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EC 500

Chapter 4The Theory of Individual

Behavior

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Headline

Packaging Firm Uses Overtime Pay to Overcome Labor Shortage

• Boxes Ltd. Produces corrugated paper containers at a small plant in Sunrise Beach, Texas. Sunrise Beach is a retirement community with an aging population, and over the past decade the size of its working population has shrunk. During the mid 2000s this labor shortage hampered Boxes Ltd.’s ability to hire enough workers to meet its growing demand and production targets. This is despite the fact that it pays $10 per hour—almost twice the local average—to its workers.

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• Last year, Boxes Ltd. Hired a new manager who instituted an overtime wage plan at the firm. Under her plan, workers earn $10 per hour for the first eight hours worked each day, and $15 per hour for each hour worked in a day in excess of eight hours. This plan eliminated the firm’s problems, as the firm’s production levels and profits are up by 20 percent this year.

• Why did the new manager institute the overtime plan instead of simply raising the wage rate in an attempt to attract more workers to the firm?

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Which one do you prefer? Why?

• Cash Gift or In-kind Gift?

• 10% Discount Coupon or Buy-one, Get-one Free?

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OverviewI. Consumer Behavior

– Indifference Curve Analysis– Consumer Preference Ordering

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

III. Consumer EquilibriumIV. Indifference Curve Analysis & Demand Curves

– Individual Demand– Market Demand

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1. 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

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Consumer Preference Ordering Properties

• Completeness

• More is Better

• Diminishing Marginal Rate of Substitution

• Transitivity

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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

– is indifferent between A and C (they are on the same indifference curve).

– will prefer B to A.– will prefer B to C.

I.

II.

III.

Good Y

Good X

A

C

B

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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

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Diminishing Marginal Rate of Substitution

• Marginal Rate of Substitution– 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 X1 3 42

100

50

33.33 25

A

B

CD

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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 X21

100

5

50

7

75

A

B

C

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2. 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)XM/PY

M/PX

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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

YNew Budget Line for a price decrease.

M0/PY

M0/PX

M2/PY

M2/PX

M1/PY

M1/PX

M0/PY

M0/PX0M0/PX1

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3. 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.

I.

II.

III.

X

Y

Consumer Equilibrium

M/PY

M/PX

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Price Changes and Consumer Equilibrium

• Substitute Goods– An increase (decrease) in the price of good X

leads to an increase (decrease) in the consumption of good Y.

• Examples: – Coke and Pepsi.– Verizon Wireless or T-Mobile.

• Complementary Goods– An increase (decrease) in the price of good X

leads to a decrease (increase) in the consumption of good Y.

• Examples:– DVD and DVD players.– Computer CPUs and monitors.

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Complementary Goods (example)

When the price of good X falls and the consumption of Y rises, then X and Y are complementary goods. (PX1

> PX2)

Pretzels (Y)

Beer (X)

II

I0

Y2

Y1

X1 X2

A

B

M/PX1M/PX2

M/PY1

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Income Changes and Consumer 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.

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4. 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

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5. 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

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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

D2D1

Individual Demand Curves

Market Demand Curve

1 2 1 2 3

DM

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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.

6. A Classic Marketing Application: “Buy-one, Get-one Deal”

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• Points:– New budget constraint is ADEF.

• Why horizontal?• Why parallel?

– Choice• Before:• After:

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“Cash Gift vs. In-kind Gift”

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• Points– New budget constraint is on the BC line.

• Why?

– Choice• Before:• After:

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Deadweight loss of Christmas Gifts

• Dear Economist,

I don't want to be a Scrooge, but every year the Christmas extravaganza seems like a pointless hassle. Isn't it all just a waste of time and money?

Yours,

-- "Ebenezer", London

Dear Ebenezer,

I have some sympathy with you. Christmas presents are wasteful, and we even know how wasteful: 16 per cent. This figure comes from surveys by economist Joel Waldfogel, who asked how much cash his respondents would have been willing to pay to buy their Christmas presents. The answer is, sadly, 16 per cent less than what they cost.

The most inappropriate gifts, costing 50 per cent more than their value to the recipients, come from elderly relatives. Sensibly, many elect to give cash instead. Unsurprisingly, friends and partners give less wasteful gifts. It's interesting to note that the most wasteful presents are those that cost roughly between Pounds 25 and Pounds 50 - expensive enough to assuage the guilt of a hurried choice, but cheap enough not to require double-checking with those close to the recipient.

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• But giving isn't the only example of seasonal waste. While some Christmas cards are sent out of genuine goodwill, many Christmas card exchanges are sub-optimal equilibria. In other words, both parties are only sending cards to reciprocate last year's card. Both would happily agree to stop, but it is embarrassing to be the first after so many years of mechanical exchange.

However, rather than abandoning Christmas altogether as a lost cause, bear in mind that there is an emotional side to our annual ritual. Waldfogel's research explicitly excludes the "sentimental value" of gifts. You can make sure that the sentimental benefits outweigh the cost by giving smaller presents but taking more care over them. If you must give to those whose tastes you do not understand, send cash.

As for Christmas cards, wipe your Christmas card list and send cards only to those who you truly wish to. It may feel awkward to strike so many people off your list, but it will at least spare them the hassle of sending you a card next year.

If you feel that further explanation is required, send them a copy of this article - surely the ultimate yuletide gift.

Merry Christmas.

• http://www.timharford.com/deareconomist/2003/12/deadweight-loss-of-christmas.html

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Answering the Headline

• The question posed at the beginning of the chapter asked why Boxes Ltd. paid a higher overtime wage only on hours in excess of eight hours per day instead of offering workers a higher wage for every hour worked during a given day. Since Boxes Ltd. already pays twice the local market wage rate to workers, it is unlikely that increasing the wage would attract more workers to the firm. Thus, the key to the expanding its output is to get its current workers to work more hours. We will show that the overtime wage plan is a more effective means of increasing worker hours than simply raising the wage.

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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.

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Exercises and Homework

• In class– Q. 1, 10, 17

• Homework– Q. 3, 6, 11