Question 11
A firm manufactures quad bikes (“quads”). Each quad is made using one frame
(𝑥𝑥 1) and four wheels (𝑥𝑥 2). Each frame costs £10 and each wheel costs £4. The
output of the firm can hence be represented by the function
min �𝑥𝑥1,
1
4 𝑥𝑥2�
(Hint: this is similar to working with min �𝐾𝐾,
1
4 𝐿𝐿�, but instead of considering prices 𝑟𝑟 and
𝑤𝑤 you may consider prices 𝑝𝑝1 and 𝑝𝑝2 for the inputs)
a) What is an isoquant? Show the isoquants for producing two quads, three quads
and seven quads. [5 marks]
b) Derive the input demands for frames and wheels for the firm. How do they depend on the input prices? What is the maximum number of quads the firm can
produce if the number of wheels is fixed at 12? Assume that the firm is producing the maximum number of quads. What is the marginal product of adding an
extra frame? [10 marks]
c) Define the firm’s cost function and derive it. Assume that each wheel costs £4
and each frame costs £10. What is the cost of producing 7 quads? [5 marks]
d) Assume that the firm needs to pay £50 per day to rent the factory to produce
quads (this is a fixed cost). Continue to assume that each wheel costs £4 and
each frame costs £10. Suppose that the firm can only produce 10 quads per
day and the rent has already been paid for today. If the price at which the firm
can sell quads is £30 should the firm produce today? Explain your reasoning.
[5 marks]
e) Continue to assume that the daily rent is £50, each wheel costs £4 and each
frame costs £10. Suppose that the firm can only produce 10 quads per day and
the rent can be stopped (so the cost of producing zero quads is zero). If the
price at which the firm can sell quads is £30 should the firm produce today?
Explain your reasoning. [5 marks]
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UL20/0389
Question 12
For the rest of this question consider a two goods economy where Kim and Jung
can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and
Jung both enjoy driving Ferraris and having more VR headsets (so more friends
can play the same game). They start at the same (high) level of income. Kim has
an initial endowment of (𝑥𝑥𝐾𝐾
0, 𝑦𝑦𝐾𝐾
0) = (10,30) and Jung has an initial endowment of
�𝑥𝑥𝐽𝐽
0, 𝑦𝑦𝐽𝐽
0� = (30,10)
a) Illustrate the initial endowment in an Edgeworth box. Clearly label the axes and
explain the dimensions of the box. Show the indifference curve each of them is
on at the endowment point. [6 marks]
b) Consider an allocation where Kim gets (𝑥𝑥𝐾𝐾, 𝑦𝑦𝐾𝐾) = (40,40) and Jung gets the
remaining Ferraris and VR headsets. Show where this point is in the Edgeworth
box. Is this allocation Pareto efficient? Is it equitable? How likely is this to arise
in practice? [8 marks]
c) Assume that Kim has preferences 𝑈𝑈𝐾𝐾(𝑥𝑥𝐾𝐾, 𝑦𝑦𝐾𝐾) = 3𝑥𝑥𝐾𝐾 + 𝑦𝑦𝐾𝐾 and Jung has preferences 𝑈𝑈𝐽𝐽�𝑥𝑥𝐽𝐽, 𝑦𝑦𝐽𝐽� = 𝑥𝑥𝐽𝐽 + 3𝑦𝑦𝐽𝐽. Will Kim and Jung trade? Calculate the general
equilibrium allocation for Kim and Jung. Compute the utility at the endowment
point and at the general equilibrium allocation. Is the new allocation on the contract curve? [10 marks]
d) Assume that a social planner could redistribute initial wealth (the amounts of 𝑥𝑥
and 𝑦𝑦 that Kim and Jung have). Can they reallocate resources so that Kim and
Jung reach the allocation (𝑥𝑥𝐾𝐾, 𝑦𝑦𝐾𝐾) = (20,20) and �𝑥𝑥𝐽𝐽, 𝑦𝑦𝐽𝐽� = (20,20) as a general
equilibrium (i.e. post-trade) allocation? Can the social planner redistribute resources to make the allocation where Jung owns all the resources in the economy a general equilibrium allocation? [6 marks]
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UL20/0389
SECTION C: Macroeconomics
Candidates should answer ONE of the two following long questions. It is essential that
you explain your answers.
Question 13
In this question we will reflect on the Australian fires from last year. A wide part of
Australia has experienced severe fires in the last year, which made the economy much
less productive and had severe impacts on business activities.
a) Explain why you could expect negative shifts in the aggregate demand curve
following the fires. What would you expect are the drivers of this shift? Reflect
on each of the components of the aggregate demand and comment on whether
they are likely to change due to the fires. [6 marks]
b) Explain why you could expect negative shifts in the aggregate supply curve
following the fires. What would you expect are the drivers of this shift? Reflect
on each of the components of the aggregate supply and comment on whether
they are likely to change due to the fires. [6 marks]
c) Show the shifts discussed in parts a) and b) graphically. You may assume an
upward sloping AS curve for simplicity. Can you predict what happens to real
GDP and the price level? [8 marks]
d) The fires in Australia can also be considered a decrease in the country’s stock
of capital. You may use the Solow model to show what happens when capital
decreases and what the model predicts for the new growth rate. Are these consequences likely to happen in practice? [10 marks]
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Question 14
a) Allen would like to open a business to produce a software that he thinks would
be well-received by the market. However, the investment needed to start a business is very high and Allen could barely cover it on his own. The software is
very likely to be successful and generate profits, but it takes 2 years before
profits are generated. Explain why the existence of a financial intermediary, like
a bank, makes Allen’s investment more likely. [4 marks]
b) Banks are financial intermediaries engaged in maturity transformation. Explain
what it means for banks to engage in maturity transformation and what are the
risks associated with it for banks and depositors. How do banks make profits?
[8 marks]
c) Now assume that Allen needs to borrow £300 to produce his software, which
will generate £500 in two years. There are N savers in the economy, each endowed with £2 and each facing a 25% chance that there will be an emergency
and they will need their £2 back. What is the minimum value of N such that a
financial intermediary can solve the problem of getting money from savers to
borrowers? [6 marks]
d) After the 2009 financial crisis, countries in the Basel Committee on Banking
Supervision have agreed to raise the mandatory reserves for banks. Explain
what happens to the money multiplier and the bank deposit multiplier if the reserve ratio is increased and what governments need to do if they wish to maintain the previous level of broad money 𝑀𝑀. [8 marks]
e) What’s the difference between a liquidity crisis and a solvency crisis? When
Lehman Brothers went under, its debts (liabilities) were much greater than its
assets. Did Lehman Brothers experience a solvency or a liquidity issue? [4
marks]

Sample Solution