ch4-2 macro economics

8/11/2019 Ch4-2 Macro Economics

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1

CHAPTER 4: DEMAND [2]CHAPTER 4: DEMAND [2]

2

Luxury goods and necessary goods

In general, Engel curves do not have to be straight lines. That is,

the relationship between income and consumption needs not belinear.

If the demand for a good goes up by a greater proportion thanincome, we say that it is a luxury good , and if it goes up by alesser proportion than income we say that it is a necessarygood .

Of course, both luxury goods and necessary goods arenormal goods .

On the other hand, we have the case of inferior good ifthe demand goes down as income increases.

3

Own price effect VS. Cross price effect

Suppose that we decrease the price of good X

P X

Y

X

As p X decreases, thedemand quantity forgood X increases.

In this case, we say goodX is an ordinary good .

As p X decreases, thedemanded quantity forgood Y decreases.

In this particular case,good Y is a substituteof good X.

4

Income and Substitution effects of own pricechange

When the price of good X changes, the change in theconsumption of good X can be broken to two effects:The substitution effect and the income effect.The substitution effect is that component of the total effectof a price change that results from the associated changein the relative attractiveness of other goods.The income effect is that component that results from theassociated change in real purchasing power.To decompose the total effect we begin by asking: Howmuch income would the consumer need to reach hisoriginal indif ference curve?If the consumer were given a total income of that amount, itwould undo the injury caused by the loss of purchasingpower.

5

Income and Substitution effects of own pricechange

In the following example the price of shelter increases from$6 per sq yd/wk t o $24. As a res ult shel ter co nsu mpti on dec reased f rom 10 sqyd/wk to 2.How do we brake the change?

6

The Substitution and IncomeEffects of a Price Change

To get the substitutioneffect slide the new budgetB1 outward Parallel to itselfuntil it becomes tangent tothe original indifference

curve I 0.

The movement from A to Creflects The substitutioneffect.

The movement from C to Dreflects the income effect. Itis the reduction in shelterthat results from the loss inpurchasing power.



7

The Substitution and IncomeEffects of inferior good

By contrast to the case of a normal good, the income effect inan inferior good acts to offset the substitution effect

8

Income change: A brief review

Income changes have the effect of shifting the budget line in

a parallel fashion.

From the apparatus of indifference curves, we derive the incomeexpansion path , describing how the optimal consumption bundlechanges as we change the income.

If we focus only on good X,then we derive the Engelcurve for the good,describing how the optimalconsumption of good Xchanges as we change theincome.

For income changes, we canhave two possible cases:

(1) the normal good case

(2) the inferio r good case

9

Own price change: A brief review

Own-price changes have the effect of pivoting the budget line.

From the apparatus of indifference curves, we derive the priceoffer curve , describing how the optimal consumption bundlechanges as we change the price of the good in question.

If we focus only on the goodwhose price has changed, thenwe derive the demand curve forthat good, describing how theoptimal consumption of thegood changes as we change itsprice.

For own-price changes, we canhave two possible cases:

(1) the ordinar y good case

(2) the Giffen good case

10

Cross price change: A b rief review

good X is asubstitutefor good Y

p Y x

good X is acomplementto good Y

p Y x

11

MARKET DEMANDMARKET DEMAND

12

Here we see how to add up individualchoices to get total market demand .

Once we have derived the market demand cu rve,we will examine some of its properties, such as therelationship between demand and revenue.

Introduction

We have seen in earlier chapters how to model individualconsumer choice.



13

From individual to market demand

Let us use X1(p X, p Y, Mi) to represent consumer i's demandfunction for good X, and Yi(pX, p Y, Mi) consumer i's demandfunction for good Y.

Suppose that there are n consumers.

