THEORY OF CONSUMER BEHAVIOR
Practice Problems

Answer Key

1. Complete the table - See below.

Units consumed Total Utility, $ Marginal Utility, $
0
0
---
1
10
10
2
18
8
3
25
7
4
30
5
5
33
3
6
34
1

a. At which rate is total utility increasing: a constant rate, a decreasing rate, or an increasing rate?
Total utility clearly increases as more units are consumed. However, the rate of this increase is not constant. For instance, the first unit increases total utility by 10, third - by 7, sixth - by 1. The numbers illustrating the rate of increase are in the 'Marginal Utility' column.
The correct answer is: Total utility increases, but at a decreasing rate.

b. "A rational consumer will purchase only one unit of the product represented by these data, since that amount maximizes marginal utility."
The statement is false. As discussed in class, the goal of consumption is to maximize consumer surplus (not to maximize marginal utility)!!! One of the ways to arrive at the maximum of consumer surplus is to apply the optimal purchasing rule by comparing the marginal utility of each unit to price.
Therefore, the fact that the first unit gives the individual the highest marginal utility does not mean that the individual will buy only the first unit. Everything will depend on the price of the good. If, for instance, the price is as low as $6, the individual will buy 3 units (according to the optimal purchasing rule).

c. "It is possible that a rational consumer will not purchase any units of the product represented by these data."
Yes, it is possible. The statement is true. The individual will buy no units if the utility from each unit is smaller than the price. Therefore for any price above $10 a rational consumer with the given utility schedule will not purchase any units.

2. You are willing and able to pay 50 cents for today's "Washburn Review". The cost of printing the newspaper is 15 cents per copy, but you get one for free. What is your consumer surplus from the "Washburn Review"?

According to the definition, consumer surplus a person gets from a single unit equals the difference between the marginal utility derived from the unit and the selling price, CS = MU - P. In our case, MU = 50c, P = 0, so CS = 50 - 0 = 50.
The information about printing costs is irrelevant.


3. The table below contains information about the total utility Jerry gains from coffee he buys from the Corner Shop.

Cups of coffee
1
2
3
4
5
Total Utility, $
1.50
2.70
3.60
3.60
2.00

3a. Does this example exhibit the Principle of diminishing marginal utility? Explain.

Yes. The easiest way to see this is to calculate the marginal utility of each cup, or how much each cup adds to the total utility.

Cups of coffee
1
2
3
4
5
Total Utility, $
1.50
2.70
3.60
3.60
2.00
Marginal Utility, $
1.50
1.20
0.90
0
-1.60

The numbers in the bottom row are steadily decreasing, which means each successive cup is worth less that the previous one.
This is an indication of diminishing marginal utility.


3b. How many cups of coffee will Jerry buy if the price of each cup is $1? Why?

Marginal approach:
For each cup, answer the question: is it worth $1 to me, or is MU>P? Keep buying while the answer is 'yes'. Do not buy if the answer is 'no'.
Cup #1: 1.50 > 1 - buy
Cup #2: 1.20 > 1 - buy
Cup #3: 0.90 < 1 - don't buy
Jerry will buy two cups.

Aggregate approach:
Calculate Jerry's total consumer surplus for each number of cups purchased by subtracting the amount he'd have to spend from his total utility.
Then, choose the option with the maximum total consumer surplus.
One cup: 1.50 - 1.00 = 0.50
Two cups: 2.70 - (2 x 1.00) = 0.70
Three cups: 3.60 - (3 x 1.00) = 0.60
Four cups: 3.60 - (4 x 1.00) = -0.40 (note it is negative!)
Five cups: 2.00 - (5 x 1.00) = -3.00 (negative again)
The best option is to buy two cups and get a total surplus in the amount of 70 cents.

3c. How many cups of coffee will he buy if the price of each cup is 50 cents? Why?

Using the marginal approach,
1.50 > 0.50 - buy
1.20 > 0.50 - buy
0.90 > 0.50 - buy
0 < 0.50 - don't buy
Jerry will buy three cups.


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