ch04

Besanko & Braeutigam – Microeconomics, 4 th editionTest Bank

File: ch04, Chapter 4: Consumer Choice

Multiple Choice

1. uppos upposee a consu consume merr has has an an inco income me e!ual e!ual to " #hi #hich ch he$sh he$shee spe spends nds on eit eithe herr %oo %ood d or clothing. The price o% %ood %ood is gien '( )% and and the price o% clothing is gien '( )c. "% the consumer spends all o% his$her income on clothing, the e*pression %or the num'er o% units o% clothing he$she 'u(s is a+ "$)% '+ " * )c c+ "$)c d+ " ns: C -i%%icult(: as( /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

3. "% %ood %ood is is on the the *a* *a*is is and clot clothi hing ng is is on the the (a*i (a*is, s, usi using ng the the in% in%or ormat matio ion n in pro'lem 1 a'oe, the consumer is at the a+ point o% ma*imum indi%%erence. '+ (intercept. c+ interior o% the 'udge dget const nstraint. d+ origin. ns: B -i%%icult(: Medium /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

5. uppos upposee a consu consume merr has has an inco income me " 6 780 780 #hi #hich ch he$s he$she he spen spends ds on pi99a pi99a and tacos per month. The price o% pi99a pi99a is 710 and the price o% tacos is 78. "% the units units o% pi99a consumed per month is on the *a*is and the units o% tacos consumed per month is on the (a*is, the slope o% the 'udget line is e!ual to a+ 1$3 '+ 3 c+ 3 d+ 3"

Cop(right  3011 ;ohn 2ile( & ons, "nc.

41


ns: C -i%%icult(: Medium /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

4.
8. n agent consumes goods x and y, #ith prices P x = 78 per unit and P y 6 $> per unit. The consumer?s consumer?s income is I = 74>. The goernment imposes a ta* o% 71 per unit on good x. 2hat is the ne# e!uation %or %or the 'udget constraint@ constraint@ a+ y = 6 – (5/8)x y = 6 - .75x '+ y = 8 – (6/8)x c+ d+ y = 48 – 8x ns: B -i%%icult(: Medium /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

A.

The 'udget line a+ repr repres esen ents ts the the set set o% all all 'as 'aske kets ts the the con consu sume merr can can a%%o a%%ord rd.. '+ represents the set o% all 'askets the consumer can a%%ord a%%ord #hile spending all aaila'le income. c+ repr repres esen ents ts the the set set o% all all 'as 'asket ketss tha thatt gi giee the the cons consum umer er the the same same leel leel o% utilit( #hile holding spending constant. d+ repr repres esen ents ts the the set set o% all all 'ask 'asket etss in #hic #hich h the the cons consum umer er pur purch chas ases es onl( onl( one one o% the goods.


43


ns: B -i%%icult(: as( /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

.

 set o% 'askets that a consumer can purchase #ith a limited amount o% income is a+ Consumer choice '+ Consumer purchase c+ Budget Constraint d+ Budget line

ns: C -i%%icult(: as( /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

>.

uppose the price o%

A

is 730 per unit, the price o%

B

is 710 per unit, and

the consumer?s income is 71000 per month. 2hich o% the %ollo#ing 'askets is not on the consumer?s 'udget line@ a+ A = 40, B = 20 '+ A = 5, B = 90 A = 2.5, B = 95 c+ A = 20, B = 40 d+ ns: -i%%icult(: Medium /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

.


