[Maximum word count 500]
Answer only ONE question from this section. This section is worth 50 marks.
Question 1. An investor faces the following prospect: if he invests £100 in company
A, in one year he will get back 50 + 5𝑇 pounds. If he invests £100 in firm B, in one
year he will get back 100 − 15𝑇 pounds. The variable 𝑇 is a random variable with an
expected value of 4 and standard deviation of 2.
a. Obtain the expected return and standard deviation of a generic portfolio
where the investor allocates a fraction 𝑥 of his £100 to investing in company
A and 1 − 𝑥 to investing in company B. Draw the budget curve where the
standard deviation is on the horizontal axis and the expected return is on
the vertical axis.
[25 Marks]
(maximum word count 250)
b. Suppose that the utility of the investor is given by
𝑢(𝑚, 𝑠) = 𝑚 −
where 𝑚 denotes the expected return of his portfolio and 𝑠 denotes its
standard deviation. Determine how much he invests in company A and how
much he invests in company B.
[25 Marks]
(maximum word count 250)
Question 2. Consider a “linear city” on the unit interval [0,1] in which consumers are
distributed uniformly between locations 0 and 1. There are 2 sellers in this city, seller
A and seller B, offering the same product. The cost of production is £3 per unit for
each seller. If a consumer is at a distance 𝑑 to one of the sellers, their travel cost is
£2𝑑. Each consumer values the good at £10 and buys at most one unit. Suppose
seller A is fixed at location 0.2 and seller B is fixed at location 0.6. Obtain the prices
that A and B post in equilibrium.
[50 Marks]
(maximum word count 500)
[Maximum word count 500]
Answer only ONE question from this section. This section is worth 50 marks.
Question 3. Consider a three period economy where the consumer is endowed with
wealth 𝑚1 = £1,000 in period 1, 𝑚2 = £1,100 in period 2 and 𝑚3 = £1,210 in period 3.
The interest rate is 10% in all periods. The consumer’s utility function is given by
𝑢(𝑐1, 𝑐2, 𝑐3
) = 𝑐1𝑐2
where 𝑐𝑡 denotes his consumption in period 𝑡. Find out his optimal consumption
path. Be sure to specify how much he borrows or saves in each period.
[50 Marks]
(maximum word count 500)
Question 4. Find all pure and mixed strategy equilibria of the following two-player
Player 2
Player 1
Left Right
Top 7,8 4,1
Bottom 9,2 3,5
[50 marks]

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