Posted: November 1st, 2022

Advanced microeconomics

Timed Assessment
2022-2023
Advanced microeconomics
The Assessment is 2 pages and there are seven questions in whole. Reply all questions.
Notation is normal. The place supplied, comply with the notation given. In any other case, outline your
notation.
The primary 4 questions are quick reply questions. The utmost phrase restrict for these 4
questions is strictly 200 phrases every. These questions are value 10 marks every.
The remaining three questions are issues. You’ll want to present all steps in computations,
and clarify your steps. Particular person marks for the components are indicated in brackets.
You might be allowed to handwrite mathematical options and draw diagrams the place related, and
insert these as scanned photos in your solutions. All the things else must be typed. Phrase
paperwork and PDFs are each acceptable.
Question Assignment 1: Clarify why the next assertion ought to maintain:
∂v(p, w)
∂pk
= zero for any good ok provided that ∂v(p, w)
∂pi
6= zero for good i the place pk, pi zero [10 marks]
Question Assignment 2: Focus on whether or not we will derive the Pareto set of a two-agent two-good pure alternate financial system
straight from brokers’ provide curves. [10 marks]
Question Assignment three: What’s the benefit of assuming homothetic preferences? Focus on. [10 marks]
Question Assignment four: Focus on how duality idea will help policymakers with reference to provide aspect economics. [10
marks]
Question Assignment 5: Take into account a subsistence financial system the place solely two farms function. Each farms produce similar
wheat utilizing labour as the one issue of manufacturing. Know-how of those farms are given as
q1 = l
zero.5
1 −
1
three
q2
and
q2 = l
zero.5
2 −
1
three
q1
the place q1 and q2 are respective outputs of the farms with l1 and l2 the respective models of employees
they rent. Assume that the wheat market is aggressive. The worth of wheat is 1 whereas value
of labour is zero.5.
Dr Gunes Bebek
2
a. Assuming the farms owned by completely different landlords, calculate their equilibrium ranges of
outputs and earnings. [5 marks]
b. Now assume the farms function below widespread possession. Calculate earnings. [5 marks]
c. Focus on the outcomes you acquire from components b and c. [10 marks]
Question Assignment 6: Take into account a two-agent two-good barter financial system. Agent 1 solely cares about good 1, and agent 2
solely cares about good 2. There’s only one unit of fine 1, and a pair of models of fine 2 within the financial system,
which is distributed equally between the brokers whereas agent 1 owns the one unit of fine 1 in
the financial system.
a. Compute and clarify the Pareto optimum allocations. [5 marks]
b. Compute and clarify the equilibrium costs and allocations. [10 marks]
c. How would your solutions to components a and b change if agent 1 shared half of his good 1 with
agent 2? Focus on. [10 marks]
Question Assignment 7: Take into account the next 2-consumer, 2-good alternate financial system:
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, four)
R
2 = (three, 6).
a. Characterise the Pareto set as fully as doable. [5 Marks]
b. Compute the Walrasian equilibrium allocation and confirm that it’s within the core. [10 Marks]
Dr Gunes Bebek

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