Competitive Markets ME

8/9/2019 Competitive Markets ME

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Microeconomics I, IUPNA

Chapter 7. Competitive Markets: Applications

Problem Set

1. Let us assume that the US gasoline market has the following demand and suppl curves

!d" 1# $ #.%&d

!s" '( ) &swhen &s* ( and !s" # when &s+ (,

where -uantities represent millions of gallons per ear and prices refer to the amount of per gallon

a/ 0ith no ta, what are the e-uili2rium price and -uantit3

2/ Suppose the government imposes an ecise ta of 4 per gallon. 0hat will the new

e-uili2rium -uantit 2e3 0hat price will 2uers pa3 0hat price will sellers

receive3

c/ 5ind the impact of this ta on the consumer surplus and the producer surplus. 6naddition, calculate the ta collection from the government and the welfare

deadweight loss.

With a $3 tax, setting

d sQ Q=

implies

10 .5( 3 !

"

s s

s

P P

P

+ = +

=

#%stitting into the e&ation 'or

dPimplies

10dP =. #%stitting this price into the e&ation

'or &antit )eman)e) implies

5Q =

million. At these prices an) &antities, consmer srpls is

$!5 million, pro)cer srpls is $1!.5 million, an) go*ernment tax receipts are $15 million. +he


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)ea)eight loss is $1.5 million. +he )ea)eight loss measres the )i''erence %eteen potential

net %ene'its ($5- million an) the net %ene'its that are actall achie*e) ($!5 $1!.5 $15 /

$5!.5 million.

(. Suppose that the market for cigarettes in a particular town has the following suppl anddemand curves: QS"P QD" %# 8P, where the -uantities are measured in thousands of

units. Suppose that the town council needs to raise 4##,### in revenue and decides to do

this 2 taing the cigarette market. 0hat should the ecise ta 2e in order to raise the

re-uired amount of mone3

#ppose that the re&ire) tax is $T. +hen in e&ili%rim,TPP SD +=

. +his implies that

TQQ +=50

, or Q = !5 0.5T. #ince the re&ire) amont is $300,000, e mst ha*e T*Q/00. (2emem%er that Qis measre) in thosan)s o' nits. #o, T(!5 0.5T / 00. #ol*ing this

e&ation e get to possi%le *ales 'or the tax T / $!0 or T = $30. 4ither one ol) generate

$300,000 in tax re*enes, thogh o' corse T = $!0 ol) )o so ith a smaller )ea)eight loss.

4. 6n a perfectl competitive market, the market demand curve is given 2 Qd" (## 8 %Pd,

and the market suppl curve is given 2 Qd" 4%Ps.

a/ 5ind the e-uili2rium market price and -uantit demanded and supplied in the a2sence

of price controls.

2/ Suppose a price ceiling of ( per unit is imposed. 0hat is the -uantit supplied with a

price ceiling of this magnitude3 0hat is the si9e of the shortage created 2 the price

ceiling3

c/ 5ind the consumer surplus and producer surplus in the a2sence of a price ceiling. 0hat

is the net economic 2enefit in the a2sence of the price ceiling3

d/ 5ind the consumer surplus and producer surplus under the price ceiling. Assume that

rationing of the scarce good is as efficient as possi2le. 0hat is the net economic 2enefit in

this case3 oes the price ceiling result in a deadweight loss3 6f so, how much is it3

a Pd= Ps/ $5 Qd= Qs/ 1"5 nits.

% Qs/ "0 nits.

c +he srpls implications o' a price ceiling are shon %elo.


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0ith ;o &rice Ceiling 0ith &rice Ceiling:

consumer surplus )

producer surplus/

A67Iero 74I= ($1,!0 74I= ($1,!0

5or the -uestions ?'@, use the following information. he market for gi9mos is competitive,

with an upward sloping suppl curve and a downward sloping demand curve. 0ith no

government intervention, the e-uili2rium price would 2e (% and the e-uili2rium -uantit

would 2e 1#,### gi9mos. Consider the following programs of government intervention:

P

Q

40

200

D

S

175

5

A

B

F E

2

19070

C

G

I

120

H

J K L

70


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&rogram 6: he government imposes an ecise ta of ( per gi9mo

&rogram 66: he government provides a su2sid of ( per gi9mo for gi9mo producers.

