Answer to Question #222114 in Microeconomics for M Arefin

Question

Suppose consumers face the utility function:
U (Xi, Yt) = XiYt; for i = 1, 2, ... ... ... ..., M

Firms face the cost function:
Cj(qj) = q2j + F

(a) Solve for equilibrium in perfect competition.
(b) Show the effect of change in income on equilibrium quantity.

Answer 1

a)

$U=xy\\M=p_xx+p_yy\\mu_x=y\\mu_y=x$

$\frac {mu_x}{p_x}=\frac{mu_y}{p_y}=\frac {y}{p_x}=\frac{x}{p_y}\\y=\frac{p_x}{p_y}X or X=\frac{p_y}{p_x}y$