Ollie has a utility function U(x, y)= (x + 2)(y + 3).The price of x is $1 and the price of y is $1.When he maximizes his utility subject to his budget constraint, he consumes positive amounts of both goods.Ollie consumes
A)exactly as many units of x as of y.
B)1 more unit of x than he consumes of y.
C)1 more unit of y than he consumes of x.
D)2 more units of x than he consumes of y.
E)None of the above.

Question

Quizplus · Accepted Answer

To maximize his utility, Ollie must choose the combination of x and y that gives him the highest U(x,y) given his budget constraint. His budget constraint is p_1x + p_2y = M, where p_1 = $1, p_2 = $1, and M is his income. To make things easier, we can set M = $4 (since both goods cost $1, he can afford to buy up to 4 units of either or a combination of the two).

Now we can rearrange the budget constraint to y = 4 - x. We can substitute this into the utility function to get U(x) = (x+2)(7-3x), which is a quadratic function. To find the maximum, we take the derivative of U(x) with respect to x and set it equal to 0:

U'(x) = -8x + 10 = 0
x = 5/4

So Ollie spends 5/4 of his budget on x and 3/4 of his budget on y. Since he can only buy whole units of each good, he buys 1 unit of y and 2 units of x, which satisfies B).

Ollie Has a Utility Function U(x, Y)= (X + 2)(y