Question

The following table shows William's utility from consuming slices of cake and cans of Sprite. Slices of Cake Total Utility from Cake Marginal Utility from Last Slice Cans of Sprite Total Utility Marginal Utility from Sprite from Last Can 0 0 0 1 36 36 1 30 30 2 66 30 2 55 25 3 90 24 3 75 20 4 108 18 4 90 15 5 120 12 5 56 6 126 6 100 10 6 105 5 Suppose William has $3.30 per week to spend on cake and Sprite. The price of a slice of cake is $0.60 and the price of a can of Sprite is $0.50. If William wants to maximize his utility, he should buy☐ slice(s) of cake and can(s) of Sprite.

Answer 1

To maximize utility with a budget of $3.30, William should purchase 5 cans of Sprite and 5 slices of cake. This allocation optimizes his utility by balancing the marginal utility per dollar for both items.

To maximize utility with a budget constraint, William should allocate his $3.30 to maximize the total utility per dollar spent.

1. Calculate the Marginal Utility per Dollar for each item:

- For Cake: Marginal Utility / Price per slice = 6 / 0.60 = 10

- For Sprite: Marginal Utility / Price per can = 5 / 0.50 = 10

2. Allocate the budget to the item with the higher Marginal Utility per Dollar:

- Since the Marginal Utility per Dollar is the same for both Cake and Sprite, William can allocate his budget to either item.

Therefore, he should buy 5 cans of Sprite and 5 slices of cake to maximize his utility within the budget constraint.