Suppose you have the following utility function U xy x2y2 a

Suppose you have the following utility function U (x,y) = x²y² and you have $80 to spend between goods x and y. The prices are the following. P_x=2 and P_y=4.

A) Write down the budget constraint

B)How many units of y is the market willing to exchange for one additional unit of x?

C) What is the marginal utility of x and y?

D) How many units of y is the \"consumer\" willing to exchange for one unit of x while holding the utility level constant when y=4 and x=2?

E) Given the above prices, income and preferences, what is the utility maximizing level of x? and y?

Solution

A. The budget constraint –

I = Px*X+Py*Y, where I is the income to spend, Px and Py are prices of commodity X and Y respectively, x and Y are quantities of commodities X and Y respectively.

B.

The marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility.

MRS = MUx/MUy

C.

MUx = U/x =2xy²

MUy = U/y = =2yx²

MRS = MUx/MUy = 2xy² / 2yx²

= y/x

D. If Y=4 and X = 2 then Y/X = 4/2 = 2