Frank's utility function is U = 10X + 6Y. Frank has a budget of $60 to spend on goods X and Y. The price of good X is $3 and the price of good Y is $2. How many units of good X and good Y does Frank purchase?
A) X = 20 and Y = 0
B) X = 0 and Y = 10
C) X = 15 and Y = 5
D) X = 10 and Y = 20

Question

Quizplus · Accepted Answer

Frank maximizes his utility by spending his entire budget on the good that provides the highest marginal utility per dollar. The marginal utility per dollar for X is 10/3 and for Y is 6/2 = 3.33. Since 10/3 > 3.33, Frank spends all $60 on X, buying 20 units (60/3 = 20).

Frank's Utility Function Is U = 10X + 6Y