Milton consumes two commodities in a perfect market system. The price of x is $4 and the price of y is $1. His utility function is U(x, y) = xy. He is endowed with 76 units of good x and no y. Find his consumption of good y.

Question

Quizplus · Accepted Answer

Milton's budget constraint can be expressed as 4x + y = M, where M is his income. Since he is endowed with 76 units of x and no y, his income is equal to 4(76) = 304. Using his utility function, we can set up the following optimization problem:

Maximize U(x,y) = xy, subject to 4x + y = 304

We can solve this using the method of Lagrange multipliers. Let L = xy + λ(304 - 4x - y). Taking partial derivatives with respect to x, y, and λ and setting them equal to zero, we get:

∂L/∂x = y - 4λ = 0 
∂L/∂y = x - λ = 0 
∂L/∂λ = 304 - 4x - y = 0

Solving these equations simultaneously, we get x = 76 and y = 152. Therefore, Milton's consumption of good y is 152.

Milton Consumes Two Commodities in a Perfect Market System