Casey consumes two goods,hamburgers and ice cream sandwiches.He has maximized his utility given his income.Ice cream sandwiches costs $2,and he consumes them to the point where the marginal utility he receives is 6.Hamburgers cost $4,and the relationship between the marginal utility that Casey gets from eating hamburgers and the number he eats per month is as follows: How many hamburgers does Casey buy each month?

Question

Casey consumes two goods,hamburgers and ice cream sandwiches.He has maximized his utility given his income.Ice cream sandwiches costs $2,and he consumes them to the point where the marginal utility he receives is 6.Hamburgers cost $4,and the relationship between the marginal utility that Casey gets from eating hamburgers and the number he eats per month is as follows:  How many hamburgers does Casey buy each month?

Quizplus · Accepted Answer

Since Casey has maximized his utility given his income, he must equate the marginal utility per dollar spent on both goods. 
For ice cream sandwiches, the marginal utility per dollar spent is 6/2 = 3. 
For hamburgers, we can use the given marginal utility function to find the marginal utility per dollar spent at different levels of consumption:

MU/Price = (22 - 0.5x)/4

At x = 0, MU/Price = 22/4 = 5.5 
At x = 1, MU/Price = (22 - 0.5)/4 = 5.375 
At x = 2, MU/Price = (22 - 1)/4 = 5.25 
At x = 3, MU/Price = (22 - 1.5(3))/4 = 4.875 
At x = 4, MU/Price = (22 - 2(4))/4 = 4

Thus, the marginal utility per dollar spent on hamburgers decreases as more are consumed. The highest MU/Price value is at x = 1, so Casey should buy one hamburger per month.

Casey Consumes Two Goods,hamburgers and Ice Cream Sandwiches