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Course: MicroeconomicsText: Varians Intermediate

Microeconomics

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In Chapter 6, we talk about how demandchanges when price and income changeindividually.

In this chapter, we want to further analyzehow the change in price changes the

demand. In particular, we decompose the change in

quantity demanded due to price change

into substitution effectand income effect. 2

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What happens when a commoditys pricedecreases?

Substitution effect: the commodity is

relatively cheaper, so consumers usemore of it, instead of other commodities,which are now relatively more expensive.

Income effect: the consumers budgetof $m can purchase more than before,as if the consumers income rose, with

consequent income effects on quantities

demanded. 3

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x2

x1

Original choice

Consumers budget is $m.

2p

m

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x1

Lower price for commodity 1

pivots the constraint outwards.

Consumers budget is $y.x2

2p

m

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x1

Lower price for commodity 1

pivots the constraint outwards.

Consumers budget is $m.x2

Now only $m are needed to buy theoriginal bundle at the new prices,

as if the consumers income has

increased by $m -- $m.

2p

m

2

'

p

m

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Slutsky asserted that if, at the newprices,

If less income is needed to buy the originalbundle then real income is increased

If more income is needed to buy theoriginal bundle then real income is

decreased

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Changes to quantities demanded due tothe change in relative prices, keepingincome just enough to buy the original

bundle, are the (pure) substitution effect ofthe price change.

Changes to quantities demanded due tothe change in real income are the income

effect of the price change.8

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Slutsky discovered that changes todemand from a price change are alwaysthe sumof a pure substitution effect

and an income effect.n

i

s

ii xxx

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x2

x1

x2

x1

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x2

x1

x2

x1

11

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x2

x1

x2

x1

12

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x2

x1

x2

x2

x1 x1

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x2

x1

x2

x2

x1 x1

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x2

x1

x2

x2

x1 x1

Lower p1makes good 1 relativelycheaper and causes a substitution

from good 2 to good 1.

(x1,x2) (x1,x2)is the

pure substitution effect.

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Substitution effect is always negativelyrelated to the price change.

Note that the portion of the yellowcompensated budget line below x1 is insidethe budget set of the original budget, thusthese bundles should be less preferred than

the original bundle.As a result, the consumer must choose a

point at or more than x1with thecompensated budget, and as a result, the

substitution effect is positive for a price 16

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x2

x1

x2

x2

x1 x1

(x1,x2)

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x2

x1

x2

x2

x1 x1

(x1,x2)

The income effect is(x1,x2) (x1,x2).

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Most goods are normal (i.e. demandincreases with income).

The substitution and income effectsreinforce each other when a normal goods

own price changes.

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Since both the substitution and income effects

increase demand when own-price falls, a

normal goods ordinary demand curve slopes

down.

The Law of (Downward-Sloping) Demand

therefore always applies to normal goods.

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Some goods are inferior (i.e. demand isreduced when income is higher.)

The substitution and income effectsoppose each other when an inferior goods

own price changes.

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x2

x1

x2

x1

25

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x2

x1

x2

x1

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x2

x1

x2

x2

x1 x1

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x2

x1

x2

x2

x1 x1

The pure substitution effect is as fora normal good. But, .

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x2

x1

x2

x2

x1 x1

(x1,x2)

The pure substitution effect is as for a

normal good. But, the income effect is

in the opposite direction.

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x2

x1

x2

x2

x1 x1

(x1,x2)

The overall changes to demand arethe sums of the substitution and

income effects.

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In rare cases of extreme income-inferiority,the income effect may be larger than thesubstitution effect, causing quantity

demanded to fall as own-price rises.

Such goods are Giffen goods.

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x2

x1

x2

x1

A decrease in p1causesquantity demanded of

good 1 to fall.

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x2

x1

x2

x1x1

x2

A decrease in p1causesquantity demanded of

good 1 to fall.

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x2

x1

x2

x2

x1 x1x1

x2

Substitution effect

Income effect

A decrease in p1

causes

quantity demanded of

good 1 to fall.

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Giffen good can onlyresult when the incomeeffect of an inferiorgood is so strongthat itdominates the substitution effect.

This may be possible for poor householdswhere the low-quality necessity has taken upa large portion of expenditure.

This case is very rare, even if exists, so wehave confidence that the Law of Demandalmost always holds.

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If we denote m as the income required to

obtain the original bundle at the newprices, so that

m=p1x1+ p2x2 and m=p1x1+ p2x2. Thus the change in real income is

mm = (p1p1) x1

Or

11xpm

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The substitution effect is

The Income effect is

Total Effect

),()','( 11111 mpxmpxxs

)','(),'( 11111 mpxmpxxn

nsxxmpxmpxx 1111111 ),(),'(

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In terms of derivative (or rate of change):

Which is known as the Slutsky Equation.

(This is just a rough presentation. The toolsneed for formal derivations is not covered in

this class.)

)(

)(

11

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

xm

x

p

x

p

x

xmx

px

px

p

m

m

x

p

x

p

x

s

s

s

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Slutskys method of decomposition is not

the only reasonable way.

Hicks proposed another way of holdingreal income constant.

Instead of compensating him to be able tobuy back the original bundle, Hicks

method compensates the consumer to buyback a bundle that gives him the sameutility as before.

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Hicks Substitution Effect is also negative,because of the convex preference. (It canalso be shown by revealed preference.)

The nominal income required to maintainthe utility constant is less than the one

required to buy back the same bundle. Itimplies a larger income effect for a pricedecrease, but a smaller income effect for a

price increase. 44

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With the same tax revenue, the utility levelattained is higher with income tax thanwith the quantity tax.

But quantity tax has a stronger effect inreducing the consumption of good 1 than

income tax.

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Consider a similar case. Now a tax isimposed to reduce consumption of certaingood, but at the same time, an equivalent

amount is rebated (given back) to theconsumer.

Again, consumer has to take the rebateand tax rate constant for his decision.

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Note that the new consumption bundlemust be on the original budget line,because in equilibrium, the tax amount

and rebate are the same.

The consumer has become worse off after

this quantity tax and rebate program.

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In this chapter, a decomposition of priceeffect on quality demand is introduced.

Substitution effect: effect of change of priceholding real income constant.

Income effect: effect of change in real income.

For normal goods, both effects are negativew.r.t. a price rise.

For inferior goods, sub. effect is negative, butincome effect is positive w.r.t. a price rise.

Giffen goods can only be inferior goods withvery strong income effect.