Then the market demand for good X, also called theaggregate demand for good X, is the sum of these individualdemands over all consumers:

),,(),......,,,(1

1 iY X

n

iinY X M p p X M M p p X ∑

=

=

The analogous equation holds for good Y:

),,(),......,,,(1

1 iY X

n

iinY X M p pY M M p pY ∑

==

14

),,(),......,,,(1

1 iY X

n

iinY X M p p X M M p p X ∑

=

=

Since each individual's demand for each gooddepends on prices and his money income:

The aggregate demand will generally depend on prices andthe distribution of incomes (M1, M2, …., Mn).

But, to know the distribution of incomes, we need a lot of data.

So, it is sometimes convenient to think of the aggregatedemand as the demand of som e "representative"representativeconsumer"consumer" who has an income that is just the sum of allindividual incomes.

15

The representative consumer

It is convenient to ignore income distribution issues andthink of the aggregate demand as the demand of some"representative consumer" who has an income that is justthe sum of all indi vidual incomes.

The aggregate demand function will change from:

to:

∑

∑

=

=

≡

=

n

ii

iY X

n

iiY X

M M where

M p p x M p p X

1

1

11 ),,,(),,(

Under thisrepresentativeconsumerassumption, theaggregate demandin the economy is

jus t li ke thedemand of someindividual whofaces prices (p X,p Y)and has income M.That is, the distribution of i ncome does

not matter! Only the sum matters.

),,(),,(1

iY X

n

iiY X M p p X M p p X ∑

==

16

∑∑==

≡=n

iiiY X

n

iiY X M M where M p p X M p p X

11

),,,(),,(

If we hold constant the aggregate income M and p 2:

),( M p p X Y X

p X

X

aggregate demandcurve for good 1

),( M p p X Y X

Note that the demandcurve is drawn holdingall other prices andincomes fixed.

If income and otherprices change, the

aggregate demandcurve will shift .

17

p X

X

aggregate demandcurve for good X

),( M p p X Y X

For example, if goo ds X and Y are substitutes , thenwe know that increasing p Y will tend to increase thedemand for good X whatever its price.

This means thatincreasing the price ofgood Y will tend to shiftthe aggregate demand

curve for good X outward.

On the other hand, ifgoods X and Y arecomplements , increasingthe price of good Y willshift the aggregatedemand curve for good Xinward .

good X andgood Y aresubstitutes

18

p X

X

aggregate demandcurve for good X

),( M p p X Y X

If good X is a normalgood , there will be aninward shift in thedemand curve.

Now, suppose that there is a reduction in the income.

On the other hand, ifgood X is an inferiorgood , the demand curvewill shift out .

good X is anormal good



19

The inverse demand function

We can look at the aggregate demand curve as giving us

quantity as a function of pr ice: direct demand function, q(p).

This function measures what the quantity demanded wouldhave to be if the price is at the level p.

Alt ernati vely , we can l ook at the agg regate dem and cu rve asgiving us price as a function of quantity: inverse demandfunction, p(q).

This function measures what the market price for the goodwould have to be for q units of it to be demanded.

20

Elasticity

q q p po m= ( , )It is often of useful to have ameasure of how "responsive"demand is to a change in own

price.

p

q

aggregate demand for thegood in question

The first idea that springs to mind is to use the inverse of theslope of a demand curve as a measure of responsiveness.

Aft er all , the defi niti on ofthe slope of a demandcurve is the change inprice divided by change inquantity demanded:

∆ p

∆q

q p

curvedemand of slope ∆∆=

pq

curvedemand

of slopetheof inverse

∆∆=

So, the inverse of the slope of ademand curve looks like a measureof demand responsiveness.

21

Well, it is a measure of responsiveness - but it suffersone major drawback: It depends on the units in whichwe measure price and quantity.

For example, if we measure demand in gallons ratherthan in quarts, the slope becomes four times bigger, andhence, one over slope becomes four times smaller.

It is convenient to consider a unit-free measure ofdemand responsiveness.

Economists have chosen to use a measure known aselasticityelasticity .

q p

curvedemand of slope ∆∆=

pq

curvedemand

of slopetheof inverse

∆∆=

22

Own price elasticity of demand

The own-pri ce elasticit y of demand, , is defined to bethe percentage change in quantity demanded divided bythe percentage change in own price.

