recall that Casper's utility function is 3x + y, where x is his consumption of cocoa and y is his consumption of cheese.If the total cost of x units of cocoa is x², the price of cheese is $6, and Casper's income is $101, how many units of cocoa will he consume? A)9 B)17 C)8 D)6 E)18

Question

Quizplus · Accepted Answer

The correct answer is A because the optimal consumption of cocoa is found by solving the equation 3x + y = 101, subject to the budget constraint x^2 + 6y = 101. Substituting y = (101 - x^2)/6 into the utility function, we get U = 3x + (101 - x^2)/6 = (18x - x^3)/6. Taking the derivative of U with respect to x and setting it equal to zero, we get 18 - 3x^2 = 0, which gives x = 3.

Recall That Casper's Utility Function Is 3x + Y, Where