A

is 730 per unit, the price o%

B

is 710 per unit, and

the consumer?s income is 71000 per month. The e!uation o% the 'udget line is 1000 = 10A + 20B a+ 1000 = 20A + 10B '+ c+ 20A = 10B d+ 1000 = A + B ns: B -i%%icult(: Medium


45


/eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

10. ". "".

aluate the truth%ulness o% the %ollo#ing statements. The 'udget constraint is a %unction o% consumer pre%erences. The 'udget constraint de%ines the set o% 'askets that a consumer can purchase #ith a speci%ic leel o% income. a+ '+ c+ d+

Both " and "" are true. Both " and "" are %alse. " is trueD "" is %alse. " is %alseD "" is true.

ns: -i%%icult(: as( /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

11. ". "".

aluate the truth%ulness o% the %ollo#ing statements. ll points to the interior o% the 'udget constraint are a%%orda'le. ll points that lie on the 'udget constraint cost the same amount o% mone(. a+ '+ c+ d+

Both " and "" are true. Both " and "" are %alse. " is trueD "" is %alse. " is %alseD "" is true.

ns:  -i%%icult(: as( /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

13. et I 'e the income o% the consumer, P x 'e the price o% good x and P y 'e the price o% good y. "% good is measured along the hori9ontal a*is and good is measured y

x

along the ertical a*is, then the E x

x

intercept measures the ma*imum amount o% good

that the consumer can a%%ord, #hich can 'e e*pressed as


44


a+ P x

P y

'+ I P y

c+ I P x

d+ P x

I

ns: C -i%%icult(: Medium /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

15.

"% good

x

is measured along the hori9ontal a*is and good

y

is measured

along the ertical a*is, then the slope o% the 'udget constraint can 'e e*pressed as a+  P x P y '+

 I P y

c+

 I P x

d+

 P y P x

ns:  -i%%icult(: Medium /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

14.

"% a consumer purchases t#o goods, %ood Gmeasured along the

housing Gmeasured along the


y

x

a*is+ and

a*is+, and i% the price o% %ood is 75 per unit and the

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price o% housing is 7400 per unit, then #hat is the slope o% the consumer?s 'udget constraint i% the consumer has an income o% 7A00@ a+ 5$A00. '+ 5$400 c+ 400$A00 d+ 400$5 ns: B -i%%icult(: Medium /eading: The Budget Constraint  1 2rite the e!uation o% the 'udget constraint and graph the 'udget line.

18.

"denti%( the statement that is fal!. a+ n increase in the amount o% income changes the intercepts o% the 'udget constraint 'ut not the slope. '+ n increase in the price o% good changes 'oth the intercept and x

the slope o% the 'udget constraint. c+ n increase in the price o% good the price o% good

y

changes the

x

slope o% the 'udget constraint. d+ n increase in the price o% good y

x

x

and an e!ual percentage increase in

intercept, the

x

y

intercept, and the

and an increase in the price o% good

ma( or ma( not change the slope o% the 'udget constraint.

ns: C -i%%icult(: Medium /eading: The Budget Constraint  3 "llustrate graphicall( ho# a change in income or a change in price a%%ects the 'udget line.

1A.

uppose all prices dou'le and income triples. The 'udget line a+ #ill 'ecome steeper. '+ #ill 'ecome %latter. c+ #ill shi%t in to#ard the origin. d+ #ill shi%t out %rom the origin.

ns: -i%%icult(: Medium /eading: The Budget Constraint  3 "llustrate graphicall( ho# a change in income or a change in price a%%ects the 'udget line.


4A


1.


A

is 730 and the price o%

is plotted on the hori9ontal a*is. "% the price o%

B

is 710 and that good

A

dou'les and the price o% A

B

triples, leaing the consumer?s income unchanged, the 'udget line a+ #ill 'ecome steeper. '+ #ill 'ecome %latter. c+ #ill shi%t in to#ard the origin. d+ #ill shi%t out %rom the origin. ns: B -i%%icult(: Medium /eading: The Budget Constraint  3 "llustrate graphicall( ho# a change in income or a change in price a%%ects the 'udget line.

1>.

uppose a consumer purchases t#o goods,

and A

A

, and that the price o% B

dou'les, the consumer?s income dou'les, and the price o%

"% good

B

remains unchanged.

is plotted on the hori9ontal a*is, the 'udget line A

a+ '+ c+ d+

#ill remain unchanged. #ill 'ecome steeper. #ill 'ecome %latter. #ill shi%t out %rom the origin parallel to the original 'udget line.

ns: B -i%%icult(: Medium /eading: The Budget Constraint  3 "llustrate graphicall( ho# a change in income or a change in price a%%ects the 'udget line.

