ES10001 Exam Questions + Solutions PDF

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ES10001

University of Bath DEPARTMENT OF ECONOMICS EXAMINATION First Year INTRODUCTORY MICROECONOMICS (ES10001) – SUGGESTED SOLUTIONS _____________________________________ 17TH JANUARY 2017, 09:30 – 11:30 (2 hours) _____________________________________ A University calculator is required for this examination ANSWER ALL QUESTIONS The examination paper comprises four pages and is divided into two sections: Section A (True / False) contains eight questions at 6 marks per question (total 48 marks); Section B (Multiple Choice) comprises ten questions at 10 marks per question (total 100 marks). The examination paper thus comprises 148 marks. Note: An incorrect answer will result in a ten per cent reduction in the mark available for the question; thus an incorrect answer to a true / false question will result in a reduction of 0.6 mark and an incorrect answer to a multiple choice question will result in a reduction of 1 mark.

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Page 1 of 24

ES10001

Se c t i o nA:Tr ue/Fa l s e( 6ma r kspe rque s t i o n) 1 .I ft h e r ei sn oe n do wme n te ffe c t ,t he nt h ed e ma ndc u r v ef o raGi ffe ng o o di sa l wa y su p wa r d s l o p i n g : A. TRUE ALSE B. F So l u t i o n:

(

)

As s u met h ec o n s u me rc o n s u me sab u n d l eo fg o o d sx = x1 , x2 ,..., xn a nda s s u met h a tg o o d1i s Gi ffe n.De fin e

a st h ema x i mu mq u a n t i t yo fg o o d1t h a tt h ec o n s u me rc a nc o ns u mea t

p r i c e gi v e nh i sb u d g e ti n c o mem.An y i mp l i e s i nor d e rf o rt h eb u dg e t c o ns t r a i n tt ob es a t i s fie d .I n t u i t i v e l y ,i fd e ma n di n c r e a s e swi t hp r i c e ,a n di ft h ep r i c er i s e st os u c h a ne x t e n tt ha tt h ec o n s u me ri sd e v o t i n ga l lo fhi sb u d g e ti n c o met ot h ec o n s u mp t i o no ft h a tg o o d , t h e na n yf u r t h e ri n c r e a s e si np r i c emu s tr e s u l ti nad e c r e a s ei nc o n s u mp t i o no fg o o d1s u c ht h a t t h ed e ma ndc u r v ef o rg o o d1b e c o me sd o wn wa r ds l o p i n g( i . e .b a c k wa r db e nd i n g ) . 2 . Thee ffo r to fc a r r y i n ga numb r e l l ar e d u c e smyu t i l i t yb y½ au n i t .I fi tr a i nsa n dIh a v en o u mb r e l l a ,t h e nmyu t i l i t yf a l l sb y3u n i t swh i l s ti to n l yf a l l sb y1u n i ti fId oh a v ea nu mb r e l l a . Ic o ns i d e rt h a tt h e r ei sa5 0 %c h a nc et h a ti twi l lr a i n .I fIwa ntt oma x i mi s emye x p e c t e d u t i l i t y ,t h e nIs ho u l dc a r r ya nu mb r e l l a : A. TRUE B. F ALSE So l u t i o n: Sup p o s emyu t i l i t yi fId on o tc a r r ya nu mb r e l l ai su .Mye x p e c t e du t i l i t yi fId on otc a r r ya n 1 1 u mb r e l l ai st he n E u =0.5 u - 2 + 0.5 u - 3 =u - 1 2 .I fIc a r r ya nu mb r e l l at h e n my

{ } ( ) ( ) u s ,i fIa ma ne x pe c t e du t i l i t y e x pe c t e du t i l i t yi s E { u} =0.5( u - ) + 0.5 ( u - 1 ) =u - 1.Th 1

2

1

2

ma xi mi s e r ,Is h o ul dc a r r ya nu mb r e l l a .

