MEC 101 Solved Assignment 2022-23
MICRO ECONOMIC ANALYSIS
Course Code: MEC 001/101
Assignment Code: Asst /TMA /2022-23
Total Marks: 100
Note:
Answer all the questions.
SECTION A
Answer
the following questions in about 700 words each. The word limits do not apply
in case of numerical questions. Each question carries 20 marks.
2 × 20 = 40
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.
SECTION B
Answer
the following questions in about 400 words each. Each question carries 12
marks. 5 X 12=60
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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