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Topic 3 Substitution andIncome Efects

Suppose the price of X increases. This creates a substitution effect and an income effect.

Consumption Good Y

BC2 BC1

Consumption Good XThe Substitution Effect is due to a relative price change

X is more e!pensive relative to Y after the price change.

The slope of the budget constraint is steeper. "#ecall that pX$pYis the slope of the

budget constraint % &hen the budget constraint's slope changes( this indicates thatrelative prices have changed.)

The opportunit* cost of consuming good X has increased.

The +ncome Effect is due to a real income changes

#eal income has gone do&n because nominal income "+) sta*ed the same but the

price of X ",X) increased.

-easible set of consumption bundles is smaller.

The follo&ing chart illustrates the substitution( income( and total effects of priceincreases and decreases for normal and inferior goods.

Substitution Effect +ncome Effect Total Effect

Price Increase

ormal Good /0 /0 /0+nferior Good /0 / Either

Price Decrease

ormal Good / / /

+nferior Good / /0 Either

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Consider a decrease in the price of consumption good X. 3hen the price of X decreases(the budget constraint pivots out&ard along the a!is measuring the 4uantit* ofconsumption good X. The consumer moves from utilit* ma!imi5ing consumption bundlea to utilit* ma!imi5ing consumption bundle b. This movement is the total effect of the

price decrease. +t is &hat &e actuall* observe.

Consumption Good Y

Ya a

Yb bc 62

61

BC1 BC2

Xa Xc Xb Consumption Good X

To identif* the substitution and income effects( dra& a ne& dotted line "sho&n above)that is 7ust tangent to the original budget constraint "at point c) but &ith the same slope asthe ne& budget constraint "BC2). This dotted line &ill represent enough income to getbac8 to the original indifference curve "the original level of utilit*) but &ith the slope ofthe ne& budget constraint to reflect the ne& relative prices. +n other &ords( income isad7usted to 8eep utilit* the same from points 9 to C at the ne& relative prices.

The substitution effect is from a to c and it is positive. To see this( recall that the slope ofthe budget constraint represents the ratio of relative prices "pX$pY). 3hen the slope of thebudget constraint gets flatter( this indicates that pX$pYdecreases and that consumptiongood X has gotten relativel* less e!pensive. 9ccording to the substitution effect(consumers &ill substitute to&ard the consumption good that has gotten cheaper. Thus(the substitution effect prompts the individual to consume more of good X( &hich is thepositive effect from a to c.

3e argue that the movement from consumption bundle a to consumption bundle ccontains no income effect because both consumption bundles are on the sameindifference curve. +f there had been a change in real income( then the same level ofutilit* &ould not have been achieved.

The income effect is from c to b and it is positive. Bet&een c and b( the dotted linemoves in a parallel fashion to the ne& budget constraint. This represents the increase in

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real income or purchasing po&er e!perienced &hen prices decrease. 9n increase in realincome prompts consumers to purchase more of all normal goods( &hich is the positiveincome effect.

3e argue that the movement from c to b contains no substitution effect because the

dotted line and the ne& budget constraint have the same slope. This indicates that therehas been no relative price change bet&een these t&o lines % onl* a change in real income.+f there had been a change in relative prices( then the t&o lines &ould have had differentslopes.

ote that in this e!ample( consumption good X and consumption good Y are substitutes&hen the price of consumption good X decreases( the individual consumes less ofconsumption good Y.

3e can also sho& that in this e!ample( as the price of consumption good X decreases(total e!penditures on consumption good X increase. This is because income e4uals the

price of consumption good X multiplied b* the 4uantit* of X consumed price plus theprice of consumption good Y multiplied b* the 4uantit* of Y consumed. That is( + : pXX pYY. +n this instance( nominal income and the price of consumption good Y have notchange. Since the individual consumes less of consumption good Y &hen the price of Xdecreases( less is spent on Y. Since nominal income is unchanged( more must have beenspent on consumption good X.

