Question

The tables show the utility Parker experienced from consuming varying quantities of waffles and pancakes. Assume that waffles cost $2. 00 each, pancakes cost $1. 00 each, and that Parker has $8. 00 to spend on these two goods. Since Parker cannot afford more than four waffles or eight pancakes, the utility is given only for quantities smaller than these.

Quantity of waffles Total utility of waffles Marginal utility of waffles

1 100 100

2 180 80

3 240 60

4 270 30


Quantity of pancakes Total utility of pancakes Marginal utility of pancakes

1 40 40

2 70 30

3 90 20

4 105 15

5 115 10

6 120 5

7 123 3

8 125 2


Required:

Given his budget constraint, determine what quantities of waffles and pancakes Parker will consume to maximize utility

Answer 1

To maximize utility, Parker should compare the marginal utility per dollar of waffles and pancakes and consume a combination that equates these values while fitting within the $8 budget.

Step-by-step explanation:

To determine the quantities of waffles and pancakes Parker will consume to maximize utility given his budget of $8, we calculate the marginal utility per dollar for each. This is the marginal utility of a good divided by its price. We look for the combination of waffles and pancakes that maximizes total utility without exceeding the budget constraint.

For waffles at $2 each, marginal utility per dollar is:

• 50 utils per dollar for the first waffle (100 utils / $2)
• 40 utils per dollar for the second waffle (80 utils / $2)
• 30 utils per dollar for the third waffle (60 utils / $2)
• 15 utils per dollar for the fourth waffle (30 utils / $2)

For pancakes at $1 each, marginal utility per dollar is:

• 40 utils per dollar for the first pancake (40 utils / $1)
• 30 utils per dollar for the second pancake (30 utils / $1)
• 20 utils per dollar for the third pancake (20 utils / $1)
• 15 utils per dollar for the fourth pancake (15 utils / $1)
• 10 utils per dollar for the fifth pancake (10 utils / $1)
• 5 utils per dollar for the sixth pancake (5 utils / $1)
• 3 utils per dollar for the seventh pancake (3 utils / $1)
• 2 utils per dollar for the eighth pancake (2 utils / $1)

Parker should consume the combination of goods where the marginal utility per dollar spent is equal, starting with the highest and moving to the next highest until the budget is exhausted. The optimal combination, without calculating every possibility, seems to start with waffles and then include pancakes when the marginal utility per dollar of waffles falls below that of pancakes. We continue this process until the budget of $8 is spent.