Economics 1 Bentz Fall 2002 Topic3

DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1

© Andreas Bentz page 1

Dartmouth College, Department of Economics: Economics 1, Fall ‘02Dartmouth College, Department of Economics: Economics 1, Fall ‘02Dartmouth College, Department of Economics: Economics 1, Fall ‘02

Topic 3: Consumer TheoryTopic 3: Consumer Theory

Economics 1, Fall 2002Andreas Bentz

Based Primarily on Frank Chapters 3 - 5

2

Rational Consumer ChoiceRational Consumer Choice

“A rational individual always chooses to dowhat she most prefers to do, given the optionsthat are open to her.”

Two questions:– How do we describe the options open to a

consumer?» Individuals operate under constraints.

– How do we describe preferences?» We use indifference curves to represent preferences.



3

Two Goods are EnoughTwo Goods are Enough

In what follows, we will only study the choicebetween two goods.

– This allows us to draw (two-dimensional) diagrams.

– (And: Two goods are often enough: for instance, ifwe are interested in your choice about how muchpizza to consume, we could make the two goods“pizza” and “money spent on everything else.”)


ConstraintsConstraints

Open Opportunities



5

ConstraintsConstraints

Typically, we operate under many constraints:– time constraint:

» How do you allocate time to the following activities: eating,sleeping, going to class, homework?

– budget constraint:» How do you allocate your income to different consumption

goods?

We will be interested in budget constraints:how do you allocate your expenditure?

– (We will later discuss the problem of how toallocate your time between leisure and work.)

6

Bundles of GoodsBundles of Goods

Definition: A bundle of goods is a particularcombination of quantities of (two or more) goods.

– For instance, a bundle could be: (10 slices pizza, 6 tubsHäagen-Dazs).

– Another bundle could be: (20 slices pizza, 0 tubs Häagen-Dazs)

– (A bundle is just a vector whose elements are the quantities ofgoods.)

We will often talk generally about two goods, good 1and good 2.

– If we want to talk about a bundle that has quantity x1 of good1, and quantity x2 of good 2, we write this as (x1, x2).



7

Bundles of Goods, cont’dBundles of Goods, cont’d

Graphically, we can illustrate bundles like this:bundle A: (10 slices of pizza, 6 tubs Häagen-Dazs)

bundle B: (20 slices of pizza, 0 tubs Häagen-Dazs)

Häagen-Dazs

pizza

12

6

0 10 20

A

B

8

Budget SetBudget Set

The budget set tells you how much you can afford,given your income and given prices:

– It is also sometimes called the affordable set.

Suppose one slice of pizza costs $1.75 and a tub ofHäagen-Dazs $2:

– bundle A (10 slices pizza, 6 tub Häagen-Dazs) costs $29.50

– bundle B (20 slices pizza, 0 tubs Häagen-Dazs) costs $35

Suppose you have $30.– (Economists call this your income, or sometimes, your

wealth.)

Bundle A is in your budget set. Bundle B is not in yourbudget set.



9

Budget Set, cont’dBudget Set, cont’d

We could now ask: how much pizza andHäagen-Dazs could you buy with $30?

Buying x1 slices of pizza and x2 tubs ofHäagen-Dazs costs

– $1.75 · x1 + $2 · x2

Since you have $30 (your income), you canbuy any combination of pizza and ice creamthat costs $30 or less:

– $1.75 · x1 + $2 · x2 < $30

This is your budget set.

10

Budget Set, cont’dBudget Set, cont’d

More generally, if you want to buy an amountx1 of good 1 (which costs p1), and x2 of good 2(which costs p2), the cost of bundle (x1, x2) is:

– p1 x1 + p2 x2

Suppose that your income is m. Then you canbuy any bundle with a total cost of less than(or just equal) m. That is, your budget set isdescribed by:

– p1 x1 + p2 x2 < m



11

Budget ConstraintBudget Constraint

In fact, you will always spend all your income(not spending it all would amount to throwing itaway):

Your budget constraint tells you which bundlesyou can just afford (with your income and atgiven prices).