3e can also determine that the demand curve for consumption good X is inelastic. 3hena price increase results in an increase in total e!penditures "or( total revenue from thefirm's perspective)( demand is inelastic.

o&( sho& this for an inferior good

Consumption Good Y

b

Yb a

Ya 62

c 61

BC1 BC2

Xa Xb Xc Consumption Good X

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Y

C

9 61

B

62 B2 B1 Cigarettes

The substitution effect is from point 9 to C and its negative. The income effect is frompoint C to B and its positive. The total effect is &hat is left over "9 to B) and it isnegative.

You are the manager of an ad agenc* that does &or8 for a local tire compan*. Youremplo*ees are planning an ad campaign. Smith sho&s *ou his la*out tire sale( 2 offour regular price of D per tire. Bro&n sho&s *ou her la*out tire sale( bu* three tires atthe regular price of D each( get the Athone -#EE. You must decide bet&een themar8eting approaches. Being a former economics ma7or( *ou construct an indifferencemap &ith tires on the hori5ontal a!is and consumption of other goods =C> on the vertical

a!is( *ou add the relevant budget lines for both pricing schemes and reasonableindifference curves. Fet the price of other consumption goods =C> be normali5ed to be,"C): D1.. Fet income be + : DA. Based on *our anal*sis( &hich approach seemsli8el* to sell more tires@ E!plain( using an indifference map belo&.

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=C>

DA

D2

D2

D

; A H Tires

3ould *ou rather have D1. &orth of apples or D1. in cash@ ,robabl* theD1. in cash( because it allo&s *ou to spend the gift an* &a* *ou choose.9lternativel*( if + gave *ou D1. &orth of apples( ho& much cash &ould + have to give*ou instead to ma8e *ou e4uall* &ell off@ D.@ 3ould *ou rather have D. in

cash or D1. &orth of apples@ D;.@ 3ould *ou rather have D;. in cash orD1. &orth of apples@

Consider targeted ta! cuts versus income ta! cuts. To spur *ouths to get more education(suppose the federal government begins subsidi5ing the cost of school 00 reducing its costto the consumer b* having the government pa* for a fraction of the price of education."9ssume that individuals can consume either education or units of compositeconsumption item =Y>. 9lso( let the price per unit of consumption item =Y> be D1.).

Fet the price of a unit of education be I,I initiall*. +n the figure belo&( dra& a ne&budget constraint representing the price of a unit of education decreasing to ,"10s) &here

IsI is the subsid* the federal government pa*s to reduce the cost of a unit of education.

9fter dra&ing the ne& budget constraint( dra& the modeled consumerJs ne& indifferencecurve( labeled 62( representing the ne& e4uilibrium consumption of units of educationand good IYI.

-inall*( indicate graphicall* &hat the total cost of the subsid* program is for the federalgovernment.

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Consumption Good Y

61

BC1

6nits of Education(Hint: make the changes in the budget constraint stark)

o& suppose that a different plan to help consumers is proposed. Some mightdisapprove of the subsid* plan described above because it onl* re&ards individuals forcertain behavior 00 as e!emplified b* the fact that *ou onl* get a discount if *ou bu* unitsof education. +nstead( this plan gives a lump0sum cash transfer "li8e an income ta! cut) toconsumers and lets them decide ho& to spend the mone*. +n particular( this plan givesconsumers e!actl* enough cash to get to the ne& level of utilit* *ou dre& above( 62.

Graphicall*( indicate ho& much cash this plan &ould have had to give the modeled

individual in order to increase his utilit* from indifference curve 61to 62.

3hich plan costs more( the first or second@

3hich plan gets consumers to consume more units of education@

The first plan lo&ers the price of education via the subsid*. Thus( the budget constraintpivots out&ard along the =education> a!is. The ne& budget constraint under is labeledBC9.

The ne& utilit* ma!imi5ing indifference curve is 62on budget constraint BC9. 9lso( the

ne& utilit* ma!imi5ing consumption bundle is =9> &ith L9units of education.