&rogram 666: he government imposes a price floor of 4#.

&rogram 6B: he government imposes a price ceiling of (#.

&rogram B: he government allows no more than ,### gi9mos to 2e produced.

?. 0hich of these programs would lead to a less than 1#,### units echanged in the

market3 Driefl eplain.

Program I +he excise tax ill increase the price consmers pa to a le*el a%o*e $!5, an) loerthe price pro)cers recei*e to a le*el %elo $!5 ths, the &antit exchange) in the mar?et ill

'all %elo 10,000 nits.

Program II With the s%si), the price pro)cers recei*e ill increase to a le*el a%o*e $!5 the

price consmers recei*e ill 'all %elo $!5. +hs, the e&ili%rim &antit exchange) ill rise

to a le*el a%o*e 10,000.

Program III. With the price 'loor o' $30, consmers ill % less than 10,000 gi@mos, so 'eer

than 10,000 ill %e exchange) in the mar?et.

Program I. With the price ceiling o' $!0, pro)cers ill sppl less than 10,000 gi@mos, so'eer than 10,000 ill %e exchange) in the mar?et.

Program . 6 go*ernment 'iat, 'eer than 10,000 gi@mos ill %e exchange).

%. Under which of these programs will the market clear3 Driefl eplain.

With the excise tax or the s%si), the mar?et ill clear (Programs I an) II.

With the price 'loor (Program III there ill %e excess sppl, so the mar?et ill not clear.

With the price ceiling (Program I there ill %e excess )eman), so the mar?et ill not clear.

With the pro)ction &ota (Program the price consmers pa ill excee) $!5, so there ill %e

excess sppl. +he mar?et ill not clear.


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@. 0hich of these programs would surel lead to an increase in consumer surplus3 Driefl

eplain.

With the excise tax (Program I the price consmers pa ill rise, so consmer srpls ill

srel 'all.

With the s%si) (Program II the price consmers pa ill 'all, so consmer srpls ill srel

rise.

With the price 'loor (Program III the price consmers pa ill rise, so consmer srpls ill

srel 'all.

With the price ceiling (Program III the price consmers pa ill 'all, %t so ill the &antit

pro)ce). 7onsmer srpls ma 'all. +his can occr i' the price 'loor is so lo that *er 'e

nits are pro)ce) (an) ths a*aila%le 'or prchase % consmers.

With the pro)ction &ota (Program the price consmers pa ill rise, so consmer srpls

ill srel 'all.

7. Suppose the market for corn in &ulmonia is competitive. ;o imports and eports are

possi2le. he demand curve is Qd" 1# 8Pd, where, Qdis the -uantit demanded >in millions

of 2ushels/ when the price consumers pa isPd

. he suppl curve is

where Qsis the -uantit supplied >in millions of 2ushels/ when the price producers receive

isPs.

a/ 0hat are the e-uili2rium price and -uantit3

2/ At the e-uili2rium in part >a/, what is consumer surplus3 producer surplus3 deadweightloss3 Show all of these graphicall.

c/ Suppose the government imposes an ecise ta of ( per unit to raise government

revenues. 0hat will the new e-uili2rium -uantit 2e3 0hat price will 2uers pa3 0hat

price will sellers receive3


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d/ At the e-uili2rium in part >c/, what is consumer surplus3 producer surplus3 the impact

on the government 2udget >here a positive num2er, the government ta receipts/3

deadweight loss3 Show all of these graphicall.

e/ Suppose the government has a change of heart a2out the importance of corn revenues to

the happiness of the &ulmonian farmers. he ta is removed, and a su2sid of 1 per unit isgranted to corn producers. 0hat will the e-uili2rium -uantit 2e3 0hat price will the

2uer pa3 0hat amount >including the su2sid/ will corn farmers receive3

f/ At the e-uili2rium in part >e/, what is consumer surplus3 producer surplus3 0hat will 2e

the total cost to the government3 deadweight loss3 Show all of these graphicall.

g/ Berif that for our answers to parts >2/, >d/, and >f/ the following sum is alwas the

same: consumer surplus ) producer surplus ) 2udgetar impact ) deadweight loss. 0h is

the sum e-ual in all three cases3

a #etting

d sQ Q=

reslts in

10 -

$" per %shel

P P

P

= +

=

#%stitting this reslt into the )eman) e&ation gi*es

3Q =

million %shels.

