Question

In spending all his income on beer and pizza, Fred finds that the marginal utility of the last pizza he consumed is 8, and the marginal utility of the last bottle of beer is 4. The price of a bottle of beer is $1.50. If Fred has maximized his utility, the price of pizza must be

Answer 1

Answer:

For a utility maximization, the pizza's price has to be $3.

Explanation:

The condiction to said that the utility has been maximized, is that the marginal utility for every dollar is the same for every factor (in this case, pizza and beer).

We can express that as

$\frac{dU/dpizza}{P_{pizza}}= \frac{dU/dbeer}{P_{beer}}$

Being dU/dpizza the marginal utility of pizza and dU/dbeer

If we want to know the price of pizza, we have to rearrange the equation

$\frac{dU/dpizza}{P_{pizza}}= \frac{dU/dbeer}{P_{beer}}\\\\P_{pizza}=P_{beer}*\frac{dU/dpizza}{dU/dbeer}}\\P_{pizza}=1.5*(8/4)=1.5*2=3$

In this case, for a utility maximization, the pizza's price has to be $3.