ECO2024: Microeconomics of Markets – Final Exam

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ECO2024: Microeconomics of Markets – Final Exam

1.    Consider a two-person, two-commodity exchange economy. Utility functions of the individuals are given by: ui(x1(i), x2(i)) = (x1(i)) . (x2(i)) , where i = A, B , for individual A and B, respectively, and the endowments are given by A  = (1, 2) and B  = (2, 1).

(i)           Characterize the set of Pareto-efficient allocations as completely as possible. (10 marks)

(ii)          Characterize the Core of this economy. (10 marks)

(iii)         Draw the set of Pareto-efficient allocations and the Core in an Edgeworth Box. (10 marks)

(iv)         Find the Walrasian equilibrium of this economy. (10 marks)

2.    Consider a consumer who wants to spend £30 towards purchasing two goods: Apples and Bananas. Price of bananas is constant at £1 per banana, but price of apples is £2 per apple for the first 10 apples purchased, and £1 thereafter. Write down the budget line equation(s) for this consumer. Draw the budget set for this consumer. Explain your steps. (12 marks)

3.    A firm wants to enter a new market, and its main concern is about the reaction of an incumbent company that currently is making a profit of £100,000. If the reaction is aggressive, the challenger will suffer a loss of £10,000, and the incumbent’s profits will be reduced to only £20,000 (because of the costs of the fight). On the other hand, if the incumbent chooses to accommodate to the new market scenario, then the two firms will share the £100,000 profit equally. Obviously, the challenger can always choose to stay out if that seems to be the best choice (with a profit of £0).

(a)   Formulate this as an extensive form game. (4 marks)

(b)   Find the pure strategy Nash equilibria of this game. Are these Nash equilibria sequentially rational?

If not, why? Explain your answers. (8 marks)

(c)   Find the Rollback equilibrium of this game and compare it with the equilibrium profiles found in part (b). Comment. (6 marks)

4.  Consider the following normal-form game.

A

B

C

D

T

1, 1

2, 2

3, 4

9, 3

B

2, 5

3, 3

1, 2

7, 1

Find all pure Nash equilibria and one mixed Nash equilibrium of this game. (15 marks)

5.    Two residents, Tesla and Edison, must, simultaneously and independently, decide how much to contribute towards street lightings in their neighbourhood.  If Tesla contributes X1  and Edison contributes X2 , the total units of streetlights which they will receive are 2(X1  + X2  + X1X2). Assume X1  and X2  are positive numbers. Due to the location of their properties, the costs for their contributions differ. Tesla must pay a cost of X1(2) for contributing towards streetlights and  Edison  pays  a  higher cost of 2X2(2)   for contributing towards streetlights. Compute the Nash equilibrium levels of contribution for both these residents . How many

streetlights will be available to the residents? Comment. (15 marks)


2023-01-14