mec-001 - micronomic analysis 2015

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MEC-001

M ASTER OF ARTS (ECONOM ICS)

Term-End Examination

June, 2015

07836

MEC-001 : MICROECONOMIC ANALYSIS

Time : 3 hours

aximum Marks : 100

Note : Attempt questions from each section as per

instructions given

SECTION A

Answer any two questions from this section

x 20=40

1

Consider a small country with two individuals,

Anita and Babar, and two goods, corn (C) and

chicken (H). Anita and Babar have utility

functions given by

A

U = 0.21n C + 0.8 in

H,

U

B

= 0.8 in

C + 0.2 in

H.

The economy as a whole is endowed with

100 un its of corn and 50 un its of chicken.

(a)

Solve for the marginal rates of substitution

between corn and chicken for Anita and

Babar. Show the condition that represents

allocative efficiency in C and H.

(b)

Derive Anita and Babar's demands for

C and H as a function of prices (P) and

income (I).

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(c)

Assume that Anita has an endowment of C

equal to a and an endowment of H equal to

13. Solve for the equilibrium price ratio in

terms of a and 13.

(d)

Suppose Anita has 80 units of corn and

10 units of chicken. Calculate the

quantities consumed by Anita and Babar in

equilibrium.

2.

Suppose the quality of used cars runs from good,

worth 2,900 to sellers and 3,000 to buyers,

down to bad ones worth 1,900 to sellers and

2,000 to buyers. Between these two extremes

are cars of every quantity level, always worth

100 more to buyers than to sellers. Assume

that there are 1001 cars and there is just one car

per increase of 0.10 in quality, i.e., the first car

worth

,900 to its owner and ,000 to

buyers, a second worth 1,90010 to its owner

and 2,00010 to buyers and so on. Assume that

the market has inelastic supply and elastic

demand at every level of quality.

(a)

At price p = 1,900, what is the number of

cars that would be offered for sale ?

(b) At price p, what is the value of buyers of

the average car being sold ? What happens

to demand, if p exceeds 2,100 ?

(c)

What would be the equilibrium price in

such a car market ? How many cars will

change hands ?

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3.

There are two firms in an industry facing market

demand : Q = 3200 — 1600 P. Their costs are

given as follows :

Firm 1 : TC

1

(q

1

) = 0.25 q

1

Firm 2 : TC

2

(q2

) = 0.5 q

2

If firm 1 is a leader and firm 2 a follower, solve

for Stackelberg output levels, market price and

profit levels of the firms.

4.

What is the central contribution of Arrow to the

development of the theory of social welfare ? Do

you agree with his formulation of the theory ?

Give reasons in support of your answer.

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SECTION B

Answer any

five

questions from this section

x12=60

5. Suppose an industry with n = 100 identical firms

faces the inverse demand curve : P = 1000 and

50 + (q. )

2

total cost : TC(q

i) =

1

he Ministry of

Health declared the product of the industry to be

unhealthy. Consequently, its demand dropped to

6400

P =

Solve for short-run and long-run

equilibrium price — quantity combinations for the

industry.

6. Write short notes on any

two

of the following :

(a)

Envelope Theorem

(b)

First Welfare Theorem

(c)

Moral Hazard

7. If the consumer's utility function is given as

u(x1

, x2) =

(x1/2

1 + x

1/2

2

)2,

(a)

formulate the expenditure minimisation

problem.

(b)

derive Hicksian demands for x

1

and x

2

.

1

(c)

derive the expenditure function.

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Firm 2

.

Enter o not enter

Enter

o not enter

8. There are N people living in a village engaged in

fishing (F) and public transport services (T). The

utility function of each of these people is given

as Ui = (fi)2

. T. If the production possibility

frontier is depicted by F

2

+ 3T

2

= 1800, find the

Pareto-optimal provision of T.

9.

Consider the sequential game being played

between two U.S. firms thinking about entering

the Indian market. Firm 1 has a headstart in

completing the legal process and moves first,

choosing whether to enter or not. Firm 2 moves

second and is deciding whether to enter or not.

The profit for each firm is shown in the game tree

below :

Firm 1

Enter o not enter

(1, — 1)

6, 0) 2, 4)

2, 0)

(a) Find the subgame Perfect Nash

Equilibrium outcome of the game. List the

associated strategies of the two firms.

(b) How might firm 2 end up with a better

outcome i.e., another Nash Equilibrium ?

Why is this Nash Equilibrium not realistic

as the one in (a) ?

MEC-001

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10. Suppose you face the following lottery. You

earn 1 of 3 possible grades in the examination :

A n A , a C or an F w ith the probabilities

–

– —

.

A 10

C

10

F

10

Assume that your current wealth is 400. If you

receive an A , you gain 500. However, if you

get an F , you lose 300. If you receive a C ,

you do not gain or lose anything.

If your u tility function is given as u (w ) = /(1);74 ,

w here w = w ealth,

(a)

what is your expected utility after the

test ?

(b)

what is the certainty equivalent level of

w ealth in this test ?

11. W hich key features of W illiamson's model help in

better understanding of the behaviour of a firm ?

G ive details to support your answ er.

MEC-001



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mec-001 - micronomic analysis 2015

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