a certain poverty threshold. Food stamps have a dollar value that can be used at supermarkets for food purchases as if the stamps were cash, but the food stamps cannot be used for anything other than food.
A: Suppose the program provides $500 of food stamps per month to a particular family that has a fixed income of $1,000 permonth.
(a)With “dollars spent on food” on the horizontal axis and “dollars spent on non-food items” on the vertical, illustrate this family’smonthly budget constraint. How does the opportunity cost of food change along the budget constraint you have drawn?
(b) How would this family’s budget constraint differ if the government replaced the food stamp program with a cash subsidy program that simply gave this family $500 in cash instead of $500 in food stamps? Which would the family prefer, and what does your answer depend on?
(c) How would the budget constraint change if the government simply agreed to reimburse the family for half its food expenses?
(d) If the government spends the same amount for this family on the program described in (c) as it did on the food stamp program, how much food will the family consume? Illustrate the amount the government is spending as a vertical distance between the budget lines you have drawn.
B:
Write down the mathematical expression for the choice set you drew in 2.13A(a), letting x1 represent dollars spent on food and x2 represent dollars spent on non-food consumption. How does this expression change in 2.13A(b) and 2.13A(c)?