% At the e&ili%rim, consmer srpls is

1! (10 "3 -.5 =

an) pro)cer srpls is

1! (" -3 -.5 =

. +here is no )ea)eight loss in this case an) total net %ene'its e&al $; million.


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0.00

5.00

10.00

15.00

0 ! - : 10

!uantit >millions of 2ushels/

&rice

#pplBeman)

A

6

In the graph a%o*e, area A represents consmer srpls an) area 6 represents pro)cer srpls.

c I' the go*ernment imposes an excise tax o' $!, the ne e&ili%rim ill %e

10 ( ! -

$ per %shel

s sP P

P

+ = +

=

#%stitting %ac? into the e&ation 'or

dPiel)s

:dP =, an) s%stitting

sPinto the sppl

e&ation implies!Q =

million.

) No the consmer srpls is

1! (10 :! ! =

, the pro)cer srpls is

1! ( -! ! =

, the

tax receipts are

!(! -=

, an) the )ea)eight loss is

1! (: (3 ! 1 =

(all measre) in millions

o' )ollars.


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0.00

!.00

-.00.00

:.00

10.00

1!.00

1-.00

0 ! -


&

rice

#ppl

Beman)A

6

#ppl !

7 B 4

In the graph a%o*e, area A represents consmer srpls, area 6 represents pro)cer srpls, areas

7B represent go*ernment tax receipts, an) area 4 represents the )ea)eight loss.

e I' the go*ernment pro*i)es a s%si) o' $1, the ne e&ili%rim ill %e

10 ( 1 -

$".5 per %shel

s s

s

P P

P

= +

=

#%stitting %ac? into the e&ation 'or

dPiel)s

.5dP =, an) s%stitting

sPinto the sppl

e&ation implies

3.5Q =

million.

' No the consmer srpls is

1! (10 .53.5 .1!5 =

, the pro)cer srpls is

1! (".5 -3.5 .1!5 =

, the s%si) pai) is1(3.5 3.5 =

(negati*e since the go*ernment is

paing this amont, an) the )ea)eight loss is

1! (".5 .5(3.5 3 0.!5 =

(all measre) in

millions o' )ollars.


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!.50

3.50

-.505.50

.50

".50

:.50

;.50

0 0.5 1 1.5 ! !.5 3 3.5 - -.5 5


&rice

#pplBeman)

A6 #ppl 9 1

7

B4

8

In the graph a%o*e, areas A64 represent consmer srpls, areas 678 represent pro)cer

srpls, areas 67B4 represent the go*ernment s%si) pament, an) area B represents the

)ea)eight loss.

g 8or part (%, the sm o' consmer srpls, pro)cer srpls, %)getar impact, an)

)ea)eight loss is-.5 -.5 0 0 ;+ + + =

'or part (), the sm is! ! - 1 ;+ + + =

an) 'or part (' it

is .1!5 .1!5 3.5 0.!5 / ;. (As a%o*e, all are measre) in millions o' )ollars. +hese

sms are all the same %ecase the )ea)eight loss measres the )i''erence %eteen net %ene'its

(in terms o' CS, PS, an) %)getar impact n)er the competiti*e otcome an) net %ene'its n)er

a 'orm o' go*ernment inter*ention.

. 6n a perfectl competitive market, the market demand and market suppl curves are

given 2 Qd" 1### 81#Pdand Qd" 4#Ps. Suppose the government provides a su2sid of (#

per unit to all sellers in the market.

a/ 5ind the e-uili2rium -uantit demanded and supplied find the e-uili2rium market

price paid 2 2uers

find the e-uili2rium after'su2sid price received 2 firms.