ε

ε

A 10 percen t in crease i nprice is the same percentageincrease whether the price ismeasured in Americandollars or English pounds.

Thus, measuringincreases in percentageterms keeps thedefinition of elasticityunit-free.

q

p

p

q

p p

qq

p p

qq

pin

qin

∆

∆=∆

∆

=∆

∆

=∆

∆≡100

100

%

%ε

23

ε ≡ =%%

∆∆

∆ ∆in qin p

% in q associated with 1% in p

ε ≡ =30%5%

∆∆

∆ ∆in qin p

6% in q associated with 1% in p

curvedemand theof slopetheq p

q p

pq

Note

1*

:

=∆∆=ε

The own-price elasticity can be expressed asthe ratio of own price to quantity multiplied bythe inverse of the slope of the demand curve.

24

ε ≡ = =%%

∆∆

∆

∆∆∆

in qin p

qq p

p

pq

q p

The sign of the elasticity of demand isgenerally negative, since demandcurves invariably have a negative slope. - 2 or - 3It is tedious to keep referring to a price elasticity of minussomething-or-other, so it is common in verbal discussion to referto price elastici ties of 2 or 3, rather than -2 or -3.

To avoid confusion, we will keepthe signs straight in thediscussion by referring to theabsolute value of elasticity.

2 3or



25

A 1% increase in the price of the good will c ausea 0.5% reduction in the demand quantity.

ε = - 0.5

ε = 0 5. Good X

ε = - 1.5

ε = 15.

A 1% increase in the price of th good will causea 1.5% reducti on in the demand quantity.

Good Y

Which of the two goods is more own-price elastic?

Good Y is more own-pric e elastic . The absolut e valueof its own price elasticity is larger than that of good X.

26

OWN-PRICE: Elastic VS. Inelastic

A 1% increase in the price of the good will causea 0.5% reduction in the demand quantity.ε = - 0.5

ε = 0 5. This good is own-price inelastic.

ε = - 1.5

ε = 15.

A 1% increase in the price of the good will causea 1.5% reduction in the demand quantity.

This good is own-price elastic.

ε = - 1.0

ε = 10.

A 1% increase in the price of the good will causea 1% reduction in the demand quantity.

The elasticity i s unitary.

27

If a good has an own-price elasticity of demand greater than1 in absolute value we say that it has an elastic demand.

If a good has an own-price elasticity of demand less than 1in absolute value we say that it has an inelastic demand.

If a good has an own-price elasticity of demand of exactly 1in absolute value we say that it has unit elastic demand.

The own-price elasticity of demand for an ordinary good isa negative number because the demand curve isdownwardly sloped.

However, the own-price elasticity of demand for a Giffen

good is a positive number because, in this case, thedemand curve i s upwardly s loped.

28

elasticinelastic

unitary

0- infinity + infinity-1

own-price elasticity

ordinary good Giffen good

q

p

ordinary good

q

p

Giffen good

29

ε = = pq

q p

pq the slope of the demand curve

∆∆ *

1

p

q

p

q

slope = - 0 slope = - infinity

elasticity = - infinity elasticity = - 0

Perfectly Elastic Perfectly Inelastic

The flatter the demand curve is, the more own-priceelastic is the demand.

30

p

q

p

q

flatter steeper

That is, the flatter the demand curve is, the moreroom there is for the quantity to adjustment.

The flatter the demand curve is, the more own-priceelastic is the demand.



31

Elasticity and close substitutes

Take our example of red pens and blue pens. Suppose thateveryone regards them as perfect substi tutes. Then, red pensand blue pens must sell for the same price.

Now think what would happen to the demand for red pens iftheir price should rise , and the price of blue pens staysconstant.

Clearly the demand for red pens would drop to zero.

In other words, the demand for red pens is very elastic.This is because it has a perfect substitute.

