Posted: April 12th, 2022

Advanced microeconomics

Timed Assessment
2022-2023
Advanced microeconomics
The assessment is two pages and there are seven questions in total. Answer all questions.
Notation is standard. Where provided, follow the notation given. Otherwise, define your
notation.
The first four questions are short answer questions. The maximum word limit for these four
questions is strictly 200 words each. These questions are worth 10 marks each.
The remaining three questions are problems. You need to show all steps in computations,
and explain your steps. Individual marks for the parts are indicated in brackets.
You are allowed to handwrite mathematical solutions and draw diagrams where relevant, and
insert these as scanned pictures in your answers. Everything else should be typed. Word
documents and PDFs are both acceptable.
Question 1: Explain why the following statement should hold:
∂v(p, w)
∂pk
= 0 for any good k only if ∂v(p, w)
∂pi
6= 0 for good i where pk, pi 0 [10 marks]
Question 2: Discuss whether we can derive the Pareto set of a two-agent two-good pure exchange economy
directly from agents’ offer curves. [10 marks]
Question 3: What is the advantage of assuming homothetic preferences? Discuss. [10 marks]
Question 4: Discuss how duality theory can help policymakers with regards to supply side economics. [10
marks]
Question 5: Consider a subsistence economy where only two farms operate. Both farms produce identical
wheat using labour as the only factor of production. Technology of these farms are given as
q1 = l
0.5
1 −
1
3
q2
and
q2 = l
0.5
2 −
1
3
q1
where q1 and q2 are respective outputs of the farms with l1 and l2 the respective units of workers
they hire. Assume that the wheat market is competitive. The price of wheat is 1 while price
of labour is 0.5.
Dr Gunes Bebek
2
a. Assuming the farms owned by different landlords, calculate their equilibrium levels of
outputs and profits. [5 marks]
b. Now assume the farms operate under common ownership. Calculate profits. [5 marks]
c. Discuss the results you obtain from parts b and c. [10 marks]
Question 6: Consider a two-agent two-good barter economy. Agent 1 only cares about good 1, and agent 2
only cares about good 2. There is only 1 unit of good 1, and 2 units of good 2 in the economy,
which is distributed equally between the agents while agent 1 owns the only unit of good 1 in
the economy.
a. Compute and explain the Pareto optimal allocations. [5 marks]
b. Compute and explain the equilibrium prices and allocations. [10 marks]
c. How would your answers to parts a and b change if agent 1 shared half of his good 1 with
agent 2? Discuss. [10 marks]
Question 7: Consider the following 2-consumer, 2-good exchange economy:
u
1
(x
1
1
, x1
2
) = (x
1
1x
1
2
)
2
u
2
(x
2
1
, x2
2
) = ln x
2
1 + 2 ln x
2
2
R
1 = (18, 4)
R
2 = (3, 6).
a. Characterise the Pareto set as completely as possible. [5 Marks]
b. Compute the Walrasian equilibrium allocation and verify that it is in the core. [10 Marks]
Dr Gunes Bebek

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