(

)

n d 3 . An i n d i v i du a ll i v e sf o rt wo p e r i o ds ,i se n d o we d wi t hl i f e t i mei n c o me y = y1 , y2 a

(

)

e r eyt a n d ct ,t=1 ,2 ,d e n o t e s ma xi mi s e su t i l i t yo v e rl i f e t i mec o n s u mp t i o n c = c1 ,c2 wh r e s p e c t i v e l ye n d o wme n ti n c o mea n dc o n s u mpt i o ni np e r i o dt .I ft h ei n d i v i d ua li sa b l et o b o r r o wa ndl e n da ta ne x o g e n ou sr a t eo fi n t e r e s tr ,a n di fh ec h oo s e st ob o r r o wi np e r i o do ne s u c ht h a t h e nhewi l lb ed e fin i t e l ywo r s eo ffi ft h er a t eo fi n t e r e s tr i s e s : c1 > y1 ,t A. TRUE B. FALSE

Page 2 of 24

ES10001 So l u t i o n: I ti sp o s s i b l et h a ta tah i g h e rr a t eo fi nt e r e s tt hei n d i v i d u a lc h o o s e st ob e c omeal e n d e ra n dc o u l d b eb e t t e ro ff.Th i sp o s s i b i l i t yi si l l u s t r a t e di nFi g ur e2 :

c2 , y2

E1

y02

I1

y0

c02

E0 I0

0

y10

c10

c1, y1 1

Fi g u r e3 4. A person who is averse to risk at all levels of wealth would never take a risk with his wealth: A. TRUE B. FALSE Solution: An individual who is risk averse would not buy a £2 lottery ticket that offers a 50% chance of winning £4 and a 50% chance of winning nothing. But that does not mean that he would not accept a gamble with better odds in favour of winning £4. More generally, consider an individual with initial wealth of £150. Such a person would not be prepared to take a risk that involved spending £150 on a lottery that yielded a 50% chance of winning £200 and a 50% chance of winning £100 since the expected utility from this lottery, u , is less than the utility of £150 with certainty – i.e. u < u £150 . They would, however, be prepared to take a risk that that involved spending £150 on a lottery that yielded a 60% chance of winning £200 and a 40% chance of winning £100. The expected wealth from this latter lottery is £160 and implies an expected utility of u > u £150 .

(

(

)

)

Page 3 of 24

ES10001

u(w)

(

B

)

u £200

u u £150 u

(

(

)

u £100

)

0

D

u(w)

E

C A

£100

£150

£160

£200

w

Figure 1

5.

If a monopolist stays in business when a price ceiling is introduced then there will be excess demand as a result of the price control: A. TRUE B. FALSE

Solution: If the maximum price is set at p in Figure 2 then the monopolist will supply q but demand will be q1 thus leaving q1 - q unsatisfied. If however, the maximum price is set at a point about the intersection of MC with AR then there will no unsatisfied demand.

Page 4 of 24

ES10001

p

MC pm

p MR 0

q

AR q1

qm

q

Figure 2

9.

6. Ben and Grace sell identical bottled spring water through the daily aggregate demand function qd p =100 - 50 p. Each morning, they set their selling price for their spring water knowing that consumers will only buy from the cheapest source and if they set the same price, then each will supply one half of the total demand. If a bottle of spring water costs c = £0.50 to make, then the equilibrium price if Ben and Grace collude is £2 higher than the equilibrium price if they do not collude:

( )

A. B.

TRUE FALSE

Solution: First note that:

Page 5 of 24

ES10001

qd ( p) =100 - 50 p Þ 50 p=100 - q Þ pd ( q ) =AR =2 - 0.02q Þ MR =2 - 0.04q If Ben and Grace do not collude then, by engaging in Bertrand competition they will reach a Bertrand equilibrium in which:

pB = pG = pb =0.5 =MC =AC By colluding, however, they will chose the monopoly profit maximising price vis:

( )

( )

MR qm =2 - 0.04qm =0.5 =MC qm Þ 0.04qm =1.5 Þ qm =37.5 Suc ht h a t :