2/ 5ind the consumer surplus and producer surplus in the a2sence of the su2sid. 0hat is

the net economic 2enefit in the a2sence of a su2sid3

c/ 5ind the consumer surplus and producer surplus in the presence of the su2sid. 0hat is

the impact of the su2sid on the government 2udget3 0hat is the net economic 2enefit

under the su2sid program3


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d/ oes the su2sid result in a deadweight loss3 6f so, how much is it3

In this case, the a'ter9s%si) price recei*e) % sellers isPs= Pd !0. +he mar?et9clearing

con)ition is 1000 10P/ 30(P !0, hereP)enotes the mar?et price. +his impliesP/ 10an) Q/ ;00. #ince sellers recei*e the s%si),P = Pd/ 10 an)Ps= Pd !0 / 30. +he srpls

implications o' the s%si) are shon %elo

0ith ;o Su2sid 0ith Su2sid 6mpact of the

Su2sid

Consumer surplus A6

($!:,1!5

A678ero 678


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F. 6n a perfectl competitive market, the market demand curve is Qd" 1# 8Pd, and the

market suppl curve is Q

s

" 1.%P

s

.

a/ Berif that the market e-uili2rium price and -uantit in the a2sence of government

intervention arePd"Ps" ? and Qd" Qs" @.

2/ Consider two possi2le government interventions: >1/ A price ceiling of 1 per unit >(/ a

su2sid of % per unit paid to producers. Berif that the e-uili2rium market price paid 2

consumers under the su2sid e-uals 1, the same as the price ceiling. Are the -uantities

supplied and demanded the same under each government intervention3

c/ Gow will consumer surplus differ in these different government interventions3

d/ 5or which form of intervention will we epect the product to 2e purchased 2 consumers

with the highest willingness to pa3

e/ 0hich government intervention results in the lower deadweight loss and wh3

a 10 P/ 1.5PP/ - an) Q/ 10 - / .

P

Q

100

1,000

D

S

750

25S - 20

10

30

A

B

C

E

F GH

I

900


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% Un)er a $5 s%si) pai) to pro)cer, mar?et priceP/Pdan) the a'ter9s%si) price

recei*e) % pro)cers isPs/Pd5. +hs 10 P/ 1.5(P 5 P/ 1.

c 7onsmer srpls n)er the s%si) ill %e greater than the consmer srpls n)er a

price ceiling. Un)er %oth inter*entions, consmers pa the same price, %t n)er s%si)ies

consmers are spplie) as mch as the )eman) at the $1 mar?et price, hile n)er price

ceilings, consmers get less than the )eman) at the $1 ceiling price.

) #%si)ies. Un)er s%si)ies, %ecase consmers get hat the )eman) at the mar?et price,

there is no possi%ilit o' consmers ith a loer illingness to pa getting the goo) hile

consmers ith a higher illingness to pa )o not get the goo). +his is a possi%ilit ith a priceceiling.

e +he s%si) has the smaller )ea)eight loss. +he )ea)eight loss n)er the price ceiling

(assming e''icient rationing is area 7=I, hich e&als 1.:"5. +he )ea)eight loss n)er

the s%si) is area C, hich e&als ".5.

P

Q

10

10

D

S

4

A

B

1

1.5

S - 5

96

C

E

F

G

H

I

J K

L

M


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1#. Consider a perfectl competitive market in which the market demand curve is given 2

Qd" (# 8 (Pdand the market suppl curve is given 2 Qs" (Ps.

a/ 5ind the e-uili2rium price and -uantit in the a2sence of government intervention.

2/ Suppose the government imposes a price ceiling of 4 per unit. Gow much is supplied3

c/ Suppose, as an alternative, the government imposes a production -uota limiting the

-uantit supplied to @ units. 0hat is the market price under this tpe of intervention3 6s

the -uantit supplied under the price ceiling greater than, less than, or the same as the

-uantit under the production -uota3

d/ Assuming that under price controls rationing is as efficient as possi2le and under the

-uota, the allocation is as efficient as possi2le, under which program is the deadweight loss

larger: the price ceiling or the production -uota3

e/ Assuming that under price controls rationing is as inefficient as possi2le, while under the-uota the allocation is as efficient as possi2le, under which program is the deadweight loss

larger: the price ceiling or the production -uota3

f/ Assuming that under price controls rationing is as inefficient as possi2le, while under the

-uota the allocation is as inefficient as possi2le, under which program is the deadweight

loss larger: the price ceiling or the production -uota3

a CettingP = Pd= Ps)enote the mar?et price in the a%sence o' go*ernment inter*ention,

e ha*e !0 !P/ !PP/ 5. +he e&ili%rim &antit is this 10 nits.

