Let an average consumers utility function be the Cobb-Douglas function U (x1; x2) = x1 x1 2 with 0

(a) Derive the consumers demand functions for goods x1 and x2.

Now suppose that the government would like to increase the welfare of this consumer, and considers two alternatives for doing so. The first is to increase the consumers income from $5000 to $6000. In this simplied setting, this is a good approximation of programs such as the earned income tax credit. Well refer this as the cash transfer program.

(b) Formulate the consumers new budget constraint. Calculate the new utility maximizing quantities or demands of good x1 and good x2. Compare your answers to those of part (a).

pla answer the beliw parts; c-f. thx

(c) Formulate the consumers budget constraint under the in-kind transfer program the key observation

is that the constraint is no longer linear.

(d) We now examine the implications of dierent values of . Intuitively, a higher value of corresponds to a case in which food or education is relatively more important for this consumer. First, set = 1 2. Show that the optimal value of x1 under the cash transfer exceeds 500. Explain why, in this case, the agent is equally well-off under the cash transfer and in-kind transfer program.

(e) Show that the amount of x1 consumed under the cash transfer program is increasing in this is straightforward once you have the consumers demand function for x1. Find a value with the property that the optimal value of x1 under the cash transfer program is 500. Explain why any consumer whose value of exceeds is equally well-off under the cash transfer and in-kind transfer program.

(f) Consider a consumer for whom

QUESTIONS. We now explore the useful intuition from our analysis in QUESTION 1 more explicitly. Let an average consumer's utility function be the Cobb-Douglas function () = ** with 0