The own-price elasticity of demand for a good depends toa large extent on how many close substitutes it has.

pq

32

So what?

If a good has many close substitutes, we would expect that its

demand curve would be very responsive to its price changes.

That is, its demand would be very own-price elastic .

On the other hand, if there are few close substitutes for a good,its demand curve would be very unresponsive to its pricechanges.

That is, its demand would be very own-price inelastic .

33

Example: Own pric e elasticity of a LINEARDEMAND CURVE

Consider the linear demand curve: q = a - b p

p

q

1/slope = - b

If q = 0:

?

0 = a - b p

p = a / b

a/b

If p = 0:

?q = aa

34

p

q

ε = −−b p

a bp

When p = 0, the own-priceelasticity of demand is zero.

ε = 0

When q = 0, p = a/b and theown-price elasticity of demandis (negative) infinity.

ε = ∞

At w hat val ue of p ric e is t heprice elasticity of demandequal to -1?

a/b

a

q = a - bp

bpa p

bq p

b pq

q p

−−=−=

∆∆=ε

bslope p

q −==∆∆ 1

∞−=ε 0=ε

???1−=ε

35

p

q

ε = −−b p

a bp

ε = 0

ε = ∞

a/b

a

1−=−

− pba

pb

Well, let's set the elasticity to -1:

Solve the above for p:

ba

p2

=

∞−=ε 0=ε

???1−=ε

Substitute the solution for p tothe demand equation to findthe associated q:

2a

q =

ab2

a2

ε = 1

36

p

q

ε = 0

ε = ∞

a/b

a

ab2

a2

ε = 1

Except in special cases,the magnitude of priceelasticity changes as onemoves along the demandcurve.

In other words, the magnitudeof price elasticity changes asprice changes.

ε ε = ( ) p



37

Evaluating own price elasticity at a sample point

Since the elasticity coefficient may vary along a demand

curve, It is not technically correct to say that the demandfor a commodity is own-price elastic or inelastic.

That is, demand may be own-price elastic orinelastic only within some range of the data.

In making empirical computations, a common procedureis to evaluate own-price elasticity of demand at the meanof the data.

q

p pq

*∆∆=ε

where are the priceand quantity demanded, evaluatedat the mean of the data.

qand p

38

250,20,4

,5,3,2Q

:arevariablestheof meanssampleThe

beef

===

===

SPPD M P

PP

chicken

pork beef

Write down the formula for own-price elasticity of demand for beef.

Compute the own-price elasticity of demand for beef (evaluatingat the sample means). Is the demand elastic or inelasti c? Isbeef an ordinary good or a Giffen good?

Suppose that the price of beef is projected to decrease by 2% nextmonth, what would be the percentage change in Q beef (demand)?

social anddemographicvariables

SPPD M PPP chicken pork beef 01.004.001.003.05.001.0Q

: products beef for equationdemand followingtheConsider

beef ++++−=

income

39

PUT YOUR ANSWERS HERE

75.023

5.0

,

−=

−=

∆∆

=beef

beef

beef

beef PQ

Q

P

P

Qbeef beef

ε 5.0−=∆∆

beef

beef

P

Q

The coefficient associated withPbeef in the demand equation.

A 1% increase in P beef wil l be accompanied by a 0.75%decrease in Q beef (demand).

The demand is inelastic , and beef is an ordinary good.

If Pbeef is to drop by 2%, Q beef will increase by 1.5%.[(-2%) * (-0.75) = 1.5%]

40

Own price elasticity and industry revenueRevenue is the price of a good times thequantity sold of that good: R = p q

You are the only seller in the market and are thinking aboutraisin g the pric e. What would happen to your revenue?

p q R ? or It depends on how responsive the demand is to the price change.

If the demand drops a lotdue to the price increase,revenue will fall.

If the demand drops only a littledue to the price increase,revenue will increase.

This suggests that the direction of change in revenue hassomething to do with the own-price elasticity of demand .

