# MICROECONOMICS: ECONOMICS OF UNCERTAINTY

SECTION A

[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 + 5? pounds. If he invests £100 in firm B, in one

year he will get back 100 − 15? pounds. The variable ? 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 ? of his £100 to investing in company

A and 1 − ? 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

?(?, ?) = ? −

?

2

8

where ? denotes the expected return of his portfolio and ? 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 ? to one of the sellers, their travel cost is

£2?. 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)

BST163

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SECTION B

[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 ?1 = £1,000 in period 1, ?2 = £1,100 in period 2 and ?3 = £1,210 in period 3.

The interest rate is 10% in all periods. The consumer’s utility function is given by

?(?1, ?2, ?3

) = ?1?2

3

?3

where ?? denotes his consumption in period ?. 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

game.

Player 2

Player 1

Left Right

Top 7,8 4,1

Bottom 9,2 3,5

[50 marks]

(maximu

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