– The budget constraint is also sometimes called theopportunity set.

The budget constraint is described by:– p1 x1 + p2 x2 = m

12

Budget Constraint, cont’dBudget Constraint, cont’d

p1 x1 + p2 x2 = m defines the budget constraint

this can be rewritten x2 = m/p2 - (p1/p2) x1



13

Budget Constraint: SlopeBudget Constraint: Slope

The slope of the budget constraint is - (p1/p2).

This is the relative price of good 1 in terms of good 2:– As you move down the budget constraint, you trade off more

of good 1 for less of good 2.

– To buy one more unit of good 1, you need to have p1 availableto spend. Since you are on your budget constraint, you needto give up some of good 2 in order to “free up” enough moneyto buy more of good 1.

– How much of good 2 do you need to give up to “free up”amount p1?

– If you give up one unit of good 2, you “free up” amount p2. Soif you want to “free up” an amount p1, you need to give upp1/p2 units of good 2.

14

Buzz GroupBuzz Group

A family with an income of $32 to be allocatedto drink chooses its consumption of milk andbeer.

– 1 quart of milk costs $1,

– 1 sixpack of beer costs $8.

What is the budget constraint? Draw it!– The government wants to encourage people to

drink more milk, and therefore distributes vouchers;each voucher gives you a free quart of milk. Eachfamily gets 10 vouchers.

Draw the budget constraint!



15

Price Increase: Good 1Price Increase: Good 1

Budget constraint: x2 = m/p2 - (p1/p2) x1

Suppose p1 increases to p1’.– The budget constraint rotates in around the vertical

intercept.

m/p1’

16

Price Fall: Good 1Price Fall: Good 1


Suppose p1 falls to p1’’.– The budget constraint rotates out around the

vertical intercept.

m/p1’’



17

Price Increase: Both GoodsPrice Increase: Both Goods

Suppose p1 increases to 2p1 (p1 doubles).

Suppose p2 increases to 2p2 (p2 doubles).

m/2p1

m/2p2

18

Income ChangesIncome Changes

Suppose your income halves. This is just the same asif all prices had doubled:

– Consider the vertical intercept: m/p2.

– Double price: m/2p2.

– This is just the same as (m/2)/p2 (i.e. halving income).

– Similarly for the horizontal intercept.

m/2p2

= (m/2)/p2

m/2p1

= (m/2)/p1



19

Income Changes, cont’dIncome Changes, cont’d


Generally, if income increases, the slope ofthe budget constraint remains unchanged: it isa parallel shift.

– If income increases, the budget constraint shiftsout.

– If income decreases, the budget constraint shifts in.

20

More than two GoodsMore than two Goods

What if there are more than 2 goods that theconsumer can choose between?

We can always represent this as a choicebetween one good (which we call x) and“money spent on all other goods” or acomposite good (which we call y):

– That is, we envisage the consumer to choose howmuch of her income to allocate to one good, andhow much to allocate to all other goods.

– You can think of y as the amount of income theconsumer has left after buying (some of) x.



21

More than two Goods, cont’dMore than two Goods, cont’d

If we think about the composite good in termsof “money left over”, this good has a price of 1.

– budget constraint (two goods): x2 = m/p2 - (p1/p2) x1

– budget constraint (x and y): y = m - p1 x1

22

“Available Options”“Available Options”


We now have an interpretation of “… optionsopen to her”:

A rational individual always chooses toconsume the bundle that she most prefers,from all the bundles on her budget constraint.




PreferencesPreferences

As You Like It

24


We have now developedour tool for modeling“the options open to theconsumer.” We haveused this consumptionspace:

We need some way ofrepresenting yourpreference ordering overdifferent bundles ofgoods.

Now we need torepresent yourpreferences overdifferent bundles ofgoods.