1. "% a consumer purchases t#o goods, %ood Gmeasured along the *a*isa*is+ and housing Gmeasured along the a*is+, then #hat happens to the slope o% the y

consumer?s 'udget constraint i% the price o% %ood %alls@ a+ The ne# 'udget constraint shi%ts in#ard 'ut is parallel to the original 'udget constraint. '+ The ne# 'udget constraint piots in#ard Gto#ards the origin+ along the a*is. The ne# slope is steeper than the original slope. x

c+ x

The ne# 'udget constraint piots in#ard Gto#ards the origin+ along the a*is. The ne# slope is %latter than the original slope.


4


d+ the

x

The ne# 'udget constraint piots out#ard Ga#a( %rom the origin+ along a*is. The ne# slope is %latter than the original slope.

ns: -i%%icult(: Medium /eading: The Budget Constraint  3 "llustrate graphicall( ho# a change in income or a change in price a%%ects the 'udget line.

30. uppose that a consumer?s income triples. /o#eer, at the same time, 'oth the price o% and the price o% also triple. This consumer has e*perienced x

y

a+ an increase in purchasing po#er. '+ a decrease in purchasing po#er. c+ no change in purchasing po#er. d+ a piot in the 'udget constraint #ith an undetermined e%%ect on purchasing po#er. ns: C -i%%icult(: Medium /eading: The Budget Constraint  3 "llustrate graphicall( ho# a change in income or a change in price a%%ects the 'udget line.

31. uppose that the !uantit( o% pi99as consumed per month is on the *a*is and the !uantit( o% tacos consumed per month is on the (a*is, an increase in the price o% pi99a holding the price o% tacos constant #ill a+ cause the 'udget line to shi%t in#ard to#ard the origin in a parallel %ashion. '+ cause the (intercept to remain the same, 'ut the *intercept #ill moe closer to the origin. c+ cause the 'udget line to shi%t out#ard %rom the origin in a parallel %ashion. d+ cause the *intercept to shi%t a#a( %rom the origin. ns: B -i%%icult(: Medium /eading: The Budget Constraint  3 "llustrate graphicall( ho# a change in income or a change in price a%%ects the 'udget line.

33. Hien the e*pression min G*,(+ e*penditure P x x I P y y su'Ject to:

4>


a+ '+ c+ d+

x and P x. onl(
ns: C -i%%icult(: Medium /eading: ptimal Choice  5 -escri'e the conditions %or optimal consumer choice.

35. Consumer choice o% the 'asket o% goods that Ga+ ma*imi9es utilit( G'+ allo#s his$her to lie #ithin the 'udget constraint and Gc+ includes a positie amount o% all commodities is the consumer?s a+ ptimal choice '+ Ma*imum choice c+ "nterior optimum d+ Consumer choice ns: C -i%%icult(: as( /eading: ptimal Choice  5 -escri'e the conditions %or optimal consumer choice.

34.

The theor( o% consumer choice a+ descri'es ho# a consumer chooses 'et#een di%%erent 'udget constraints. '+ descri'es ho# a consumer chooses 'et#een di%%erent income leels. c+ descri'es ho# a consumer allocates her limited income among aaila'le goods and serices. d+ descri'es ho# a consumer allocates her limited pre%erences among aaila'le income leels.

ns: C -i%%icult(: as( /eading: ptimal Choice  5 -escri'e the conditions %or optimal consumer choice.

38.

The tangenc( condition %or the optimal choice %or a consumer is gien '( a+ ML x,y 6 P y /P x '+ M< x$M< y 6 1 c+ ML x,y 6 P x /P y


4


d+

M< x$M< y 6 P y /P x

ns: C -i%%icult(: Medium /eading: ptimal Choice  4 "llustrate graphicall( the tangenc( condition %or optimal consumer choice.

