Economics 711 Midterm Exam October 2010

Q1. Suppose that a preference ordering on R^L₊ can be represented by the utility function

u (x) = _l=1∑^L(α_l(x_l-δ_l)^ρl-1/ρl

with _l=1∑^Lα_l = 1, and α_l ≥ 0 and ρ_l < 1, and _l=1∑^Lp_lδ_l < w, where p · x ≤ w is the budget constraint.

(a) Find the Frisch demand functions.

(b) Suppose that L = 2, δ₁ = 1, δ₂ = 2, α₁ = ½, α₂ = ½, ρ₁ = ½, ρ₂ = ¾, p₁ = 1, p₂ = 1, w = 23. What is the optimal consumption plan?

Q2. Assume that a firm is risk neutral with respect to profits and that if there is any uncertainty in prices, production decisions are made after the resolution of such uncertainty. Suppose that the firm faces a choice between two alternatives. In the first, prices are uncertain. In the second, prices are non random and equal to the expected price vector in the first alternative. Show that a firm that maximizes expected profits will prefer the first alternative over the second.

Q3. An expected utility maximizer with constant relative risk aversion and wealth w buys α units of insurance at price q against a loss D that occurs with probability π, where q > π. Find α.

Q4. Pick TWO of the following assertions. State whether they are true, false or ambiguous, and explain why.

(a) A rise in the wage rate implies a rise in the firm's marginal cost curve.

(b) If a production technology has production isoquants defined by y² = K² + L², the cost function has L-shaped contours in the factor prices (i.e. the combinations of v and w which keep c(v, w, y) constant, for fixed y, lie on an L-shaped isocost curve).

(c) The utility function u(x₁, x₂) = x²₁x²₂ is not quasi-concave, so the expenditure function derived from this utility function is not concave in prices.