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# Theory of Consumer Choice

By Roy Wallace,2014-01-29 07:15
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Theory of Consumer Choiceof,co,OF

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Chapter 5: Theory of Consumer’s Choice

In this chapter, we will introduce a model of how consumers choose what to

consume. There are four elements in this model of consumer choice:

1- Consumer’s income,

2- Prices of goods,

3- Consumer’s tastes & preferences. Preferences rank different combinations of

goods according to the utility (benefit, satisfaction) they yield.

4- The assumption that consumers pick the bundle that maximizes their utility

level.

5.1 Budget Constraint

Consumer’s income and prices of goods together describe the consumer’s budget

constraint. The budget constraint describes combinations of goods that the consumer can afford. Assume that you have an income of 100 TL per week. Also, assume that there are only two goods that you need: kebap and baklavas. Suppose one kebap costs 10 TL and one baklava (kg) costs 20 TL. This information is sufficient to draw a budget constraint. Let us put number of baklavas on the vertical axis and number of kebaps on the horizontal axis. The easiest way to draw a budget constraint is to consider the extreme points. If you choose to spend your money completely on kebap, you can buy 10 kebaps and zero baklavas. On the other extreme, if you spend your money completely on baklavas, you can buy 5 baklavas and zero kebaps. Now draw the points that the budget constraint crosses the axes. Then join these points and draw the budget line.

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Qty. of Baklava

5

L

K

Qty of Kebap 10

FIGURE 24

In between these two extreme points, there are other combinations of baklavas and kebaps that you are spending all of your income such as:

8 kebaps and one baklava,

6 kebaps and two baklavas,

4 kebaps and three baklavas,

2 kebaps and four baklavas. These points are all on the budget line. How about a

point such as L = (9, 3)? Point L is unaffordable, since it costs the consumer 150 TL

to buy it. How about a point such as K = (4,2) ? It is affordable, and costs only 80 TL. But the consumer does not spend all of his income at K. We assume that there is no saving in this model, so choosing this point does not make sense for the consumer. Notice the tradeoff between the two goods: if you want to consume more food, you have to buy less baklavas. This tradeoff is constant along the budget line: for every additional baklava, two kebaps have to be given up. Or in other words, for every additional kebap, half a baklava must be given up. This is called relative price. The

relative price of baklavas in terms of kebaps is 2 kebaps per baklava. The relative

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price of kebaps in terms of baklavas is ? baklavas per kebap. Relative price of kebaps in terms of baklavas is equal to the ratio of the price of a kebap divided by the price of a baklava, i.e. P/ P. K B

The relative price can also be found by the slope of the budget line. The slope of a

line is the change in the vertical distance divided by the change in the horizontal distance. As the qty. of baklavas increases, qty. of kebaps decreases, therefore slope of the budget line is negative. There is a close relationship between the slope of the budget line and relative price of goods. Slope of the budget line can be found by the negative of the relative price of kebaps in terms of baklavas. In our example, slope is -1/2.

5.2 Tastes & Preferences

The budget constraint shows what the consumer can afford to buy given her income and prices of goods. Now, we will talk about how different consumers could have different preferences. This is the third element of our model of consumer choice: Consumer’s tastes & preferences rank different combinations of goods according to the utility (benefit, satisfaction) they yield. For example, some people like food more than other people. Some people may consume cigarettes while some others do not. We are trying to incorporate those preferences of consumers into our model. There are 4 assumptions that we make about preferences:

1- First, we assume that consumers are able to rank alternative

combinations of goods according to the utility they provide,

2- While they do this ranking, we assume that consumers are consistent, i.e.

they behave in a rational, logical way. For example, consider the three bundles: A = (3, 3), B = (2, 4) and C = (1, 5). If the consumer prefers A to B, and also prefers B to C, he must prefer A to C.

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3- More is better. Consumers prefer larger quantities of goods to smaller quantities. For example, if A = (3, 3) and C = (4, 4), then C must be preferred to A. We need more info. in order to know the ranking between A = (3,3) and B = (3,4) or A and F. Let us show the implication of this assumption on Figure 25. Qty. of

Baklava

Preferred to A 5 B C F

A D

A is preferred to E

here

Qty of Kebap 10

FIGURE 25

For a given point A, the northeast region of A is preferred to A. The southwest region is worse than A, so A is preferred to this region. To rank the northwest and southeast regions, we need to have more detailed information on preferences. Before we mention Assumption 4, we need to learn Marginal rate of Substitution:

Marginal Rate of Substitution

Keeping total utility (satisfaction) constant, how many baklavas would you give up in

order to get one more kebap? This amount is the marginal rate of substitution (MRS).

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Qty. of Baklava

U2 U3

5

K

A

H U3 L

U2

Qty. of 10

Kebap

FIGURE 26

Of course, this depends on your initial position: how many kebaps and baklavas you already have. If you already have a lot of baklavas to start with, then you are ready to give up a lot of baklavas for one kebap right? Then, on Figure 26, if you are at a position that has very little kebaps such as point K = (1, 4), then you are ready to give up a lot of baklavas. Let us say you are ready to give up exactly two baklavas for one kebap. So you come to point H = (2, 2). Point K and point H gives you equal utility.

Notice that between points K and H, marginal rate of substitution is two baklavas for

one kebap.