41

Change in industry revenue R = p qLet the price change to: p p+ ∆Let the quantity change to: q q+ ∆

We have a new revenue of:

R p p q q

p q q p p q p q

new = + += + + +

( ) ( )∆ ∆∆ ∆ ∆ ∆

Subtracting R from R new we have:

∆ ∆ ∆ ∆ ∆ R q p p q p q= + +

42

∆ ∆ ∆ ∆ ∆ R q p p q p q= + +

For small values of and , the last term can safelybe neglected.

∆ p ∆q

a small number timesanother small number

Thus, the expression for the change in revenuecan be approximated by:

q p pq R ∆+∆≈∆

That is, the change in revenue is roughly equal to theoriginal quantity times the change in price plus the originalprice times the change in quantity .



43

R = p q∆ ∆ ∆ ∆ ∆ R q p p q p q= + +

q p pq R ∆+∆≈∆

price

quantity

The original price and

quantity are p and q,respectively.

p

q

Thus, the originalrevenue is pq.

originalrevenue, pqWhen the price

increases, we add arectangular area on thetop of the box, whichis:

q p∆

p p+ ∆q p∆

44

price

quantity

p

q

p p+ ∆

To reflect thequantityreduction, weneed to subtractan area on theside of the box,which is: p q∆

q q+ ∆

originalrevenue, pq

p q∆

The leftover part,

∆ ∆ p q

is the little squarein the corner ofthe box.

∆ ∆ p q

This leftover part will bevery small relative tothe other magnitudes.

∆ ∆ ∆ ∆ ∆ R q p p q p q= + +

q p pq R ∆+∆≈∆

q p∆

45

So, there are two main effects on the revenue when oneincreases the price:

Positive Effect: q p∆

p q∆Negative Effect:

Why is this second effect negative? ∆q < 0

When will the net result of these two effects be positi ve? Thatis, when will an increase in the price be followed by an increasein the revenue?

Two effects on revenues

q p pq R ∆+∆≈∆

46∆ ∆ ∆ R q p p q= +

???0when willis,That >∆+∆ q p pq

Divide the expression by p∆

q pq p

+ >∆∆ 0 q

q pq

q p

+ >∆∆ 0

pq

q p

∆∆

> − 1 ε > − 1

ε < 1

0- infinity + infinity-1

inelastic

47

The revenue will increase as the price is increased if theown-price elasticity of demand is less than 1 is absolutevalue. That is, if the demand is own-price inelastic .

Inelastic:p q R

The revenue will decrease as the price is increased ifthe own-price elasticity of demand is greater than 1 isabsolute value. That is, if the demand is own-priceelastic .

Elastic: p q R

If the price elasticity is unitary, what would happen tothe revenue when price increases?

48

Demand is OwnPrice Inelastic:

p q

Demand is OwnPrice Elastic: p q

Quantity is not responsive to the price change.

inelastic

demand

Quantity is responsive to the price change.elasticdemand

NOW, THE OTHER SIDE OF THE MIRROR:IS THE PRICE RESPONSIVE TO A CHANGE IN

QUANTITY? [PRICE FLEXIBILITY]

Price is responsive to the quantity change. flexibleprice

Price is not responsive to the quantity change.inflexibleprice



49

Marginal revenue and own price elasticity

Marginal Revenue is the additional

revenue to an additional unit of output. M R

R

q≡

∆

∆We saw earlier that the change in revenue is given by:

∆ ∆ ∆ R p q q p= +

M R p q q p

q

p q pq

pq p p q

≡ +

= + = +

∆ ∆∆

∆∆

∆∆1

50

M R pq p p q

≡ +1∆∆

What is the secondterm inside thebrackets?

Nope, it's not elasticity. It is the reciprocal of elasticity.

q p

p q p q

q p

∆∆ ∆

∆

= =1 1ε M R p≡ +1

1ε

MR p≡ +−1

105.