9ssuming the cost of good Y is D1. per unit( then the cost of the first plan is 92091dollars( represented b* the vertical distance from 91 to 92. To see this( note that thevertical distance bet&een BC1and BC9at L9units of education is 92091. +f the cost ofeach unit of Y "on the vertical a!is) is D1.( then the vertical distance bet&een 92 and91 represents the cost of the subsid* program. +n other &ords( the government &ould

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have to give the individual an amount of mone* e4ual to 92091 in order to ma8econsumption bundle 9 attainable.

To get to indifference curve 62via more income &ith no relative price change( theoriginal budget constraint &ould have to shift out&ard until it becomes 7ust tangent to the

ne& indifference curve "62). This occurs at consumption bundle B on indifference curve62&ith LBunits of education. 9gain assuming the cost of a unit of Y is D1.( theincrease in income needed to get to 62under the original prices is the distance bet&eenB2 and B1. This is the distance bet&een the parallel lines BC1and FineB. So( thegovernment &ould have to give cash e4ual to B20B1.

B20B1 is clearl* less than 92091. So( the first plan costs more than the second plan.

The first plan gets the individual to consume more education "L9) than the second plan"LB).

Good Y

b a

92 B2 62

61

91( B1 BC1 FineB BC9

LB L96nits of Education

This illustrates the difference bet&een targeted ta! cuts and income ta! cuts. +t alsodepicts different underl*ing philosophies about utilit* ma!imi5ation % &hether consumerscan ma!imi5e their o&n utilit* or &hether the government 8no&s better ho& to ma!imi5econsumers' utilit*. This can be related to the charit* e!ample % &hether the homelessperson better 8no&s ho& to ma!imi5e his utilit* or the charit* organi5ation.

9lso( notice that if the amount spent on the subsid* &as instead given to consumers( thenconsumers &ould have been able to attain a higher level of utilit* on a higher indifferencecurve. -or e!ample( &ould *ou rather have D1. &orth of apples or D1. in cash@,robabl* the D1. in cash( because it allo&s *ou to spend the gift an* &a* *ouchoose.

So( &ould *ou rather have targeted ta! cuts "li8e education subsidies) or an income ta!cut@ 3ould *ou rather have D2. cash or D2. &orth of food@

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Problem Set 3 Substitution and IncomeEfects

1. -igure 1 belo& represents Millard's preferences for co8e and deodorant. +nitiall* atpoint =a>( Millard consumes L1units of deodorant. &hichcontains L2units of deodorant at a price of p2.a) 9ccording to -igure 1 belo&( are co8e and deodorant substitutes or

complements@b) B* &hat amount did Millard's e4uilibrium consumption of deodorant fall as a

result of the price change@c) 9ccording to -igure 1( find the substitution effect of the increase in the price

of deodorant. +s the substitution effect positive or negative( and ho& large is itin terms of 4uantit* of deodorant@

d) 9ccording to -igure 1( find the income effect of the increase in the price ofdeodorant. +s the income effect positive or negative and ho& large is it in

terms of 4uantit* of deodorant@e) +s deodorant a normal or an inferior good@

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f) -or this part of the 4uestion( assume coats are an inferior good. 9ssuming coatsare an inferior good( &hat &ould the sign of the substitution effect and incomeeffect be to an increase in the priceof &inter coats@

Sno& Tires

9 B

C

BC1 BC2

L9

LC

LB

Coats

;. Pne of ,resident ClintonJs goals for 1OOH is to pass legislation to ma8e child caremore affordable. Suppose ,resident Clinton uses government subsidies to reduce theprice of a unit of childcare. Fet a unit of childcare be an hour of childcare per child.a) No *ou thin8 a unit of childcare is a normal or inferior good@ E!plain *our

ans&er.b) 6sing an indifference map complete &ith budget constraint( graph the effect of a

decline in the price of a unit of childcare "8eeping in mind &hat 8ind of good *oubelieve a unit of child care to be). Graph units of child care on the hori5ontal a!isand composite consumption good ICI on the vertical a!is.

c) 6sing *our diagram dra&n in part b( decompose the effect of ClintonJs childcaresubsid* that *ou have dra&n into the substitution and income effect. E!plain *ouradditions to *our diagram. State &hether the substitution and income effects arepositive or negative. Your ans&ers and graphical additions should correspondcorrectl* &ith *our ans&er to part a.

d) 9ccording to *our diagram( did the modeled consumerJs e!penditures on units ofchild care increase or decrease &hen the price of a unit of childcare decreased.E!plain briefl*.

