Question

2. Yan has preferences over chocolate(x)and vanilla(y)ice cream that are represented by the following utility function: u(x,y) = xy4 3 Notice the power (4/3) just affects good y.

(a) Yan is an ice cream connoisseur, meaning, when deciding how much ice cream to buy, there is a minimum level of utility he must reach with ice cream consumption. But he doesn’t want to spend too much money because he is a graduate student. Setup Yan’s constrained expenditure minimization problem. (1 point)

(b) Solve the above problem for Yan’s compensated demand functions and his minimized expenditure as functions of px,py, ¯ u. (7 points)

(c) Define Shephard’s lemma and explain why it is useful for economics research. (2 points)

(d) Prove Shephard’s lemma holds for good x (you don’t have to do good y, but you can if you would like extra practice).

Answer 1