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.
A)76
B)157
C)152
D)162
E)None of the above.

Question

Quizplus · Accepted Answer

Since Milton has no initial endowment of good y, he can only consume y by purchasing it with the money he gets by selling some of his good x.

Let Milton consume x and y in quantities x1 and y1 respectively. Then his total expenditure would be:

4x1 + y1 = income or 4x1 = income - y1

As Milton wants to maximize his utility, he will choose the quantities of x and y such that their marginal utilities are equal to each other:

MUx/MUy = Px/Py

=> MUx/MUy = 4

=> (d/dx (xy))/ (d/dy (xy)) = 4

=> y/x = 4/1

=> y1/x1 = 4/1

=> y1 = 4x1

Substituting this value in the budget equation, we get:

4x1 + 4x1 = income

=> x1 = income/8

As Milton is endowed with 76 units of good x, his maximum income would be 4*76 = 304

Therefore, his consumption of good x would be:

x1 = 304/8 = 38

And his consumption of good y would be:

y1 = 4x1 = 4*38 = 152

Hence, the answer is C) 152.

Milton Consumes Two Commodities in a Perfect Market System