( )

pm = pd qm =2 - 0.02qm Þ

( )

pm = pd qm =2 - 0.02(37.5) Þ

( )

pm = pd qm =2 - 0.75 =1.25 Se eFi g u r e3

Page 6 of 24

ES10001

p 4

3

MC

2

0

100

MR 200

AR 400

q

Figure 4

7 . Be nc o n s u me st wog o o d s ,xa n dy ,a n da l wa y sd e v o t e s4 5p e rc e n to fh i si n c o met ot h e c o n s u mp t i o no ft h ef o r me r .Hi si n c o mee l a s t i c i t i e so fd e ma ndf ort h et wog oo d sxa n dya r e r e s p e c t i v e l yExm =0 . 4 5a n dEym =0 . 5 5: A: B:

TRUE FALSE

Solution: Consider good x:

pxx=0.45m Þ x=0.45

m px

Define:

x0 =0.45

m0 px

and:

Page 7 of 24

ES10001

x1 =0.45

m1 px

Thus:

Dx=x1 - x0 =

0.45 ( m1 - m0) px

Þ Dx=

0.45 Dm px

Þ Dx 0.45 = Dm px Thus:

E mx =

Dx m 0.45 m 0.45 m px × = × = × × =1 Dm x px 0.45 m px x

And similarly for good y. 8.

Be nl i v e si nat wo g o o dwo r l d .Ani n c r e a s ei nt h ep r i c eo fg o o d1wi l li n c r e a s ehi sd e ma n d f o r g o od 2 p r o v i d i n g h i s o wn p r i c e e l a s t i c i t y o f d e ma n d f o r g o od 1 , ,i sl e s st h a n1 : A: B:

TRUE FALSE

Solution: Write the two-good budget constraint as:

m= p1 x1 + p2 x2 when the price of good 1 changes, we have:

m= p1¢x1¢ + p2 x2¢ Thus:

Page 8 of 24

ES10001

( p¢x¢ + p x¢ ) - ( p x + p x ) =( m- m) 1 1

2 2

1 1

Þ

2 2

(

)

p¢1x1¢ - p1 x1 + p2 x2¢ - x2 =0 Þ p2 Dx2 =- p1¢x1¢ + p1 x1 Þ

(

p2 Dx2 =- p1¢x1¢ + p1 x1 + p1¢x1 - p1¢x1 Þ

(

) (

)

)

p2 Dx2 =- p1¢ x1¢ - x1 - p1¢- p1 x1 Þ p2 Dx2 =- p1¢Dx1 - Dp1 x1 Þ p2

Dx2 Dp1

=- p1¢

Dx1 Dp1

- x1

Þ p2 Dx2 Dx1 p1¢ -1 =Dp1 x1 x1 Dp1 If the change in price and quantity is very small then p1¢ ® p1 and x1¢ ® x1 such that:

Dx2 p2 Dx p × =- 1 × 1 - 1 Dp1 x1 Dp1 x1 Þ Dx2 p2 × ºE12 =E11 - 1 Dp1 x1 Thus, since p2 > 0 and x1 > 0 , it must be that case that Dx2 Dp1 > 0 iff . Intuitively, if demand for one good is elastic, then an increase in the price of that good will result in a decrease in expenditure on that good. If the money income and the price of the other good are held constant, then it must be the case that spending on, and thus demand for, the other good will increase. Section B: Multiple Choice (10 marks per question) 9 .A monopolist produces output at zero cost and faces two types of consumer, H and L, with demand curves qHd =50 - 0.5p and qdL =40 - 0.5 p. The profit maximising second-degree

(

)(

)

packages, éë PL ,qL , PH ,qH ûù , are: Page 9 of 24

ES10001 A. B. C. D. E.

(1500, 30), (2000, 50) (1300, 20), (2100, 40) (1200, 20), (2400, 50) (1500, 30), (1900, 50) (1500, 30), (1800, 50)

Solution: See Figure 5.

p 100 a DH 80 i A

B

b

40 C

D

20 F

h

E

G

g 30

0

c H

f 40

I

d

q

50

J

DL

e

Figure 5

The monopolist’s aim is to maximise profits by extracting as much consumer surplus (CS) from the two types of individual as possible. Note that the monopolist cannot identify individual types, but he knows that the two types exit. Thus, for example, he could offer two packages: pL ,40 = (A + C + F + G); and pH ,50 = (A + B + C + D + E + F + G + H + I).