25

Preference OrderingsPreference Orderings

This is where the rationality assumption isimportant:

– Completeness: You can always rank two bundlesagainst each other: more preferred, less preferredor indifferent (equally preferred).

26

Preference Ordering, cont’dPreference Ordering, cont’d

What else can we assume about preferences?– “More is better” (monotonicity): If one bundle has

more of all goods, you prefer it.

worse

better?

?



27

Indifference CurvesIndifference Curves

Suppose you areindifferent between(equally prefer) thefollowing bundles:pizza Häagen-Dazs

10 6 6 8 18 4 4 12

pizza

Häagen-Dazs

12

10

8

6

4

2

2 4 6 8 10 12 14 16 18 20

The curve connecting all the bundles that you areindifferent between (all the bundles that you equallyprefer) is called an indifference curve.

28

Indifference Curves, cont’dIndifference Curves, cont’d

An indifference curveseparates theconsumption spaceinto:

– those bundles thatare more preferredthan any bundles onthe indifference curve,and:

– those bundles thatare less preferredthan any bundles onthe indifference curve.



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B

C

A

Indifference Curves, cont’dIndifference Curves, cont’d

There are manyindifference curves:

– For every bundle, there isa curve connecting all thebundles that you preferequally:

– Bundle B is less preferredthan A; bundle C is morepreferred than A.

– As we go from B to C,there must be a bundlethat is equally aspreferred as A.

We can repeat thisprocess for everybundle.

30

Indifference MapIndifference Map

An indifference map isthe family of allindifference curves of aconsumer.

– As we know, there areinfinitely manyindifference curves - weonly draw a fewrepresentativeindifference curves ...

– … and label them I0, I1, I2,etc., in increasing order ofpreference.

I2

I0

I1



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“Most Preferred”“Most Preferred”


We now have an interpretation of “… what shemost prefers to do”:

A rational individual always chooses toconsume the bundle that is on the highestindifference curve, from all the bundles on herbudget constraint.

32

Properties of Indifference CurvesProperties of Indifference Curves

Indifference curves are downward-sloping:– “more is better” (monotonicity) assumption

– violation:



33

Properties of Properties of IndiffIndiff. Curves, cont’d. Curves, cont’d

Indifference curves cannot cross:– transitivity (the second rationality assumption)

– violation:

A

B

C

– By monotonicity: A ispreferred to B

– B is preferred to C– By transitivity: A is

preferred to C– But this is a

contradiction with thegraph, where A isequally as preferredas C.

34

Transitivity: A RefresherTransitivity: A Refresher

The preference relation is transitive if:– whenever A is preferred to B

– and B is preferred to C

– A is also preferred to C.

There are many examples of other transitiverelations:

– stronger than, taller than, richer than …



35

Transitivity: A Refresher, cont’dTransitivity: A Refresher, cont’d

Why is this a rationality requirement?– Suppose you prefer apples to bananas, and bananas to

cactus fruit.» Transitivity says that you should then also prefer apples to

cactus fruit.

– You start out with a cactus fruit. Then you should be willing toswap the cactus fruit for a banana (and give me a centbecause you prefer the banana), and then swap the bananafor an apple (and give me a cent).

– If your preferences were not transitive, i.e. you did not alsoprefer apples to cactus fruit, you should then be willing toswap your apple for a cactus fruit.

– You are back at the start (cactus fruit), but have lost 2 cents!

36

Properties of Properties of IndiffIndiff. Curves, cont’d. Curves, cont’d

Indifference curves are convex:– convexity assumption: averages are preferred to

extremes

2

8

1 7

5

4

– Bundle A is (1, 8),bundle B is (7, 2).

– The averagebundle is (4, 5).

– If averages arepreferred toextremes,indifference curvesare convex.

A

B



37

Convexity: A RefresherConvexity: A Refresher

Definition: A graph is convex if every straightline connecting two points on the graph liesentirely above the graph.

