MEC-101/001 MICROECONOMIC ANALYSIS in English Solved Assignment 2020-2021

MEC-101/001 MICROECONOMIC ANALYSIS

Solved Assignment 2020-2021

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Course Code: MEC-001
Assignment Code: MEC-001/2020-21
Total Marks: 100

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Answer all questions from this section. 2×20 = 40
1. (a) Elucidate price and output determination under Cournot and Stackelberg models of Oligopoly.
(b) Consider a market for energy drinks consisting of only one firm. The firm has a linear cost function:
C(q) = 4q, where q represents quantity produced by the firm. The market inverse demand function is
given by P(Q) = 24 − 2Q, where Q represents total industry output. Based on the given information
answer the following:
(i) What price will the firm charge? What quantity of energy drinks will the firm sell?
(ii) Now suppose a second firm enters the market. The second firm has an identical cost function. What
will be the Cournot equilibrium output for each firm?
(iii) What is the Stackelberg equilibrium output for each firm if firm 2 enters second?
(iv) How much profit will each firm make in the Cournot game? How much in Stackelberg?
(v) Which type of market do consumers prefer: monopoly, Cournot duopoly or Stackelberg duopoly?
Why?
2. (a) Consider an Edgeworth box that describes a two-person, two-commodity exchange scenario. Explain
how trade takes place between the two individuals starting from the initial endowment position. What is
the significance of the slope of the ray passing through a Pareto optimal point and the endowment point?
(b) Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y). Assume both the
individuals are endowed with 2 units of good X and 1 unit of good Y each.
Let utility functions of individual A and B be UA = min{XA,YA} and UB = min{
𝑋𝐵
4
,YB}, where Xi and Yi for i = {A,
B} represent individual i’s consumption of good X and Y respectively. Determine the aggregate excess demand
functions for each good.
SECTION B
Answer all questions from this section. 5×12 = 60
3. (a) How would you differentiate a Static game from a Dynamic game?
(b) Consider the following game.

i) Can Backward induction be applied in this game to find a solution?
(ii) What will be the Subgame Perfect Nash equilibria for the given game?
4. What is Kaldor’s compensation principle? How is it used to resolve Pareto non-comparability? How is it
different from Hick’s compensation principle?
5. (a) Explain the concept of a Homothetic production function.
Given a production function
q = AL0.5K
0.4
where q represents total production, L and K stands for labour and capital respectively, and A is the technology
coefficient. What are the returns to scale for such a production function?
(b) “Homothetic production function includes Homogeneous production function as a
special case.” Justify this statement.

6. (a) Differentiate between a Hicksian and a Walrasian demand function? Do they ever intersect? Explain.
(b) Consider a Cobb-Douglas utility function
U (X, Y) = 𝑋
1 5𝑌
4 5
where X and Y are the two goods that a consumer has an option to consume at per unit prices of PX and PY,
respectively. Assume income of the consumer to be Rs M. Determine
(a) Uncompensated demand functions for goods X and Y
(b) Compensated demand functions for goods X and Y
7. Raj expects his future earnings to be worth Rs 100. If there is some unfortunate event, his expected future
earnings will be Rs 25. The probability of an unfortunate event to occur is 2
3
, while that of things
remaining fortunate is 1
3
. Suppose his utility function is given by U(Y) = 𝑌
1 2
, where Y represents the
amount of money. Now suppose an insurance company offers to fully insure Raj against the loss of
earnings caused during an unfortunate event at an actuarially fair premium.
(i) Will Raj accept the insurance? Explain.
(ii) What would be the rate of actuarially fair premium charged in this case?
(iii) What would be the maximum amount that Raj would pay for the insurance?

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