Question

M. Using the Lagrangean multiplier technique, solve for the following quantities for a consumer with utility function u(x1, x2) = x α 1 · x β 2 , α, β > 0.

1. The demand curves x ∗ 1 (p1, p2, w) and x ∗ 2 (p1, p2, w).

2. The utility value of money, V (p1, p2, w) = u(x ∗ 1 (p1, p2, w), x∗ 2 (p1, p2, w)).

3. The marginal value of money, ∂V (p1, p2, w)/∂w.

Answer 1