A consumer has a Cobb-Douglas utility function defined over food (F) and the consumption of all other goods (C): U(F,C)= C^a F^1-a where 0 < a < 1. The individual has (fixed) income M, the price of the aggregate consumption good is 1 and the price of food is p. The government is considering implementing a food voucher pro- gram for low income individuals, which will provide vouchers en- abling consumers to purchase S units of food (i.e., the vouchers are an in-kind transfer of food valued at pS). The vouchers may only be used for food, and may not be sold on the black market. a. Draw the budget constraint facing the consumer in the pres- ence of the food voucher program. Write down the consumers maximization problem, including the budget constraint and any other relevant constraints. Determine the first-order con- ditions and solve for the demand functions for F and C, con- sidering all possible cases.
b. For arbitrary values for p and S, determine an expression for the cut-off level of income M for which the consumer is corner constrained. Say p = 2, a= .5, S 300. What is M in this case?
c. Determine the indirect utility function for all cases.
d. Again assume that p tionally that M
400.
2, a 5, S 300 and say addi- Determine the maximized level of utility for the individual under the food voucher program. Determine the maximized level of utility for the individual if instead of food vouchers, the individual was given a cash transfer T of equal monetary value to the food stamp program (i.e., TpS). The individual can spend T on either food or other consumption goods. Is the individual better or worse off with the cash transfer or the food vouchers, both of which cost the government the same amount of money?
e. What value of the cash transfer will provide the individual with the same level of utility as the food voucher program? Will this cash transfer cost the government more or less than the cost of the food voucher program? What does the above tell you about the desirability of in-kind vs. cash transfers for low income individuals?