(

)

)

( p ,50 ) since the former leaves him with CS ( p ,40 ) = 0 whilst the latter leaves him with CS ( p ,50) = - (B + D + E + H + I + J) < 0. The problem, however, is that Type-H would also prefer ( p ,40 ) to ( p ,50 ) since the former leaves him with CS ( p ,40 ) = (B + D + E + H) whilst the latter leaves him with CS ( p ,50) = 0. Thus, the monopolist must remove (B + D + E + H) from the ( p ,50 ) Note that Type-L would prefer L

( p ,40)

(

L

to

H

L

L

H

H

L

H

L

L

H

package

H

such

that

Type-H

is

indifferent

between

Page 10 of 24

the

two

packages

vis :

ES10001

CSH ( pH ,40 ) =0 =CSH ( pL ,50 ) . Note that Type-L would still prefer

(

)

( p ,40 ) L

to

( p ,50 ) H

since CSL pH ,50 = - (I + J) < 0. The monopolist, however, can increase its profits by reducing the size of the ‘Low’ package. As he does this, he will lose part of the area G (i.e. revenue lost from Type-L) but will gain part of the area (E + H) (i.e. revenue gained from Type-H). The monopolist will keep reducing the size of the ‘Low’ package until the revenue lost from Type-L equals the revenue gained from Type-H, that is until the height (g~h) equals the height (h~b). We may locate the size of the low package as follows:

( )

(

)

( )

* * * * pdH qL =100 - 2qL =2 80 - 2qL =2 pLd qL

Þ 100 - 2qL* =160 - 4qL* Þ 2q*L =60 Þ q*L =30 Thus:

pHd ( 30 ) =100 - 2 ( 30) =40 =2 éë 80 - 2( 30) ùû =2 pLd ( 30 ) And: * pL = A + C + F = (i, h, g, 0) = 20 ´30 + 1 2( 80 - 20) 30 =600 + 900 =1500

And:

p*H = (A + C + F) = (i, h, g, 0) = 20 ´30 + 1 2( 80 - 20) 30 =600 + 900 =1500 + 1

+ E = (b, c, h) =

2

( 40 - 20) 10 =100 +

+ (G + H) = (c, f, g, h) = 20 ´10 =200 + + I = (c, d, f) =

1

2

( 20 - 0) 10 =100

Þ pH* =1500 +100 + 200 +100 =1900 Thus

( p ,q ) =( 1500,30) L

L

(

) (

)

and pH ,qH = 1900,50 . Total profits to the monopolist are thus

p = 1500 + 1900 = 3400. Note that Type-L strictly prefers the p*L package, since it leaves

Page 11 of 24

ES10001

(

)

(

)

him with CSL 1500,30 = 0 whereas the p*H package leaves him with CSL 1900,50 = - (E + H + I + J) < 0. Type-H is indifferent between the two packages since they both leave him with CSH 1500,30 =CSH 1900,50 = (B + D) > 0, and thus we assume that he purchase the p*H

(

)

(

)

package: 10. All electricians in the country of Kilowatt are employed by ACME-SPARK, which is a monopolistic employer in this labour market. All electricians are paid the same hourly wage, w, and consumers pay ACME-SPARK a price of p = w for one hour of electrician labour. The marginal revenue product of one hour of electrician labour is p =9 - L 1000 , where

(

)

L denotes the number of electrician hours. The labour supply function of hourly electrician labour is Ls =- 3000 +1000w. The Government of Kilowatt realises that by imposing a minimum wage in the electrician market it can maximise welfare and by so doing it finds that the number of electrician hours employed increases by: A. B. C. D. E.