3A. t a consumer?s interior optimum solution, #hich o% the %ollo#ing #ill "# necessaril( hold true@ a+ %& x %& y 

'+ %& x %& y



P x P y

c+ %'( x , y



%'( x , y



%& x %& y

d+ P x P y

ns:  -i%%icult(: Medium /eading: ptimal Choice  8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.

3.

The Ee!ual 'ang %or the 'uck idea means that the consumer is e!uating a+ the marginal utilities o% all o% the goods purchased. '+ the prices o% all the goods purchased. c+ the marginal utilities o% the last dollar spent on each good purchased. d+ the ratios o% the last dollar spent on each good purchased.

ns: C -i%%icult(: Medium /eading: ptimal Choice  8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.


410


3>.

 corner point solution is al#a(s the optimum %or a consumer #hen a+ a uni!ue point o% tangenc( e*ists 'et#een the consumer?s indi%%erence cure and the 'udget line '+ the consumer has straight line Gconstant slope+ indi%%erence cures c+ there is no point o% tangenc( 'et#een the consumer?s indi%%erence cures and the 'udget line and the consumer does not hae straight line indi%%erence cures. d+ the consumer is indi%%erent to 'oth goods e!uall(.

ns: C -i%%icult(: /ard /eading: ptimal Choice  8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.

3.


is 730, the price o% A

is 710, and that the consumer B

is currentl( spending all aaila'le income. t the consumer?s current consumption 'asket the marginal utilit( o% is A and the marginal utilit( o% is 4. A B a+ The consumer is currentl( ma*imi9ing utilit(. '+ The consumer could increase utilit( '( consuming more o% good and A less o% good . B c+ The consumer could increase utilit( '( consuming more o% good and B less o% good . A d+ othing can 'e said a'out the consumer?s utilit( 'ecause #e do not kno# the consumer?s income or utilit( %unction. ns: C -i%%icult(: Medium /eading: ptimal Choice  8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.

50.




is currentl( spending all aaila'le income. t the consumer?s current consumption 'asket the marginal utilit( o% is > and the marginal utilit( o% is 3. A B a+ The consumer is currentl( ma*imi9ing utilit(.


411


'+

The consumer could increase utilit( '( consuming more o% good

and A

less o% good

. B

c+

The consumer could increase utilit( '( consuming more o% good

less o% good

B

and

. A

d+ othing can 'e said a'out the consumer?s utilit( 'ecause #e do not kno# the consumer?s income or utilit( %unction. ns: B -i%%icult(: Medium /eading: ptimal Choice  8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.

51.




is currentl( spending all aaila'le income. t the consumer?s current consumption 'asket the marginal utilit( o% is > and the marginal utilit( o% is 4. A B a+ The consumer is currentl( ma*imi9ing utilit(. '+ The consumer could increase utilit( '( consuming more o% good and A less o% good . B c+ The consumer could increase utilit( '( consuming more o% good and B less o% good . A d+ othing can 'e said a'out the consumer?s utilit( 'ecause #e do not kno# the consumer?s income or utilit( %unction. ns:  -i%%icult(: Medium /eading: ptimal Choice  8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.

53.

uppose the price o% good

suppose

x

and %& x



y

is 78 and the price o% good

y

is 7. lso,

. 2hich o% the %ollo#ing 'askets could 'e an %& y



x

interior optimum@


413


a+ '+ c+ d+

x = 5, y = 7 x = 4, y = 6 x = 7, y = 5 x = 6, y = 4

ns: C -i%%icult(: Medium /eading: ptimal Choice  8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.

55. uppose that &(x,y) = *"(x,y). Further suppose that P x = 78 per unit and P y 6 710 per unit and income is I = 7108. For this consumer, the optimal 'asket to 'u( #ould 'e a+ (x,y) = (9,) '+ (x,y) = (,1) (x,y) = (1,) c+ d+ (x,y) = (,9) ns: -i%%icult(: Medium /eading: ptimal Choice  8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.

