Consumer Choice Theory
Reading: Chapter 6 of Tucker
Overview:
Understanding Utility
Utility: the satisfaction, or pleasure, that people receive from consuming a good or service. Utility received from consumption of goods or services varies from person to person.
Total utility: the amount of satisfaction received from all the units of a good or service consumed.
Marginal utility: the change in total utility from one additional unit of a good or service. Marginal utility measures the amount of extra utility received from consuming each additional unit.
Law of diminishing marginal utility: the principle that the extra satisfaction of a good or service declines as people consume more in a given period.
A Marginal Utility (MU) graph slopes downward, depicting the declining utility received for each additional unit consumed in a given period of time. The slope of the MU curve will vary depending on circumstances and the individual person.
A Total Utility (TU) graph slopes upward, depicting the increased total satisfaction received from consuming additional units. The curve becomes flatter, however, as marginal utility decreases with each additional unit.
Consumer Equilibrium
Marginal analysis (from chapter 2) helps determine how additional satisfaction relates to price.
Consumer equilibrium: a condition in which total utility cannot increase by spending more of a given budget on one good and spending less on another good.
Consumer equilibrium example:
|
Number of Rides |
Total Utility, Pony Ride |
Total Utility, Zipper |
Total Utility, Hammerhead |
Total Utility, Roller Coaster |
|
1 |
6 |
28 |
18 |
24 |
|
2 |
11 |
54 |
34 |
46 |
|
3 |
15 |
78 |
48 |
66 |
|
4 |
18 |
100 |
60 |
84 |
|
5 |
20 |
120 |
70 |
100 |
|
6 |
21 |
138 |
78 |
112 |
|
7 |
21.6 |
130 |
84 |
115 |
|
8 |
22 |
100 |
88 |
80 |
|
9 |
22.2 |
60 |
90 |
10 |
Now we need to compute marginal utility (MU) and marginal utility per dollar spent on each ride (MU/P). Assume that each ride costs $4.
|
Pony Ride |
Zipper |
Hammerhead |
Roller Coaster |
|||||
|
Number of Rides |
MUP |
MUP/P |
MUZ |
MUZ/P |
MUH |
MUH/P |
MUR |
MUR/P |
|
1 |
6 |
1.5 |
28 |
7 |
18 |
4.5 |
24 |
6 |
|
2 |
5 |
1.25 |
26 |
6.5 |
16 |
4 |
22 |
5.5 |
|
3 |
4 |
1 |
24 |
6 |
14 |
3.5 |
20 |
5 |
|
4 |
3 |
0.75 |
22 |
5.5 |
12 |
3 |
18 |
4.5 |
|
5 |
2 |
0.5 |
20 |
5 |
10 |
2.5 |
16 |
4 |
|
6 |
1 |
0.25 |
18 |
4.5 |
8 |
2 |
12 |
3 |
|
7 |
0.6 |
0.15 |
-8 |
-2 |
6 |
1.5 |
3 |
0.75 |
|
8 |
0.4 |
0.1 |
-30 |
-7.5 |
4 |
1 |
-35 |
-8.75 |
|
9 |
0.2 |
0.05 |
-40 |
-10 |
2 |
0.5 |
-70 |
-17.5 |
Now if we have the preferences given from the marginal utility data above, a per-ride price of $4, and if we have $24 to spend, then what is the utility-maximizing combination of rides?
Solution: Incrementally pick rides based on the largest marginal utility per dollar spent.
Order of picks: Z, Z, Z, R, R, and Z. Therefore we ride the Zipper 4 times and the Roller Coaster 2 times. We have fully spent our amusement park budget of $24. What is our total utility?
Riding the Zipper four times yields total utility of 100 utils. Riding the Roller Coaster twice yields a total utility of 46. Therefore total utility from spending our $24 at the amusement park is 146 utils.
Is this a consumer equilibrium?
1. Is the MU/P is equal for the last units of the goods consumed? Try and see....
Yes. It is equal to 5.5 for both the Zipper and the Roller Coaster.
2. Can we change our consumption bundle and get more total utility while not spending more than our $24 budget? Try and see....