To avoid confusion dueto the fact that own-priceelasticity is a negativenumber, we rewrites theexpression as:

M R p≡ −11

ε

MR p≡ −11

05.

51

If the demand is inelastic , then marginalrevenue is negative. So, revenuedecreases as you increase output.

p p R M 325.01

1 −=−≡

price is flexible

If the demand is unitary , then marginalrevenue is zero. So, revenue does notchange as you increase output.

00.1

11 =−≡ p R M

price flexibility is unitary

If the demand is elastic , then marginalrevenue is positive. So, revenueincreases as you increase output.

M R p≡ −11

ε

p p R M 5.00.2

11 =−≡

price is not flexible

52

Both sides of the mirror

If the demand is inelastic ,revenue decreases as youincrease output.

If the demand is inelastic ,revenue increases as youincrease price.

If the demand is unitary ,revenue does not change asyou increase output.

If the demand is unitary ,revenue does not changeas you increase price.

If the demand is elastic ,

revenue increases as youincrease output.

If the demand is elastic ,revenue decreases as youincrease price.

53

Income elasticity

The income elasticity of demand is used to describe how thequantity demanded responds to a change in income:

income elasticity of demand =% change in quantity demanded

% change in income

ε m

in qin income

qqm

m

qqm

m

≡ = =%%

∆∆

∆

∆

∆

∆

100

100

ε m

in q

in mmq

q

m≡ =%

%

∆∆

∆∆

54

ε m

in qin m

mq

qm

≡ =%%

∆∆

∆∆

A normal good is one for w hich an increasein income leads to an increase in demand. 0>

∆∆

mq

The income elasticity of demand is positive.

Further, we say the good is a luxury good if itsincome elasticity of demand is greater than 1.

An inferior good is one for w hich an increase inincome leads to a decrease in demand. 0<

∆∆

mq

The income elasticity of demand is negative.



61

Two goods are substitutes if their cross-priceelasticity is positive .

Two goods are complements if their cross-priceelasticity is negative .

Two goods are independent if their cross-priceelasticity is zero .

ε m

in q

in mmq

q

m≡ =%

%

∆∆

∆∆P

Q

P

QQ P

PQ

62

complementssubstitutes

0- infinity + infinity

1

Cross-Price Elasticity

Independent goods

1q

1 p

p 2 increase

goods 1 and 2 are complements1q

1 p

p 2 increase

goods 1 and 2 are substitutes

63

Evaluating cross price elasticity at a sample point

In making empirical computations, a common procedureis to evaluate cross-price elasticity of demand at the meanof the data.

Consider the cross-price elasticity of demand for good 1with respect to a change in the price of good 2:

1

2

2

1 *21 q

p pq

pq ∆∆=ε

where are the priceof good 2 and quantity of good 1,evaluated at the mean of thedata.

12 qand p

64

250,20,4

,5,3,2Q

:arevariablestheof meanssampleThe

beef

===

===

SPPD M P

PP

chicken

pork beef

Write down the formula for the cross-price elasticity of demandfor beef with respect to pork price.

Compute the cross-price elasticity (evaluating at the samplemeans). Are beef and pork substitutes or complements?

Suppose the price of pork is projected to decrease by 2% nextmonth, what would be the percentage change in Q beef (demand)?

SPPD M PPP chicken pork beef 01.004.001.003.05.001.0Q

: products beef for equationdemand followingtheConsider

beef ++++−=

income

social anddemographicvariables

65

PUT YOUR ANSWERS HERE

075.02

503.0

,

=

=

∆∆

=beef

pork

pork

beef PQ

Q

P

P

Qbeef beef

ε 03.0=∆∆

pork

beef

p

Q

The coefficient associated withP

porkin the demand equation.

A 1% increase in P pork will be accompanied by a 0.075%increase in Q beef (demand).

Beef and pork are substitutes.

If Ppork is to drop by 2%, Q beef willdecrease by 0.15%.[(-2%) * (0.075) = -0.15%]

ch4-2 macro economics

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