38

Marginal Rate of SubstitutionMarginal Rate of Substitution

The slope of the budget constraint had a “nice”interpretation:

– The slope of the budget constraint is the rate at which you cantrade off less of good 2 for more of good 1.

The slope of an indifference curve has a similarinterpretation:

– The slope of the indifference curve is the rate at which you arewilling to trade off less of good 2 for more of good 1 … withoutmaking you any better or worse off.

The (absolute value of the) slope of the indifferencecurve is therefore referred to as the marginal rate ofsubstitution (MRS).

– (Note that the MRS changes along an indifference curve.)



39

MRS, cont’dMRS, cont’d

In order to acquire a little more of good 1, howmuch of good 2 are you willing to give up (sothat you are neither better nor worse off)?

– At bundle A, to acquirea little (∆x1) more ofgood 1, you need togive up ∆x2 of good 2.

∆x1

- ∆x2– If ∆x1 is small enough,

this ratio approximatesthe slope of theindifference curve at A.

A

Slope=-MRS at A

40


Why is it called the marginal rate ofsubstitution?

– It tells us at what rate (or, ratio) the consumer iswilling to substitute one good for the other … at themargin:

– “at the margin” means that this refers to smallchanges: how much is the consumer willing to giveup of one good in order to get just a little more ofthe other good?

» Remember Topic 1 (Thinking Like an Economist): theimportance of marginal analysis.



41


As we move down theindifference curve (youhave more and more ofgood 1), the MRSdeclines:

– You are willing to give upless and less of good 2 inexchange for an extra unitof good 1.

– Or: you are more willingto give up a little of good1 (in exchange for more ofgood 2) the more youhave of good 1.

This is just the fact thatconsumers like variety:

– You don’t like to consumea lot of one and not muchof the other good.

42

Special Indifference CurvesSpecial Indifference Curves

Here, goods 1 and 2are one-for-onesubstitutes:

– giving up one unit ofgood 2 for one more unitof good 1 gives theconsumer an equallypreferred bundle.

Examples:– Coke and Pepsi– tea and coffee– Trek and Cannondale

Indifference curves of perfect substitutes:

1

1



43

Special Indifference Curves, cont’dSpecial Indifference Curves, cont’d

Indifference curves of perfect complements:Here, goods 1 and 2are (one-for-one)complements:

– Suppose you have oneunit of each good. Onemore unit of one good(but not the other) givesyou an equally preferredbundle.

Examples:– vodka and Coke– skis and bindings– left and right shoes

44

Special Indifference Curves, cont’dSpecial Indifference Curves, cont’d

Here, the consumerdoes not care aboutgood 1:

– If this consumer getsmore of good 1, sheconsumes a bundle thatshe neither prefers nor“dis-prefers”.

Examples:– green peppers on pizza?



45


You have to choose between two “goods:”general consumption and work. Draw some ofyour indifference curves.

(Presumably you don’t like work, but do likeconsumption. Also assume that you arerational, i.e. that you prefer averages toextremes.)


… only connect… only connect

Choosing the Most Preferredof the Available Options



47

Rational Consumer ChoiceRational Consumer Choice

We have now interpreted:– “A rational individual always chooses to do what

she most prefers to do, given the options that areopen to her.”

as:– “A rational individual always chooses to consume

the bundle that is on the highest indifference curve,from all the bundles on her budget constraint.”

All we now need to do is put indifferencecurves and budget constraint together.

48

Rational Consumer Choice, cont’dRational Consumer Choice, cont’d



49


So bundle A cannot bethe optimal choice:

– The consumer prefers abundle to the right.

Could bundle A be anoptimal choice?

– At bundle A, the MRS isgreater than the (absolutevalue of the) slope of thebudget constraint, that is:

– In order to get one moreunit of good 1, theconsumer would bewilling to give up more ofgood 2 (MRS!) than shehas to at given prices(slope of budgetconstraint!).

