Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

Managerial Economics & Business Strategy

Chapter 4 The Theory of

Individual Behavior

4-2

Overview I. Consumer Behavior

–  Indifference Curve Analysis. –  Consumer Preference Ordering.

II. Constraints –  The Budget Constraint. –  Changes in Income. –  Changes in Prices.

III. Consumer Equilibrium IV. Demand Curves

–  Individual Demand. –  Market Demand.

4-3

Consumer Behavior §  Consumer Opportunities

–  The possible goods and services consumer can afford to consume.

§  Consumer Preferences –  The goods and services consumers actually consume.

§  Given the choice between 2 bundles of goods a consumer either: –  Prefers bundle A to bundle B: A ≻ B. –  Prefers bundle B to bundle A: A ≺ B. –  Is indifferent between the two: A ~ B.

4-4

Indifference Curve Analysis

Indifference Curve –  A curve that defines the

combinations of 2 or more goods that give a consumer the same level of satisfaction.

Marginal Rate of Substitution –  The rate at which a consumer is

willing to substitute one good for another and maintain the same satisfaction level.

I. II.

III.

Good Y

Good X

4-5

Consumer Preference Ordering Properties

§  Completeness §  More is Better §  Diminishing Marginal Rate of Substitution §  Transitivity

4-6

Complete Preferences

§  Completeness Property –  Consumer is capable of expressing

preferences (or indifference) between all possible bundles.

(“I don’t know” is NOT an option!) •  If the only bundles available to a

consumer are A, B, and C, then the consumer w  is indifferent between A and C

(they are on the same indifference curve).

w  will prefer B to A. w  will prefer B to C.

I. II.

III.

Good Y

Good X

A

C

B

4-7

More Is Better! §  More Is Better Property

–  Bundles that have at least as much of every good and more of some good are preferred to other bundles.

•  Bundle B is preferred to A since B contains at least as much of good Y and strictly more of good X.

•  Bundle B is also preferred to C since B contains at least as much of good X and strictly more of good Y.

•  More generally, all bundles on ICIII are preferred to bundles on ICII or ICI. And all bundles on ICII are preferred to ICI.

I. II.

III.

Good Y

Good X

A

C

B

1

33.33

100

3

4-8

Diminishing MRS §  MRS

–  The amount of good Y the consumer is willing to give up to maintain the same satisfaction level decreases as more of good X is acquired.

–  The rate at which a consumer is willing to substitute one good for another and maintain the same satisfaction level.

§  To go from consumption bundle A to B the consumer must give up 50 units of Y to get one additional unit of X.

§  To go from consumption bundle B to C the consumer must give up 16.67 units of Y to get one additional unit of X.

§  To go from consumption bundle C to D the consumer must give up only 8.33 units of Y to get one additional unit of X.

I. II.

III.

Good Y

Good X 1 3 4 2

100

50

33.33 25

A

B

C D

4-9

Consistent Bundle Orderings

§  Transitivity Property –  For the three bundles A, B, and C,

the transitivity property implies that if C ≻ B and B ≻ A, then C ≻ A.

–  Transitive preferences along with the more-is-better property imply that

•  indifference curves will not intersect.

•  the consumer will not get caught in a perpetual cycle of indecision.

I. II.

III.

Good Y

Good X 2 1

100

5

50

7

75

A

B

C

4-10

The Budget Constraint §  Opportunity Set

–  The set of consumption bundles that are affordable.

•  PxX + PyY ≤ M.

§  Budget Line –  The bundles of goods that exhaust a

consumers income. •  PxX + PyY = M.

§  Market Rate of Substitution –  The slope of the budget line

•  -Px / Py.

Y

X

The Opportunity Set

Budget Line

Y = M/PY – (PX/PY)X M/PY

M/PX

4-11

Changes in the Budget Line §  Changes in Income

–  Increases lead to a parallel, outward shift in the budget line (M1 > M0).

–  Decreases lead to a parallel, downward shift (M2 < M0).

§  Changes in Price –  A decreases in the price of

good X rotates the budget line counter-clockwise (PX0

> PX1).

–  An increases rotates the budget line clockwise (not shown).

X

Y

X

Y New Budget Line for a price decrease.

M0/PY

M0/PX

M2/PY

M2/PX

M1/PY

M1/PX

M0/PY

M0/PX0 M0/PX1

4-12

Consumer Equilibrium

§  The equilibrium consumption bundle is the affordable bundle that yields the highest level of satisfaction. –  Consumer equilibrium

occurs at a point where MRS = PX / PY.

–  Equivalently, the slope of the indifference curve equals the budget line.

(Tangency condition) I.

II.

III.

X

Y

Consumer Equilibrium

M/PY

M/PX

4-13

Income Changes and Equilibrium

§  Normal Goods – Good X is a normal good if an increase

(decrease) in income leads to an increase (decrease) in its consumption.

§  Inferior Goods – Good X is an inferior good if an increase

(decrease) in income leads to a decrease (increase) in its consumption.

4-14

Normal Goods & Inferior Goods

Y: An increase in income increases the consumption of normal goods.

(M0 < M1).