No. Therefore riding the Zipper four times and the Roller Coaster twice is a consumer equilibrium.
Deriving a Consumer Demand Curve:
We can derive a consumer's demand curve using the consumer equilibrium methods outlined above. What do we need to do in order to derive a demand curve for one of the rides?
We need to vary the price of one of the rides and see how that change in rides changes the consumption bundle (quantities of various rides chosen) in the consumer equilibrium. We can only change one price, and we must keep preferences and everything else constant (ceteris paribus). This process is called "comparative statics" in economics.
Let's suppose that the amusement park offers a discount price of $2 per ride for the Roller Coaster. Ceteris paribus, how will that change the consumer equilibrium?
|
Pony Ride |
Zipper |
Hammerhead |
Roller Coaster |
|||||
|
Number of Rides |
MUP |
MUP/4 |
MUZ |
MUZ/4 |
MUH |
MUH/4 |
MUR |
MUR/2 |
|
1 |
6 |
1.5 |
28 |
7 |
18 |
4.5 |
24 |
12 |
|
2 |
5 |
1.25 |
26 |
6.5 |
16 |
4 |
22 |
11 |
|
3 |
4 |
1 |
24 |
6 |
14 |
3.5 |
20 |
10 |
|
4 |
3 |
0.75 |
22 |
5.5 |
12 |
3 |
18 |
9 |
|
5 |
2 |
0.5 |
20 |
5 |
10 |
2.5 |
16 |
8 |
|
6 |
1 |
0.25 |
18 |
4.5 |
8 |
2 |
12 |
6 |
|
7 |
0.6 |
0.15 |
-8 |
-2 |
6 |
1.5 |
3 |
1.5 |
|
8 |
0.4 |
0.1 |
-30 |
-7.5 |
4 |
1 |
-35 |
-17.5 |
|
9 |
0.2 |
0.05 |
-40 |
-10 |
2 |
0.5 |
-70 |
-35 |
Now we need to derive the new consumer equilibrium
Order of picks: R,R,R,R,R,Z,Z,Z,R. Therefore we ride the Zipper 3 times and the Roller Coaster 6 times. Prove to yourself that this is a consumer equilibrium....
Derive this consumer's demand curve for the Roller Coaster ride: We now have two (p,q) pairs that we can use to "connect the dots" and draw a demand curve. One is ($4, 2) and the other is ($2,6). Does the law of demand hold for this consumer's demand for the Roller Coaster ride? Based on the impact of the price reduction for the Roller Coaster ride on the number of Zipper rides, are the Roller Coaster and the Zipper substitutes or complements to this consumer?
Substitutes, since when the price of the Roller Coaster went down, consumption of the Zipper also went down.
What is the price elasticity of demand for the Roller Coaster?
Ed
= 4/4 divided by 2/3
= 1.5, which is elastic.
Consumer Equilibrium and the Law of Demand
Declining marginal utility tells us that with each extra quantity consumed, less value is gained by the consumer. Consumers, therefore, are willing to pay less for each extra unit. The demand curve is downward-sloping.
Suppose two goods have the same marginal utility per dollar value. If the price of one of these goods drops, then the marginal utility per dollar value INCREASES for that good. The decline in price causes the consumer to buy more of that good in order to reach maximum total utility. Again, the demand curve is downward-sloping.
Explaining the Demand Curve Using the Income Effect and the Substitution Effect
There are other ways to explain the demand curve without trying to determine utility -- the income effect and the substitution effect.
Purchasing power and real income are synonymous. As price increases, purchasing power declines. As price declines, purchasing power increases.
Income effect: the change in quantity demanded of a good or service caused by a change in real income (purchasing power).
As real income increases, the ability to buy goods and services increases, and so demand increases.
Relative price is the price of one good compared to another good.
Substitution effect: the change in quantity demanded of a good or service caused by the change in its price relative to substitutes.
If two goods are substitutes and the price of one good falls compared to the other, consumers will purchase more of the less-expensive good -- demand for the less-expensive good will increase.
The income effect and the substitution effect are complementary. When the price of a normal good falls, the income effect and the substitution effect combine to cause the quantity demanded to increase.