A

50


So bundle B cannot bethe optimal choice:

– The consumer prefers abundle to the left.

Could bundle B be anoptimal choice?

– At bundle B, the MRS isless than the (absolutevalue of the) slope of thebudget constraint, that is:

– In order to be willing togive up unit of good 1, theconsumer would need tobe compensated with lessof good 2 (MRS!) thanshe could get at givenprices (slope of budgetconstraint!).

B



51

Rational Consumer Choice,cont’dRational Consumer Choice,cont’d

Implication: at theoptimal choice (if it is aninterior solution),

The only bundle forwhich no argument likethe previous can beconstructed is the“optimal choice” bundle,the bundle (x1*, x2*).

– At that bundle, the MRSequals the (absolutevalue of the) slope of thebudget constraint.

– Neither a bundle to theleft or to the right is morepreferred.

MRS = p1 / p2.

52

Corner SolutionCorner Solution

At corner solutions, theequality MRS = p1 / p2

need not always hold.

The optimal solutionneed not always be at apoint of tangency:

– At the bundle labeled“optimal choice”, supposethe consumer were toconsume more of good 1:

– To get one more unit ofgood 1, she would haveto give up more of good 2(slope of budgetconstraint) than she iswilling to (MRS).

– “optimal choice” is optimal




Application:Application:Cash or In-Kind Transfers?Cash or In-Kind Transfers?

Medicare or Money?

54


A direct money transfershifts the budgetconstraint out:

– this is just an increase inincome.

– Example: $100

money spent on healthcare

y

An in-kind transferallows the individual toconsume morehealthcare - not more ofanything else:

– Example: $100 inhealthcare



55

ChoiceChoice

For this consumer, thereis no difference betweenan in-kind transferprogram and a directmoney transfer:

– With direct moneytransfers, she willconsume bundle B.


y

A– With in-kind transfers, she

will consume bundle B.

56

Choice, cont’dChoice, cont’d

This consumer wouldprefer to receive a directmoney transfer:

– With direct moneytransfers, she willconsume bundle B.


y

A– With in-kind transfers, she

will consume bundle C.

On economic grounds,money transfers are“better” than in-kindtransfers.



57

Buzz Group: True or False?Buzz Group: True or False?

The price of food rises by 10% and disposableincome by 5%. A man initially spending halfhis income on food would be neither better norworse off as a result of these changes.


DemandDemand

Individual DemandMarket Demand



59

y

x

The Price-Consumption CurveThe Price-Consumption Curve

Suppose we lowered theprice of good X.

Whenever the price ofgood X changes, theconsumer optimizes,and consumes heroptimal bundle.

PCC

The set of all optimalbundles, as we changethe price of one good, isthe price-consumptioncurve (PCC)

60

Individual DemandIndividual Demand y

x

x

p

p’

p’’

p’’’

p’’’’ D

Whenever price changes,the consumer optimizes:

– As the price of good Xchanges, the consumerchooses to buy differentquantities of good X.

– Plotting the prices of goodX and the quantity of goodX the consumer chooses toconsume at that price givesthe ...

Consumer’s (individual)demand for good X.



61

Income-Consumption CurveIncome-Consumption Curve

Recall the price-consumption curve:

– We can derive a similarcurve for changes inincome:

– Whenever incomechanges, the consumeroptimizes and consumesher optimal bundle.

y

x

ICC

The set of all optimalbundles, as we changeincome, is the income-consumption curve (ICC)

62

y

x I

x

Engel Engel CurveCurve

Whenever incomechanges, the consumeroptimizes:

– As the consumer’sincome changes, shechooses to buy differentquantities of good X.

– Plotting the consumer’sincome and the quantityof good X the consumerchooses to consume withthat income, gives us the:

I’’’’

I’’’

I’’

I’ Engel curve




Behind Individual DemandBehind Individual Demand

Income and Substitution Effects

64

Behind Individual DemandBehind Individual Demand

What happens as price falls (holding moneyincome constant)?

