John gets a weekly allowance of $$20$ from his parents. The only thing he has a real interest in buying is a big slice of pizza after school for $$2$ per slice. Below shows his marginal utility for each slice consumed.

Quantity

Marginal Utility per Pizza Slice

Marginal Utility per Funnel Cake

$1$

$20$ 

$50$

$2$

$12$

$40$

$3$

$10$

$32$

$4$

$6$

$20$

$5$

$2$

$12$

$6$

$0$

$0$

$7$

$-2$

$-12$

$8$

$-6$

$-20$

a$)$ What is the optimal quantity of pizza slices for John to buy? Explain.

The optimal quantity for of pizza slices for John to buy is $5,$ as the marginal utility for the $5$th slice of pizza is $2,$ which is equal to the marginal cost. Every pizza$’$s slices marginal utility before this one is above the marginal cost, and every one after the fifth is lower then it$.$

b$)$ If John purchased eight slices, what total utility would he enjoy?

If he purchased eight slices, the total utility would be $42$ utils.

c$)$ The school starts selling funnel cakes for $$4,$ which John discovers offers the marginal utility per cake shown on the same table. Complete a table that shows the marginal utility per dollar for each slice of pizza and each funnel cake $($in separate columns$).$

Quantity

Marginal Utility per dollar of Pizza Slice

Marginal Utility per dollar of Funnel Cake

$1$

$10$

$12\mathrm{.}5$

$2$

$6$

$10$

$3$

$5$

$8$

$4$

$3$

$5$

$5$

$1$

$3$

$6$

$0$

$0$

$7$

$-1$

$-3$

$8$

$-3$

$-5$

d$)$ Assuming John's parents do not allow him to use any savings, what is his optimal consumption bundle of pizza and funnel cakes? Explain.

His optimal consumption bundle would be four funnel cakes. This is due to the first, second, third, and fourth MU$/1$$ of each funnel cake being higher than that of the pizza. And, in total, he can only afford four funnel cakes overall.

e$)$ At John's optimal consumption bundle, what total utility will he gain?

$142$ total utility is gained.