At point H, if you think of having one more kebap, you do not want to give up two baklavas anymore. In fact, you think that you can give up one more baklava only if you can get three more kebaps. That is, you are equally happy with H if you come to a point such as L = (5, 1). Notice that your marginal rate of substitution between H

and L is 1/3 baklavas for one kebap. So MRS has declined sharply as we move

towards more kebaps and less baklavas. This is commonsense because consumers

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prefer more balanced combinations of goods to more extreme combinations.

This property is called diminishing marginal rate of substitution property and is an

important element of our model:

4- Preferences exhibit diminishing marginal rate of substitution. That is,

consumers prefer more balanced combinations of goods to more extreme combinations.

Indifference Curves

Notice that points K, H and L gives the consumer the same utility. Assuming all the points on the curve that connects these points also yield the same utility, we call

this curve an indifference curve. The consumer is indifferent to all the points on

an indifference curve. She has the same satisfaction levels at all points on the curve. Let us name this curve UU. 22

There is a special relationship between MRS and the slope of the indifference curve. MRS is the absolute value of the slope of the indifference curve. For example,

between points K and H, slope of the indifference curve is -2, MRS is 2. Between points H and L, slope of the indifference curve is -1/3, MRS is 1/3. Properties of Indifference Curves: Notice that one can draw other indifference

curves that represent a smaller or a larger utility level. Consider a bundle such as A = (3, 3) on the graph. This bundle includes more of both kebaps and baklavas than point H. Therefore it must be on a higher indifference curve such as UU. Consider 33

bundle S = (1, 1). This bundle must be on a lower indifference curve because it includes less of both kebaps and baklavas.

Can indifference curves be positively sloped? No, because if they were, we would

be saying that when we increase both goods, utility stays constant. This cannot be true. Therefore, indifference curves are always negatively sloped.

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Can indifference curves CROSS each other? No! SKIP THE PROOF!!!!!

Let us suppose they can.

Qty. of

Baklava

U

5

U’

Z Y U’

X

U

Qty. of Şiş 10

kebap

FIGURE 27. CAN INDIFFERENCE CURVES CROSS EACH OTHER?

Is there a problem here? Let us think about it. Bundles X and Y are on the same indifference curve, so they must yield the same level of utility. Also, bundles Y and Z

are on the same indifference curve, so they also must yield the same utility. But then,

X and Z must yield the same level of utility. But there is a problem here: We have assumed at the beginning that more is better. If more is better, bundle Z must have

a greater utility than bundle X because bundle Z has a greater number of kebaps and baklava than bundle X.

Therefore, indifference curves cannot intersect.

5.3 Consumer Chooses the Bundle That Maximizes Her Utility In this part, we combine the two sides of this problem: the budget constraint and preferences. Which point does the consumer choose? First, consider the fact that

the consumer will choose a point ON the budget line. Let us show why this is the

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case on the graph: With an income of 100 TL and price of a kebap is 10 TL and price of a baklava is 20 TL, the budget constraint is the same as before. Let us draw this budget line.

Qty. of Baklava U3 U2 U1

5 B

L U3

C

U2

U1

Qty of Şiş kebap 10

FIGURE 28

Not interior of the budget set, because this leaves some income unspent. Not a point outside of the budget, because those points are unaffordable. The consumer makes the best possible choice on the budget line.

But there are many points on the budget line. Which point does the consumer choose on the budget line? She chooses the point that gives her maximum possible utility. How do we know which point is that? We draw indifference curves. Add TWO indifference curves on the above graph. U1U1 passes below the budget line, U3U3 passes above the budget set. Ask them if the consumer chooses U3U3 because it gives highest utility. What is the problem?

Since the consumer will choose a point ON the budget line, this could be on U1U1. Consider a point such as B on U1U1. It is affordable. But does the consumer

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maximize her utility at B? Is there a higher indifference curve that gives better utility? YES, we can draw higher indifference curves. Draw another indifference curve that is higher than U1U1 but still not tangent. Show that still utility can be increased by drawing another one. Do this until they are convinced that it is the highest

affordable curve that is tangent to the budget line.

Ask yourself if you can show another point that is better than C and still affordable? Give a little time.

Point C = (4, 3) is the point chosen. What is interesting at this point? At this point, the slope of the indifference curve (-MRS) is equal to the slope of the budget

constraint (-relative price). In other words, at the optimal choice, MRS = relative

price.

The slope of the budget constraint shows the relative price of kebaps in terms of baklavas: P/ P. Since prices are constant, this is always equal to ?. The optimal K B

choice happens at a point where MRS (=1/2 at optimal choice) is equal to the relative price of baklavas in terms of kebaps (1/2).

5.4 Applications of the Model

1- When Preferences are Different

Consider the following application to see how this model produces different choices when preferences are different.

Consider Joseph who only likes kebap and Iris who only likes baklava. Joseph’s

preferences are vertical lines:

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Baklava

Şiş Preferences of Joseph kebap

FIGURE 29

Which combination do you expect Joseph would choose? Is he more likely to

demand more kebaps or more baklavas?

Now consider the preferences of Iris, a baklava lover: Her indifference curves are flat

lines.

Baklava

Şiş

Preferences of Iris kebap

FIGURE 30

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