– The good is now relatively cheaper (relative toother goods).

» Typically, the consumer will substitute away from othergoods, and towards the good for which the price hasfallen.

» This is the substitution effect.

– The consumer is now “wealthier” (she could stillbuy the same bundle and have money left over).

» Typically, this will lead the consumer to buy more of thatgood as her wealth increases.

» This is the income effect (wealth effect).



65

Behind Individual Demand, cont’dBehind Individual Demand, cont’d

Similarly for a price increase (holding moneyincome constant):

– The good is now relatively more expensive.» Typically, the consumer will want to consume less of it.

– The consumer is now “less wealthy”: she could notstill buy the same bundle.

» Typically, the consumer will want to consume less of thegood as her wealth falls.

66

Total Effect of a Price IncreaseTotal Effect of a Price Increase

y

x

AC

The total effect of aprice increase is thechange in thequantity demandedof a good inresponse to achange in its price:

– Here, it is themovement frombundle A to bundle C.



67

Substitution EffectSubstitution Effect

To isolate the substitution effect, ask:– How much extra income would the consumer need

to be able to reach her original indifference curve,after the loss of purchasing power due to the priceincrease?

– If (hypothetically) the consumer were to get thisextra income, she would be back on her originalindifference curve. But since relative prices havechanged, she will typically choose to consume adifferent bundle to that consumed originally.

– This is the substitution effect (Hicks).

68

y

x

AC

B

Substitution Effect, cont’dSubstitution Effect, cont’d

The substitution effect isthe movement frombundle A to bundle B.

The substitution effectisolates the effect that aconsumer is likely tosubstitute away from agood whose price hasincreased.

– Given just enough extraincome to reach heroriginal indifferencecurve, the consumerwould still (typically)choose to consume abundle (B) different fromthe original bundle (A).



69

Income EffectIncome Effect

To isolate the income effect, ask:– How much extra income would the consumer need

to be able to reach her original indifference curve,after the loss of purchasing power due to the priceincrease?

– If (hypothetically) the consumer were to get thisextra income, she would (most likely) consumedifferent amounts of the good than she would if shewere not compensated with this extra income.

– This is the income effect (Hicks).

70

Income Effect, cont’dIncome Effect, cont’d

The income effect isthe movement frombundle B to bundle C.

The income effectisolates the effect that aconsumer is likely toconsume less after aprice has increased(lower purchasing power).

– Given just enough extraincome to reach heroriginal indifference curve,the consumer would(typically) choose toconsume a bundle (B)different from the finalbundle (C).

y

x

AC

B



71

Income and Substitution EffectsIncome and Substitution Effects y

x

AC

B

total effect

substitution effectincome effect

price increase

72

Income and Substitution EffectsIncome and Substitution Effects y

x

CA

B

total effect

substitution effect income effect

price fall



73

Substitution Effect, cont’d.Substitution Effect, cont’d.

Note that the substitution effect of a priceincrease is always negative:

– the consumer wants to substitute away from thegood that has become more expensive.

Likewise, the substitution effect of a price fallis always positive:

– the consumer wants to substitute towards the goodthat has become less expensive.

This is just a result of our assumption thatindifference curves are convex.

74

Income Effect, cont’dIncome Effect, cont’d

The income effect is more ambiguous:– For a price increase and a normal good, the income

effect is negative (i.e. reinforces the substitutioneffect.

– For a price increase and an inferior good, theincome effect is positive (i.e. works against thesubstitution effect.

… and for a price fall:– For a price fall and a normal good, the income

effect is positive.

– For a price fall and an inferior good, the incomeeffect is negative.



75

Normal and Inferior GoodsNormal and Inferior Goods

Normal goods:– For a normal good, and a price increase, the

income effect is negative.» This just expresses the fact that as your purchasing power

falls, you buy less of a good.