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Answer Key #3 Substitution andIncome Efects

9ns&er to 4uestion 1.

a) Complements because &hen ,Nincreases( deodorant decreases and co8edecreases.

b) 9 to B or L2% L1c) 9 to C or L;% L1( &hich is negative /0.

d) C to B or L;% L2( &hich is negative /0.

e) Neodorant is a normal good because a decrease in real income results in lessdeodorant being consumed "because the income effect of a price increase isnegative).

f) +ncrease. The budget constraint is given b* + : ,CC ,NN. +ncome "+) and,Csta* constant( co8e decreases( so total e!penditures on co8e decrease. Theprice of deodorant increases and deodorant decreases( so the change in thetotal e!penditure on deodorant appears to be ambiguous. But( if income did

not change( and if &e're spending less on co8e( then &e've got to be spendingmore on deodorant.

9ns&er to 4uestion 2.a) Sno& tires and &inter coats are substitutes &hen the price of &inter coats goes do&n(

more &inter coats are consumed but fe&er &inter tires are consumed. Consumersappear to be substituting sno& tiers &ith &inter coats. This sho&n b* the movementfrom consumption bundle 9 to bundle B as the price of &inter coats increases.Bundle B contains more &inter coats and fe&er sno& tires.

b) The substitution effect sho&s ho& consumers respond to a relative price change&ithout a change in real income. -rom point 9 to ,oint C( there has been a relative

price change but no change in purchasing po&er the substitution effect is L9to LCand its positive.

c) The +ncome effect sho&s ho& consumers respond to a change in real income &ithrelative prices remaining the same. -rom point C to point B there has been a changein real income but no change in relative prices because the dotted line and budgetconstraint BC2have the same slope the income effect is L

Cto LBand its positive.d) The total effect is the combined substitution effect and income effect. The total effect

is &hat &e actuall* observe L9to LBand its positive.e) 3hen the price of a good goes do&n( normal goods have positive substitution(

income( and total effectsQ inferior goods have positive substitution and total effectsand negative income effects.

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Fet Childcare be a normal good. BC2reflects the subsid*( &hich reduces the realprice of childcare.

=C>

9 B

C

BC1 BC2

Substitution Effect / +ncome Effect /

Total Effect /

b) 3hen the real price of childcare declines( &e observe a movement from point=a> to point =b> on BC2. This is the total effect and it is positive.

c) The substitution effect is from point a to point c. ,oint c represents optimalconsumption under the ne& relative prices but the no change in real income.The substitution effect is positive. The income effect is from point c to pointb. This sho&s the reaction of a consumer to a change in real income. Therehas been no change in relative prices bet&een point c and point b. Theincome effect is positive and the total effect is positive "TE : SE +E).

d) + : ,CCCC ,C C. +ncome remains constant. Total e!penditures on C

decrease because ,Cis constant and C decreases. Therefore( totale!penditures on CC &ent up.

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o& let Childcare be an inferior good. BC2reflects the subsid*( &hich reduces the realprice of childcare.

=C>

B

9

C

BC1 BC2

Substitution Effect / +ncome Effect /0

Total Effect /

e) 3hen the real price of childcare declines( &e observe a movement from point=a> to point =b> on BC2. This is the total effect and its positive.

f) The substitution effect is from point a to point c. The substitution effect ispositive. The income effect is from point c to point b. The income effect isnegative and the total effect is positive "TE : SE +E).

g) + : ,CCCC ,C C. +ncome remains constant. Total e!penditures on C increasebecause ,Cis constant and C increases. Therefore( total e!penditures on CC&ent do&n.

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