% +he &antit spplie) n)er a price ceiling o' $3 per nit is nits, as shon in the 'irst

pictre %elo.

c +he mar?et9clearing price hen a pro)ction &ota o' is impose) is gi*en %

/ !0 !PorP/ ".

) 2e'erring to the graph %elo, the )ea)eight loss n)er a nit pro)ction &ota

(assming e''icient allocation o' &otas an) the )ea)eight loss n)er a $3 per nit price ceiling

(assming e''icient rationing are the same an) e&al area 7 8.


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e +he )ea)eight loss n)er a $3 price ceiling ith ine''icient rationing is e&al to areas

6748, hich or?s to %e $3!. +his is necessaril %igger than the )ea)eight loss n)er the

pro)ction &ota %ecase ine''icient rationing entails an a))itional )ea)eight loss (area 6 4

that is not present ith a price ceiling ith e''icient rationing.

' In this case, the )ea)eight loss n)er a pro)ction &ota in hich allocation is as

ine''icient as possi%le is the same as the )ea)eight n)er a price ceiling in hich the rationing

is as ine''icient as possi%le. =ereDs h. In the secon) pictre %elo, pro)cer srpls hen the

&ota is ratione) to the highest cost pro)cers illing to pro)ce at the mar?et9clearing price

ith a 9nit &ota is gi*en % the sha)e) triangle. +he area o' this triangle is e&al to the area o'

triangle


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11. 5igure 1#.1 2elow shows the suppl and demand curves for cigarettes. he

e-uili2rium price in the market is ( per pack if the government does not intervene, and

the -uantit echanged in the market is 1,### million packs. Suppose the government has

decided to discourage smoking and is considering two possi2le policies that would reduce

the -uantit sold to @## million packs. he two policies are >i/ a ta on cigarettes and >ii/ a

law setting a minimum price for cigarettes. Anal9e each of the policies, using the graph

and filling in the ta2le on the net page.

P

Q

10

20

D

S

5

A

B

3

6 10

C

E

G

F

7

148

4


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a 6ase) on the graph, the go*ernment ol) nee) to set a tax o' $!.00 per nit to achie*e

the go*ernmentDs target o' 00 million nits sol). 6 setting a tax at $!.00, the sppl cr*e ill

shi't par) % $!.00 an) intersect the )eman) cr*e at$3.00P =

an)

00Q =

, the ne mar?et

e&ili%rim. Alternati*el, the go*ernment col) set a minimm price (price 'loor atP = $3.00,

at hich point consmers ol) onl )eman) Q = 00 million nits.

%+ax Minimm Price

What price per nit ol) consmers paE $3.00 $3.00

What price per nit ol) pro)cers recei*eE $1.00 $3.00

What area represents consmer srplsE 8 8


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What area represents the largest pro)cer

srpls n)er the policE

6 674

What area represents the smallest pro)cer

srpls n)er the policE

6 ero

What area represents smallest )ea)eight

loss possi%le n)er the policE


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d/ As an alternative wa to support a price of 1%, suppose the government purchases the

difference 2etween the -uantit demanded at a price of 1% and the -uantit supplied. Gow

much does the government spend on this price support program3

e/ 5ill in the following ta2le for the government purchases program:

a CetP = Pd= Ps)enote the mar?et e&ili%rim price in the a%sence o' go*ernment

inter*ention. +he mar?et e&ili%rim price is 'on) % sol*ing 500 10P/ -0P, hich gi*es s

P/ $10. +he e&ili%rim &antit is 500 10(10 / -00 nits.

% I' the go*ernment )esignates a spport price o' $15, the &antit )eman)e) ol) %e 500

10(15 / 350 nits, hile the &antit spplie) ol) %e -0(15 / 00 nits.

c (#ee 'igre %elo


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With no

program

With acreage

limitation program

Impact o'

program

7onsmer srpls A67

($:,000

A

($,1!5

9 6 7

(9$1,:"5

Pro)cer srpls


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500

50

0

#

B

10

15

00

A

6 7 4

8

Competitive Markets ME

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