Inferior goods:– For an inferior good, and a price increase, the

income effect is positive.» That is, as your income falls, you buy more of the good.

» Example: Grand Union own-brand white bread?

76

Inferior GoodInferior Good y

x

C

total effect

substitution effect

income effect

price increaseB

A



77

Inferior Good & its Inferior Good & its Engel Engel CurveCurve y

x I

x

I’’’

I’’

I’

Engel curve

y

x I

x

I’’’

I’’

I’

normal good inferior good

Engel curve

78

Inferior Goods: ExamplesInferior Goods: Examples



79

Giffen Giffen GoodGood

When a good is so strongly inferior that theincome effect outweighs the substitution effect,it is called a Giffen good.

– How likely is this?» Not very. (Any examples?)

– Giffen goods imply an upward sloping demandcurve.


Consumer SurplusConsumer Surplus

How are you?Good.

How good?



81

Measuring WelfareMeasuring Welfare

It is often important to have a measure of howmuch individuals benefit from a transaction.

– Example (cost-benefit analysis):» It is often easy to evaluate the costs of building a new

road.

» How do we measure the benefit (to consumers)?

Consumer surplus is a way of measuring howmuch a consumer benefits from buying acertain quantity of a good.

» (“Buying” includes buying at a zero price, as in theexample of the road, above.)

82

Consumer SurplusConsumer Surplus

How much do you valuethe first, second, … unitof a good that you buy?

The demand curve tellsyou what your marginalwillingness to pay is:how much you are justwilling to pay for the first,second, … unit of thegood.

q

p

D



83

Consumer Surplus, cont’dConsumer Surplus, cont’d

The shaded area is yourconsumer surplus.

Suppose the good costsp*. You will then buy q*units.

What is your benefitfrom buying q* units at aprice of p* each?

The demand curve tellsyou what you are justwilling to pay for eachunit:

– But for all units below q*,you actually pay less!

q

p

D

p*

q*

84

Consumer Surplus, cont’dConsumer Surplus, cont’d

q

p

D

p*

q*

The area under demand curve (and over theprice of the good) is the consumer surplus.

q

p

D

p*

q*



85

q

p

D

p’

q’

p’’

q’’

Changes in Consumer SurplusChanges in Consumer Surplus

The blue shaded area isthe change in consumersurplus.

Suppose the price of agood falls from p’ to p’’.

What happens toconsumer surplus?

Compare consumersurplus when the price isp’ (and you buy q’) withconsumer surplus whenthe price is p’’ (and youbuy q’’).


Market DemandMarket Demand

1 + 1 = ?



87

Individual and Market DemandIndividual and Market Demand

This is what we have achieved so far:– description of “options available to the consumer”

(budget constraint)

– description of “most preferred” (indifference curves)

– derivation of an individual’s demand curve frompreferences and budget constraint

We now only need one last step on our way toderiving a market demand curve:

– we need to aggregate all individuals’ demandcurves for a good.

88

From Individual to Market DemandFrom Individual to Market Demand

Suppose there is a good for which there are only twopotential consumers, A and B.

Each of these two consumers has her own (individual)demand curve for the good:

– An individual’s demand curve tells us how much she will buyat any given price (and for given income).

We construct market demand from individualdemands:

– For any given price, ask this question:» What is A’s demand? What is B’s demand?

– Adding these two quantities gives us market demand at thatprice.



89

Individual to Market Demand, Individual to Market Demand, contcont..

person Ap

qA

person Bp

qB

market demandp

q


Application: Labor SupplyApplication: Labor Supply

To Work or not to Work:That is the Question.



91

Modeling StrategyModeling Strategy

What do we want to model?

What does it mean to supply (more) labor?– less leisure time

– more income = more consumption

Note that the choice between labor and leisure isautomatic:

– if you choose to work 10 hours/day, you have 14 hours ofleisure time.