Y

II

I

0

A

B

X

M0/Y

M0/X

M1/Y

M1/X X0

Y0

X1

Y1

X: An increase in income decreases the consumption of inferior goods.

(M0 < M1).

4-15

Price Changes and Equilibrium

§  Substitution Effect: The change in the amount of a good that would be consumed as the price of that good changes, holding constant all other prices and the level of utility. 

§  Income Effect: The change in the amount of a good that a consumer would buy as purchasing power changes, holding all prices constant.

4-16

Decomposing the Income and Substitution Effects

Initially, bundle A is consumed. A decrease in the price of good X expands the consumer’s opportunity set.

The substitution effect (SE) causes the consumer to move from bundle A to B.

A higher “real income” allows the consumer to achieve a higher indifference curve.

The movement from bundle B to C represents the income effect (IE). The new equilibrium is achieved at point C.

Y

II

I

0

A

X

C

B

SE

IE

X is inferior good and Y is normal good.

4-17

Decomposing the Income and Substitution Effects

Initially, bundle A is consumed. A decrease in the price of good X expands the consumer’s opportunity set.

The substitution effect (SE) causes the consumer to move from bundle A to B.

A higher “real income” allows the consumer to achieve a higher indifference curve.

The movement from bundle B to C represents the income effect (IE). The new equilibrium is achieved at point C.

Y

II

I

0

A

X

C

B

SE IE

Both X and Y are normal goods.

4-18

Income and Substitution Effects Example

U(x,y) = xy Px=1, Py=6, Py2 = 4, M = 48.   Step 1: Old equilibrium: Bundle A

MUx = y and MUy = x MUx/MUy = y/x = 1/6 6y = x 48 = Pxx + Pyy = x + 6y = 6y + 6y = 12y yA = 4, xA = 6y = 24, UA = xy = 24*4 = 96.

 

4-19

Income and Substitution Effects Example

 Step 2: New Equilibrium: Bundle C MUx/MUy = y/x = 1/4 so 4y = x 48 = Pxx + Py2y = x + 4y = 4y + 4y = 8y 48 = 8y yC= 6, xC= 4y = 24

  Step 3: Decomposition Bundle B

xy = UA = 96 & y/x = ¼ so x = 4y. Plug into U. 4y*y = 96 4y2 = 96 yB = √(24) , xB = 4√(24)

 

4-20

Income and Substitution Effects Example

SE for y: y decomposition basket – yinitial basket

= √(24) – 4 = 0.9. Lower price of y increases the consumption for y.

IE for y: yfinal basket – ydecomposition basket

= 6 – √(24) = 1.1. Lower price of y leads to an increase in real income, positive IE means y is normal good. Total change in y = 6 – 4 = 2 (=1.1+0.9).

4-21

Application: A Classic Marketing

Other goods

(Y)

II

I

0

A C

B F

D E

Pizza (X)

0.5 1 2

A buy-one, get-one free pizza deal.

4-22

Application: Joining a Club

Other goods

(Y)

II I

0

250 A

25 50

B

Golf (X) 18.75 23

Suppose Neil spends $400 per month on golf and other things. 9 holes of golf is $16, but if Neil buys a pass for $150, 9 holes is only $8.

400

4-23

Individual Demand Curve

§  An individual’s demand curve is derived from each new equilibrium point found on the indifference curve as the price of good X is varied.

X

Y

$

X

D

II

I

P0

P1

X0 X1

4-24

Individual Demand Calculation Example

U(x,y) = xy with Px, Py, and M.   Step 1: MUx = y and MUy = x

Step 2: MRSx,y = y/x = Px/Py è y = xPx/Py

Step 3: M = Pxx + Pyy = Pxx + Py * xPx/Py = 2Pxx è x = M/2Px àDemand for x

Step 4: y = xPx/Py = M/2Px * Px/Py = M/2Py è Demand for y

4-25

Market Demand

§  The market demand curve is the horizontal summation of individual demand curves.

§  It indicates the total quantity all consumers would purchase at each price point.

Q

$ $

Q

50

40

D2 D1

Individual Demand Curves Market Demand Curve

1 2 1 2 3

DM

4-26

Market Demand Calculation Example

Suppose that Bart and Homer are the only two people who drink beer. Their inverse demand curves are respectively P = 10 – 4 Qb and P = 25 – 2 Qh. Write down market demand curve for all possible prices.   Bart will only consume when the price is less than 10. Therefore his demand curve for beer is Qb = 2.5 – 0.25P when P <10 and zero otherwise. Homer will only consume if the price is less than 25. So his demand curve is Qh = 12.5 – 0.5P when P < 25 and zero otherwise.

4-27

Market Demand Calculation Example

The market demand curve is

QM = 0, if P ≥ 25

QM = 12.5− 0.5P , if 10 ≤ P < 25

QM = 15− 0.75P , if P < 10

4-28

Conclusion

§  Indifference curve properties reveal information about consumers’ preferences between bundles of goods. –  Completeness. –  More is better. –  Diminishing marginal rate of substitution. –  Transitivity.

§  Indifference curves along with price changes determine individuals’ demand curves.

§  Market demand is the horizontal summation of individuals’ demands.