54.

uppose that the ratio o% marginal utilit( to price %or good

is 10, and the A

ratio o% marginal utilit( to price %or good consumption o% goods

and A

B

is 8. ssume that %or her current

the consumer is e*periencing diminishing marginal B

utilit( %or each good. "n order %or this consumer to 'e at her utilit( ma*imi9ing point, she should a+ consume less and more . A B '+ consume more and less . A B c+ consume more and more . A B d+ do nothing – the consumer is alread( in e!uili'rium. ns: B -i%%icult(: Medium /eading: ptimal Choice


415


 8 ole %or an optimal consumption 'asket, gien in%ormation a'out income, prices and marginal utilities.

58. 2hich o% the %ollo#ing statements is true a'out the consumer?s e*penditure minimi9ation pro'lem@ a+ The consumer?s e*penditure minimi9ation pro'lem results in the same optimal 'asket as the consumer?s utilit( ma*imi9ation pro'lem i% the re!uired leel o% utilit( %or the e*penditure minimi9er is the same as the ma*imi9ed utilit( %or the utilit( ma*imi9er. '+ The consumer?s e*penditure minimi9ation pro'lem has an optimum at an e*penditure o% 9ero. c+ The consumer?s utilit( ma*imi9ation pro'lem results in a tangenc( 'et#een the 'udget constraint and an indi%%erence cure, #hereas the e*penditure minimi9ation pro'lem results in a solution #here the indi%%erence cure crosses the 'udget line. d+ The consumer al#a(s pre%ers to ma*imi9e utilit( rather than to minimi9e e*penditure. ns:  -i%%icult(: Medium /eading: ptimal Choice  A *plain #h( the optimal consumption 'asket soles 'oth a utilit( ma*imi9ation pro'lem and an e*penditure minimi9ation pro'lem.

5A. conomists descri'e consumer choice as a constrained optimi9ation pro'lem. 2hat is the consumer tr(ing to do@ a+ Ma*imi9e income su'Ject to the 'udget constraint. '+ Ma*imi9e the 'udget constraint. c+ Ma*imi9e utilit( su'Ject to the 'udget constraint. d+ Minimi9e spending. ns: C -i%%icult(: as( /eading: ptimal Choice  A *plain #h( the optimal consumption 'asket soles 'oth a utilit( ma*imi9ation pro'lem and an e*penditure ma*imi9ation pro'lem.

5. uppose that %& x = 10 and %& y = 30. Further suppose that the consumer?s 'udget constraint can 'e e*pressed as 30 x I 10 y 6 400. For this consumer, the optimal amount o% good to 'u( #ould 'e x


414


a+ '+ c+ d+

8. 0. 30. 40.

ns: B -i%%icult(: /ard /eading: ptimal Choice   *plain #h( the optimal consumption 'asket could occur at a corner point.

5>. uppose that a consumer considers co%%ee and tea to 'e per%ect su'stitutes, 'ut he re!uires t#o cups o% tea to gie up one cup o% co%%ee. This consumer?s 'udget constraint can 'e #ritten as 5 + T 6 10. 2hat should the consumer 'u(@ a+ 3 cups o% tea and no co%%ee. '+ 10 cups o% tea and no co%%ee c+ 5 cups o% co%%ee and no tea. d+ 4 cups o% co%%ee and no tea. ns: B -i%%icult(: Medium /eading: ptimal Choice   *plain #h( the optimal consumption 'asket could occur at a corner point.

5. uppose ;ohn is planning to Join a sports clu'. Mem'ership in the clu' #ill allo# ;ohn to s#im at the pool %or hal% price. ormall( s#imming %or an hour #ould cost 710. "% ;ohn has an income o% 71000, the clu' mem'ership %ee is 7100, and #e plot the num'er o% isits to the pool on the hori9ontal a*is and a composite Eother goods #hich hae a price o% 71 on the ertical a*is, the slope o% ;ohn?s 'udget line a%ter Joining the clu' #ill 'e a+ –10 '+ –8 c+ –3 d+ –1 ns: B -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.