So we will model the choice between two goods:leisure and consumption. Why?

– Presumably, both leisure and income are goods, not “bads”.

92

Modelling Modelling Strategy, cont’dStrategy, cont’d

We will work in this space:

leisure (h)

consumption (c)

24 hrslabor



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Notation:– l: hours of labor

– h: hours of leisure

– t: max. time available (endowment of time)

– (therefore: t - h = l)

– w: wage rate (per hour)

– c: consumption (composite good)

– p: price of consumption

Watch out:– This notation is slightly different from Frank’s.

94


Remember what the budget constraint says:– money spent = income

– p · c = m

– p · c = w · l

– p · c = w · (t - h)

– p · c = w · t - w · h

– c = (w / p) · t - (w / p) · h

Recall the interpretation of the slope of thebudget constraint as relative price:

– (w / p), the “real wage” is the price of leisure, or itsopportunity cost.



95


h

c

t

(w/p) t

slope: -(w/p)

96


Both goods (consumption and leisure) are“goods” (not “bads”) … that is, you prefer tohave more of both.

And you prefer averages to extremes:Indifference curves should therefore have the“normal” (convex) shape.



97

Preferences and Optimal ChoicePreferences and Optimal Choice

h

c

t

(w/p) t

98

Comparative Comparative StaticsStatics

h

c

t

(w’’/p) t

(w’/p) t

(w’’’/p) t

Effects of varying wage rate (w’’’ > w’’ > w’):– recall budget constraint: c = (w/p) t - (w/p) l

PCC

w

l

w’’’

w’’

w’

S

Implication: labor supply



99

Comparative Comparative StaticsStatics, cont’d, cont’d

What’s going on?– As the price for leisure increases from w’ to w’’, the

consumer consumes less leisure (as we wouldexpect).

– As the price for leisure increases from w’’ to w’’’,the consumer consumes more leisure. Is thiscounterintuitive?

» Does this mean leisure is a Giffen good?

» (Answer: No.)

100

Income and Substitution EffectsIncome and Substitution Effects

Substitution and incomeeffects operate in theopposite direction. Here, theincome effect is stronger.

As we would expect, thesubstitution effect (A to B) fromthis price increase is negative:

– As the price for leisureincreases, consumers substituteaway from leisure (work more).

The income effect (B to C) ispositive:

– Really this is not surprising.Leisure is a normal good: asincome rises, a consumer wantsto consume more of it.

– As the price for leisure (the wagerate) increases, the value of yourendowment increases.

h

c

t

(w’’/p) t

(w’’’/p) t

A

B C



101

The Income EffectThe Income Effect

Here, the increase in the wage does twothings:

– it increases the price of something the consumerbuys: the price (the opportunity cost) of leisure;

– it increases the value of something the consumersells: the value of her endowment (i.e. her“wealth”).

So leisure is not a Giffen good.– (In fact, we have seen that the indifference curves

are such that leisure is a normal good … and allGiffen goods are inferior goods.)

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Eve lives in a town called Paradise. For a living, sheworks on an apple farm, just outside Paradise.

– She makes $10/hr. In Paradise there is no income tax.(Assume each unit of the general consumption good costs$1.)

Draw Eve’s budget constraint for a typical day. Alsodraw some of her indifference curves.

Paradise now establishes the following income taxscheme:

– The first $50 are tax-free; additional earnings are taxed at50%.

Draw Eve’s budget constraint now. What hashappened to her choice about how much to work?



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The income tax is repealed. Instead, Paradise nowintroduces the following unemployment benefitscheme:

– If you don’t work you get $50 per day. As you start earning(e.g. by working for one hour at $10/hr), your unemploymentbenefit is withdrawn dollar-for-dollar (i.e. if you work for 1 hourand earn $10, your unemployment benefit receipts are only$40).

Draw the new budget constraint. What happens toEve’s choice about how much to work?

Economics 1 Bentz Fall 2002 Topic3

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