Advanced microeconomics

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Assessment

2021-2022

Advanced microeconomics

Question 1:

Discuss the relationship between compensating variation and equivalent variation.

Question 2:

Assuming all necessary assumptions hold, discuss why every competitive equilibrium allocation is Pareto efficient but not every Pareto efficient allocation is a competitive equilibrium alloca-tion.

Question 3:

Consider a two agent two good pure exchange economy. Can we derive the Pareto set directly from agents’ offer curves? Discuss.

Question 4:

Discuss the relationship between a firm’s market power and market failure.

Question 5:

Explain why voluntary provision of public goods results in an inefficient provision.

Question 6:

Consider a two-agent two-good exchange economy. Assume the utility functions are given by  and with endowment vectors = (4, 12) and = (8, 8). Assume good is the numeraire.

a. Find the competitive equilibrium allocation and prices for this pure exchange economy. [10 marks]

b. Extend this pure exchange economy to a production economy. Suppose a firm exists which can produce good using good as input and has a production function:

Further assume each agent has an equal share of the firm. Compute a competitive equi-librium (if any exists) which has no additional production of good i.e. total availability of good remains equal to the initial endowment. [15 marks]

Question 7:

Consider a two-good exchange economy with a population of N, where there are equal number of men (m) and women (w). Each man has an endowment of 300 units of good 1; each woman has an endowment of 200 units of good 2. Each man has a utility function

and each woman has a utility function

a. Find the competitive equilibrium allocation. [10 marks]

b. Prove that the competitive equilibrium is inefficient, i.e. a discussion is not sufficient. [15 marks]