418


40. uppose that candies are usuall( sold at 70.08 a piece. The local cand( store o%%ers 3 e*tra candies %or %ree upon purchase o% an( 10 pieces. uppose that aurel gets an allo#ance o% 75.00 per #eek. 2hich o% the %ollo#ing is a fal! statement a'out her 'udget constraint i% aurel ma( consume either cand(, x, measured on the hori9ontal a*is or a composite good, y, measured on the ertical a*is and priced at 71.00 per unit@ a+ The ma*imum num'er o% candies aurel can purchase is 3. '+ The 'udget constraint has hori9ontal segments. c+ The 'udget constraint is a straight line #ith a negatie slope. d+ 2ith normall( shaped pre%erences, aurel #ill neer re%use the %ree candies. ns: C -i%%icult(: /ard /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

41. 2hen gien a choice 'et#een a cash su'sid( and a oucher #orth the same dollar amount, 'ut onl( good %or the purchase o% a single good, a+ the consumer #ill al#a(s pre%er the oucher to the cash su'sid( or 'e indi%%erent 'et#een the t#o. '+ the consumer #ill al#a(s pre%er the cash su'sid( to the oucher or #ould 'e indi%%erent 'et#een the t#o. c+ the consumer might pre%er the cash su'sid( to the oucher or might pre%er the oucher to the cash su'sid(. d+ the consumer #ould pre%er to receie neither the cash su'sid( nor the oucher. ns: B -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

43. 2hen comparing a cash su'sid( and a oucher #orth the same dollar amount, 'ut onl( good %or the purchase o% a single good, a+ a consumer can neer 'e 'etter o%% #ith a cash su'sid( than #ith a oucher. '+ a consumer can neer 'e 'etter o%% #ith a oucher than #ith a cash su'sid(. c+ a cash su'sid( #ill al#a(s make the consumer 'etter o%% than the consumer #ould 'e #ith a oucher.


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d+ a oucher #ill al#a(s make the consumer 'etter o%% than the consumer #ould 'e #ith a cash su'sid(. ns: B -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

45. "% a consumer states that he is indi%%erent 'et#een receiing a gi%t certi%icate %or 710 at the local 'ookstore and receiing 710 cash, #e can in%er that this consumer a+ #ould spend less than 710 at the 'ookstore. '+ #ould spend at least 710 at the 'ookstore. c+ #ould spend more than 710 at the 'ookstore. d+ #ould spend e*actl( 710 at the 'ookstore. ns: B -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

44. "% the goernment #ould like to induce a consumer to consume a speci%ic leel o% some good a+ a cash su'sid( s(stem #ould likel( 'e cheaper %or the goernment than a oucher s(stem. '+ a oucher s(stem #ould likel( 'e cheaper %or the goernment than a cash su'sid( s(stem. c+ the goernment should onl( use a cash su'sid( s(stem since this al#a(s make consumers 'etter o%%. d+ the goernment should onl( use a oucher s(stem since this al#a(s makes consumers 'etter o%%. ns: B -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.


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48. uppose ;ohn is planning to Join a sports clu'. Mem'ership in the clu' #ill allo# ;ohn to s#im at the pool %or hal% price. ormall( s#imming %or an hour #ould cost 710. "% ;ohn has an income o% 71000, the clu' mem'ership %ee is 7100, and #e plot the num'er o% isits to the pool on the hori9ontal a*is and a composite Eother goods #hich hae a price o% 71 on the ertical a*is, the e!uation o% ;ohn?s 'udget line a%ter Joining the clu', #here the composite good, y, is on the ertical a*is and pool isits, x, are measured on the hori9ontal a*is is a+ y 6 00 – 8 x y 6 1000 – 8 x '+ c+ y 6 1000 – 10 x d+ y = 00 – 10 x ns:  -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

