Reference no: EM131567295

Question: Consider the utility maximization problem

max xa + y subject to px + y = m

where all constants are positive, a ∈ (0, 1).

(a) Find the demand functions, x∗(p, m) and y∗(p, m).

(b) Find the partial derivatives of the demand functions w.r.t. p and m, and check their signs.

(c) How does the optimal expenditure on the x good vary with p? (Check the elasticity of px∗(p, m) w.r.t. p.)

(d) Put a = 1/2. What are the demand functions in this case? Denote the maximal utility as a function of p and m by U∗(p, m), the value function, also called the indirect utility function. Verify that ∂U∗/∂p = -x∗(p, m).