400 500 750 1000 None of the above

Solution: First note that:

Ls =- 3000 +1000w Þ ACL =w( L ) =3+ ( L 1000 ) Þ

(

TC L =w( L ) ×L =3L + L2 1000

)

Þ MCL = w¢ ( L ) ×L + w=3+ ( 2L 1000 ) Th a ti s ,t h ema r gi n a lc o s to fl a b o u ri st wi c ea ss t e e pa st h ea v e r a g ec o s to fl a b ou r .Ma r k e t e q u i l i b r i u mi sd e fin e db y

Page 12 of 24

ES10001

( )

MPRPL L* =9 -

L* 1000

=3+

( )

2L* =MC L L* 1000

Þ 3L* =6 1000 Þ L* =2000 And:

( )

( )

ACL L* =w L* =3+

L* 1000

Þ ACL ( 2000 ) =w( 2000 ) =3+

2000 1000

Þ ACL ( 2000 ) =w( 2000 ) =5 So c i a lwe l f a r ewo u l dbema x i mi s e dwh e r et h ewa g et h a two r k e r sa r ewi l l i n gt os u p p l yl a b ou rf o r e q u a l st h ewa g et h a tACMESP ARKwo ul db ewi l l i n gt op a yv i s :

( ) **

MPRPL L

=9 -

( )

L** L** =AC L L** =3+ 1000 1000

Þ 2L** =6 1000 Þ L** =3000 Th i swo u l di mp l ya ni n c r e a s ei np l u mb e rh o ur se mp l o y e do f1 0 00a n dwo ul dr e q u i r e sami n i mu m wa g eo f :

( )

( )

wmin = AC L L** =w L** =3 +

L** 1000

Þ wmin = AC L ( 3000) =w( 3000 ) =3+

3000 1000

Þ wmin =6

Page 13 of 24

ES10001 See Figure 6:

w

MCL= 3 + (2L/1000)

9

ACL= 3 + (L/1000) min w

6 5 3

MRPL = 9 – (L/1000)

0

2000

3000

9000

L

Figure 6

( )

(

)

2

11. The demand function for drangles is given by qd p =1 1+ p D. If the price of drangles is £11, then the own price elasticity,

, of demand is:

A. 7.33. B. 3.67. C. 5.50. D. 0.92. E. 1.83. Solution:

Page 14 of 24

ES10001 12. A monopolist has a constant marginal cost of £2 per unit and no fixed costs. He faces separate markets in London and Newcastle. He can set one price p1 for the London market

p2 for the Newcastle market. If demand in London is given by q1 =7000 - 700 p1 and demand in Newcastle is given by q2 =1200 - 200 p2 , then the price in London will:

and another price

A. B. C. D. E.

equal the price in Newcastle be smaller than the price in Newcastle by £2 be larger than the price in Newcastle by £4 be larger than the price in Newcastle by £2 be smaller than the price in Newcastle by £4

Solution: First, derive the two marginal revenue functions: q1 =7000 - 700 p1 Þ 700 p1 =7000 - q1 Þ

p1 = AR1 =10 - ( 1 700) q1

Þ

MR1 =10 - ( 2 700 ) q1

And: q2 =1200 - 200 p2 Þ 200 p2 =1200 - q2 Þ

p2 =AR2 =6 - ( 1 200 ) q2

Þ

MR2 =6 - (1 100 ) q2

Thus:

MR1 =10 - ( 2 700) q1 =2 =6 - ( 1 100) q2 = MR2 Thus:

Page 15 of 24

ES10001

( 2 700) q =8 1

Þ q1 =2800 Þ p1 =10 - ( 1 700 ) ×2800 =6 And:

(1 100 ) q

2

=4

Þ q2 =400 Þ p2 =6 - ( 1 200 ) ×400 =4 13. A monopolist finds that a person’s demand for its product depends on the person’s age. The inverse demand function of someone of age y can be written p =a y - b q, where

( )

a ¢( y) > 0 . The product can be produced at a constant marginal cost of c > 0 and cannot be resold from one buyer to another. If the monopolist knows the ages of its consumers and is allowed to price discriminate on age, then profit maximization implies that: A. B. C. D. E.

older people will pay higher prices and purchase less of this product older people will pay higher prices and purchase more of this product older people will pay lower prices and purchase more of this product everyone will pay the same price but older people will consume more Non...