4A. ssume that #e are modeling intertemporal consumption %or a t(pical consumer. Further assume that #e measure current consumption on the hori9ontal a*is and %uture consumption on the ertical a*is.  market e*ists #here 'orro#ing and lending can occur %or a %i*ed interest rate,  . o# identi%( the statement that is fal!. a+ 2hen a consumer can lend or 'orro# at the same interest rate, the consumer?s 'udget constraint is a straight line. '+ 2hen the rate at #hich a consumer can 'orro# is higher than the rate at #hich the consumer can lend, the consumer?s 'udget constraint is composed o% t#o straight lines #ith di%%erent slopes. c+ 2hen a consumer cannot 'orro# mone( or earn an interest rate %or saing mone(, the consumer?s 'udget constraint is a straight line. d+ 2hen a consumer has access to %inancial markets so that he$she can lend or 'orro# mone(, his$her 'udget constraint is e*panded #hen compared to his$her 'udget constraint #ithout access to %inancial markets. ns: C -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

4. uppose the goernment is considering a program to gie housing ouchers to poor people. ssuming the alue o% the oucher is greater than the amount currentl( 'eing spent on housing per month '( poor people, #hich o% the %ollo#ing must 'e true@


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a+ The housing oucher #ill necessaril( cause more units o% housing to 'e consumed '( poor people, #hereas an unrestricted cash su'sid( #ith the same dollar alue #ould not. '+ The housing oucher #ill lead to %e#er apartments %or poor people. c+  su'sid( is al#a(s pre%era'le, no matter #hat the polic( goal as it allo#s %or %reedom o% choice. d+ Noucher s(stems hae no impact on the housing market. ns:  -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

4>. uppose again the goernment o%%ers poor people a housing oucher and units o% housing is graphed on the *a*is and the composite good is graphed on the (a*is. The consumer #ill al#a(s choose to consume the e*act amount o% the housing oucher?s units o% housing #hen a+ the consumer?s indi%%erence cures are eer(#here steeper than the 'udget line. '+ the consumer chooses to moe into a 'etter school district %or educational purposes. c+ the housing oucher causes the 'udget line to shi%t to#ard the origin. d+ the consumer?s indi%%erence cures are %latter Gcloser to hori9ontal+ than the 'udget line #here it slopes do#n#ard. ns: -i%%icult(: /ard /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

4. 2hen anal(9ing ho# 'orro#ing and lending a%%ect the consumer?s 'udget constraint, #e measure spending in the current time period on the hori9ontal a*is and spending in the %uture time period on the ertical a*is. ssume that the interest rate at #hich the consumer can lend and 'orro# is 10O, income in period 1 is 71000 and income in period 3 is 71300. The point o% ma*imum current consumption can 'e e*pressed as a+ 1000I 1300$1.1. '+ 1000G1.1+ I 1300. c+ 1000I 1300 I .1 d+ 1000$1.1 I 1300$1.1 I 1.


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ns:  -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

80. 2hen anal(9ing ho# 'orro#ing and lending a%%ect the consumer?s 'udget constraint, #e measure spending in the current time period on the hori9ontal a*is and spending in the %uture time period on the ertical a*is. ssume that the interest rate at #hich the consumer can lend and 'orro# is 10O and income in period 1 is 71000 #hile income in period 3 is 71300. The point o% ma*imum %uture consumption can 'e e*pressed as a+ 1000 I 1300$1.1. '+ 1000G1.1+ I 1300. c+ 1000I1300I.1. d+ 1000$1.1 I 1300$1.1 I 1. ns: B -i%%icult(: Medium /eading: Consumer Choice #ith Composite Hoods  > "llustrate the 'udget line and optimal consumer choice graphicall( #hen one o% the goods a consumer can choose is a composite good.

81. 2hen #e do not hae in%ormation regarding a consumer?s indi%%erence map, #hich o% the %ollo#ing anal(ses can proide additional in%ormation regarding the consumer?s choices@ a+ Leealed pre%erence anal(sis. '+ "ndi%%erence cure anal(sis. c+ Market 'asket anal(sis. d+ ptimi9ation anal(sis. ns:  -i%%icult(: as( /eading: Leealed )re%erence   -escri'e the concept o% reealed pre%erence.

83.

Leealed pre%erences tells us that i% 'asket

and 'asket A

'udget constraint 'ut the consumer chooses


B

instead o% B

lie on the same

, then #e kno# that A

430


a+

is strictl( pre%erred to A

'+

B

is pre%erred to A

c+

B

d+

.

