MEC 101 Solved Assignment 2021-22

MEC 101

MICROECONOMIC ANALYSIS

Assignment

Course Code: MEC-002

Assignment Code: MEC-002/2021-22

Total Marks: 100

SECTION A

Answer all questions from this section. 2×20 = 40

1. (a) “In terms of the type of good, that is whether a good is normal or inferior, the relationship between the compensated and the uncompensated demand curves varies,” Justify the statement graphically. (8)

(b) A consumer’s preferences over goods A and B is given by the utility function U (A, B) = 𝐴 1 2 𝐵 1 3 Let pA be the price of good A, pB the price of good B and let consumer’s income be given by I.

(i) Derive the indirect utility function (6)

(ii) What is meant by Dual problem in context of the Utility and Expenditure optimisation exercise? (6)

2. (a) While modelling Insurance markets in presence of asymmetric information, a Separating equilibrium is often preferred instead of a Pooling equilibrium.” Justify the statement. Under what conditions, a separating equilibrium may also not exist. (6)

(b) Given the von Neumann-Morgenstern utility function of an individual, U (W) = 𝑙𝑛𝑊 where W stands for amount of money and ln is the natural logarithm. Comment upon attitude towards risk of such an individual with the help of a diagram. (6)

(c) Now, suppose this individual plays a game of tossing a coin where he wins Rs 2 if head turns up and nothing if tail turns up.On the basis of the given information, find

(i) The expected value of the game. (4)

(ii) The risk premium this person will be willing to pay to avoid the risk associated with the game. (4)

SECTION B

Answer all questions from this section. 5×12 = 60

3. (a) Differentiate between the Cournot and the Stackelberg models of Oligopoly.Under the Stackelberg assumptions, the Cournot solution is achieved if each firm desires to act as a follower. Do you agree? Elaborate. (6)

(b) A monopolist operates under two plants, 1 and 2. The marginal costs of the two plantsare given by MC1 = 20 + 2q1 and MC2= 10 + 5q2 where q1 and q2 represent units of output produced by plant 1 and 2 respectively. If the price of this product is given by 20 –3(q1 + q2), how much should the firm plan to produce in each plant, and at what price should it plan to sell the product? (6)

4. (a) Consider there are two firms 1 and 2 serving an entire market for a commodity. They have constant average costs of Rs 20 per unit. The firms can choose either a high price (Rs 100) or a low price (Rs 50) for their output.When both firms set a high price, total demand is1000 units which is split evenly betweenthe two firms. When both set a low price, total demand is 1800, which is again split evenly.If one firm sets a low price and the second a high price, the low-priced firm sells 1500 units, the high-priced firm only 200 units. Analyse the pricing decisions of the two firms as a non-co-operative game and attempt the following: (6)

(i) Construct the pay-off matrix, where the elements ofeach cell of the matrix are the two firms’ profits.

(ii) Derive the equilibrium set of strategies.

(iii) Explain why this is an example of the Prisoners’ Dilemma game.

(b) What is the Bayesian Nash equilibrium? How is it different from Perfect Bayesian equilibrium? (6)

5. What is Kaldor’s compensation principle? How is it different from Hick's compensation principle? (12)

6. (a) “Homothetic production function includes Homogeneous production function as a special case.” Justify this statement. (6)

(b) Consider a production function: Q = f (L), where Q represents the output and L is the factor of production. Let w be the per unit price of factor L and p be the per unit price of output Q. Using the Envelope theorem determine the supply function and the factor demand function. (6)

7. (a) What are the assumptions on which the First fundamental theorem of welfare economics rests? (4)

(b) Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y). Individual A is endowed with 1 unit of good X and none of good Y, while individual B with 1 unit of good Y and none of good X. Assuming utility function of individual A and B to be UA = (XA) α (YA) 1−α and UB = (XB) β (YB) 1−β where Xi and Yi for i = {A, B} represent individual i’s consumption of good X and Y, respectively, and α, β are constants such that 0 < α, β < 1. Determine the Walrasian equilibrium price ratio.

 

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