1
Assessment
2021-2022
Advanced microeconomics
The assessment is two pages and there are seven questions in total. Answer all questions.
Where provided, follow the notation given. Otherwise, define your notation.
The first five questions are short answer questions. The maximum word limit for these five
questions is strictly 120 words each. Equations do not count towards the 120 words. These
questions are worth 10 marks each.
The remaining two questions are problems with two parts each. You need to show all steps
in computations. These two questions are 25 marks each. Individual marks for the parts are
indicated in brackets.
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 allocation.
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
U
1
(x
1
1
, x1
2
) = x
1
1 + 4p
x
1
2
and U
2
(x
2
1
, x2
2
) = x
2
1 + 2p
x
2
2 with endowment vectors R1 = (4, 12)
and R2 = (8, 8). Assume good x2 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 x2 using good x1 as input and has a production function:
x2 = αx1
Dr Gunes Bebek
2
Further assume each agent has an equal share of the firm. Compute a competitive equilibrium (if any exists) which has no additional production of good x2 i.e. total availability
of good x2 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
U
m(x
m) = log x
m
1 + log x
m
2
and each woman has a utility function
U
w(x
w) = log x
w
2 + log x
w
1
x
m
1
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]
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