Question

3. Ultraty maximization u(x,y) =x.y 2 c) Find the optimal (2) Derwe the demand problem. M=10 (income) px = 1. Py = 2 choice 2ct, y*. for x and y.

Answer 1

1. The consumer's problem is:

max xy s.l. x +2y = 10

At equilibrium, marginal rate of substitution is equal to price ratio:

MRS = = = = x=24

Substituting this value into the consumer's budget line:

2y + 2y = 10 + y = 2.5, x = 5

Optimal choice:

(X*.Y) = (5.2.5)

2. For any prices and income , the consumer's budget line is given by:

Px. Py and M

$\small xp_x+yp_y=M$

Substituting the value of x computed using the optimality condition:

M 2M 2ypx + ypy = M + y = 2p, + Py* 2px + Py

The demand function for x and y is:

$\small (x,y)=(\frac{2M}{2p_x+p_y},\frac{M}{2p_x+p_y})$