Rules for Maximizing Utility

8. Try It

  1. Sandy is pondering how to split her time between slot machines and pinball at the local arcade. The slot machine costs $1 per game while pinball costs $2. She estimates that if she spent her entire budget at the slot machines the last game would give her only 10 utility, while the first game of pinball would give her 25 utility. Will she play at least one pinball game today, and why?
    • No. She would have to sacrifice two slot machine games to play a single game of pinball, which would cause her total utility to decline.
    • We cannot determine the answer with the given information.
    • Yes. The marginal utility per dollar of the first pinball game exceeds the marginal utility per dollar of the last slot machine game.

  2. Thomas is a graduate student who can afford only two varieties of food: canned beans and ramen noodles. If Thomas buys only one type of good he can afford either 50 packs of ramen noodles or 10 cans of beans. If the 20th pack of ramen yields Thomas a marginal utility of 10, what must be the marginal utility of the 6th can of beans for this to be the utility maximizing choice?
    • 100
    • 10
    • 50

  3. Hector has recently completed a microeconomics course and would like to put his newfound knowledge to good use maximizing his enjoyment at a pizza party. Unfortunately the host is short of cash and so the guests must pay for the pizza and diet coke they consume. The cost of a slice of pizza is $2 while the cost of a can of Pepsi is $1, and Hector has a budget of $13 to spend at the party. Hector has estimated the total utility associated with consuming different quantities of food items in the table below.
    What is Hector’s utility maximizing consumption decision?
Quantity of pizza Total Utility from pizza Quantity of Diet Pepsi Total Utility from Diet Pepsi
0 0 0 0
1 24 1 14
2 44 2 26
3 60 3 36
4 72 4 44
5 76 5 50
6 79 6 54
7 80 7 56
    • 5 pizzas and 5 pepsis
    • 4 pizzas and 5 pepsis
    • 5 pizzas and 3 pepsis
4. Answer the following question based on the table below showing the marginal utility schedules for product X and product Y for a typical consumer.

The price of product X is $4 and the price of product Y is $2. The income of the consumer is $20. When the consumer purchases the utility-maximizing combination of product X and product Y, total utility will be:

Product X Product Y
Quantity MUx Quantity MUy
1 32 1 24
2 28 2 20
3 24 3 16
4 20 4 12
5 16 5 8
    • 126
    • 156
    • 57