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M.E.C – 101
MICRO
ECONOMIC ANALYSIS MEC 101 Solved Assignment 2022-23
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Assignment I
Answer the following
questions in about 700 words each.
1. a) Consider a pure-exchange economy of
two individuals (A and B) and two goods (X and Y) Individual A is endowed with
5 units of good X and 3 units of good Y, while individual B with 3 and 4 units
of goods X and Y respectively. Assuming utility functions of individuals A and
B to be UA=XA YA 2 and UB=XB 2 YB where Xi and Yi for i= {A, B} represent
individual i’s consumption of good X and Y respectively, what will be the set
of Pareto optimal allocation in this economy?
b) Determine the conditions that need to
be fulfilled by an allocation to be termed as Pareto efficient allocation.
2. Consider a Cobb-Douglas utility
function
U
(X, Y) = Xα Y (1- α) ,
Where X and y are the two goods that a
consumer consumes at per unit prices of Px and Py respectively. Assuming the
income of the consumer to be ₹M, determine:
a. Marshallian demand function for goods
X and Y.
b. Indirect utility function for such a
consumer.
c. The maximum utility attained by the
consumer where α =1/2, Px =₹ 2, Py = ₹ 8 and M= ₹ 4000.
d. Derive Roy’s identity.
Assignment - II
Answer the following
questions in about 400 words each.
3. a.) What is excess capacity and how is
it related to the model of monopolistic competition?
b) Demand function and supply function
are given as P=25-X2 and P=2X+1 respectively, find out producer surplus and
consumer surplus.
4. a.) Define games of complete and
incomplete information
b.) From the following pay-off matrix,
where the payoffs (the negative values) are the years of possible imprisonment
for individuals A and B, determine:
(i) The optimal strategy for each individual.
(ii) Do individuals A and B face a prisoner’s dilemma?
|
|
Individual B |
||
|
Individual A |
|
Confess |
Don’t Confess |
|
Confess |
(-5, -5) |
(-1, -10) |
|
|
Don’t Confess |
(-10, -1) |
(-2, -2) |
|
5. a.) Differentiate between the Cournot
and the Bertrand model of Oligopoly.
b.) Consider an industry with two firms 1
and 2, each producing output Q1 and Q2 respectively and facing the industry
demand given by P=140-Q, where P is the market price and Q represents the total
industry output, that is Q= Q1 + Q2. Assume that each faces a marginal cost of
₹ 20 per unit with no fixed costs. Solve for the Cournot equilibrium in such an
industry.
6. a.) Given the Von Neumann-Morgenstern
utility function of an individual, U (W) =W ½ , where W stands for amount of
money. Comment upon attitude towards risk of such an individual with the help
of a diagram.
b) Now suppose this individual possesses
a building worth ₹1600. If the building catches fire, its value falls to ₹ 400.
Let the probability of building catching fire be ¼. On the basis of the given
information, find out whether the individual would be willing to pay a risk
premium of ₹ 76 to the insurance company in order to eliminate the risk
associated with the factory building.
7. Write short notes on following:
a) Moral Hazard
b) Homogeneous and Homothetic production
functions
c) Arrow prat measure of risk averseness
d) Bergson-Samuelson Social welfare
function
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