. B

is strictl( pre%erred to is pre%erred to

B

A

.

. A

ns: -i%%icult(: as( /eading: Leealed )re%erence  10 mplo( the concept o% reealed pre%erence to determine #hether o'sered choices are consistent #ith utilit( ma*imi9ation.

85. Consider the concept o% reealed pre%erence. uppose a consumer chooses 'asket  oer 'asket B #hen 'asket B costs the same amount. The consumer a+ must %ind 'asket 'etter than 'asket . A B '+ must %ind 'asket 'etter than 'asket . B A c+ must %ind 'asket at least as good as 'asket . A B d+ must %ind 'asket at least as good as 'asket . B A ns: C -i%%icult(: Medium /eading: Leealed )re%erence  10 mplo( the concept o% reealed pre%erence to determine #hether o'sered choices are consistent #ith utilit( ma*imi9ation.

84.

uppose a consumer 'u(s t#o goods,

x

and

y

, and has income o% 750.

"nitiall( P x = 5 and P y = 5 and the consumer chooses 'asket

A

#ith x =8 and y6 8.

The prices change to P x = 4 and P y 6 3 and the consumer chooses 'asket

B

#ith x 6 1

and y = 15. a+ These choices are consistent #ith utilit( ma*imi9ation. '+ These choices are not consistent #ith utilit( ma*imi9ation. c+ 2ith this in%ormation it is not possi'le to determine i% these choices are consistent #ith utilit( ma*imi9ation. d+ Basket must 'e strictl( pre%erred to 'asket . B A


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ns:  -i%%icult(: /ard /eading: Leealed )re%erence  10 mplo( the concept o% reealed pre%erence to determine #hether o'sered choices are consistent #ith utilit( ma*imi9ation.

88.


"nitiall( P x 6 5 and



>

and

y

and has income o% 750.

and the consumer chooses 'asket P y

y

x



5

A

#ith x



3

and

. The prices change to P x 6 4 and P y 6 3 and the consumer chooses 'asket

B

#ith x 6  and y 6 1. a+ These choices are consistent #ith utilit( ma*imi9ation. '+ These choices are not consistent #ith utilit( ma*imi9ation. c+ 2ith this in%ormation it is not possi'le to determine i% these choices are consistent #ith utilit( ma*imi9ation. d+ Basket must 'e strictl( pre%erred to 'asket . B A ns: B -i%%icult(: /ard /eading: Leealed )re%erence  10 mplo( the concept o% reealed pre%erence to determine #hether o'sered choices are consistent #ith utilit( ma*imi9ation.

8A.


x

and

y

and has income o% 750.

"nitiall( P x = 5 and P y = 5 and the consumer chooses 'asket

A

#ith x =  and y 6 5.

The prices change to P x = 4 and P y = 3 and the consumer chooses 'asket

B

#ith x = 8

and y = 8. a+ These choices are consistent #ith utilit( ma*imi9ation. '+ These choices are not consistent #ith utilit( ma*imi9ation. c+ 2ith this in%ormation it is not possi'le to determine i% these choices are consistent #ith utilit( ma*imi9ation. d+ Basket B must 'e pre%erred to 'asket . ns:  -i%%icult(: /ard /eading: Leealed )re%erence


433


 10 mplo( the concept o% reealed pre%erence to determine #hether o'sered choices are consistent #ith utilit( ma*imi9ation.

8.

Leealed pre%erences tells us that i% 'asket

the consumer chooses

instead o% B

a+

c+

'ut

. B

is at least as pre%erred to is strictl( pre%erred to

B

d+

B

, then #e kno# that

is strictl( pre%erred to A

costs less than 'asket

A

A

'+

A

B

.

. A

is as least as pre%erred to B

. A

ns: C -i%%icult(: Medium /eading: Leealed )re%erence  10 mplo( the concept o% reealed pre%erence to determine #hether o'sered choices are consistent #ith utilit( ma*imi9ation.


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ch04

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