Bottles of Soda Slices of Pizza

-The table above gives Ali's total utility from consuming bottles of soda and slices of pizza.The price of pizza is $2 per slice and the price of soda is $1 per bottle.Ali has $14 in his budget.When Ali maximizes his utility,how many bottles of soda does he buy?
A) fewer than 3
B) 3
C) 4
D) 5
E) more than 5

Question

Bottles of Soda	Slices of Pizza
 
-The table above gives Ali's total utility from consuming bottles of soda and slices of pizza.The price of pizza is $2 per slice and the price of soda is $1 per bottle.Ali has $14 in his budget.When Ali maximizes his utility,how many bottles of soda does he buy?
A) fewer than 3 
B) 3 
C) 4 
D) 5 
E) more than 5

Quizplus · Accepted Answer

To maximize utility, Ali should spend his entire budget on the combination of soda and pizza that gives him the highest total utility per dollar. To determine this, we need to calculate the marginal utility per dollar for each good:

Soda:
- The marginal utility of the first bottle is 18.
- The marginal utility of the second bottle is 16.
- The marginal utility of the third bottle is 14.
- The marginal utility of the fourth bottle is 12.

Pizza:
- The marginal utility of the first slice is 10.
- The marginal utility of the second slice is 8.
- The marginal utility of the third slice is 6.
- The marginal utility of the fourth slice is 4.
- The marginal utility of the fifth slice is 2.

To calculate the marginal utility per dollar, we divide the marginal utility by the price:

Soda:
- The marginal utility per dollar of the first bottle is 18/1 = 18.
- The marginal utility per dollar of the second bottle is 16/1 = 16.
- The marginal utility per dollar of the third bottle is 14/1 = 14.
- The marginal utility per dollar of the fourth bottle is 12/1 = 12.

Pizza:
- The marginal utility per dollar of the first slice is 10/2 = 5.
- The marginal utility per dollar of the second slice is 8/2 = 4.
- The marginal utility per dollar of the third slice is 6/2 = 3.
- The marginal utility per dollar of the fourth slice is 4/2 = 2.
- The marginal utility per dollar of the fifth slice is 2/2 = 1.

Based on the marginal utility per dollar ratios, Ali should buy the goods with the highest ratios first, until he has spent his entire budget. Since soda has a higher marginal utility per dollar than pizza, he should buy only soda bottles. The optimal amount of soda to buy is the amount that just exhausts his budget. Ali can buy 14 soda bottles, so he buys 4 bottles.