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C 29 AG A DVANCED ECONOMICS 2

SEMESTER TWO – 202 0/21

1) Firms 1 and 2 are participating in a quantity setting oligopoly, in which they face the common (linear) inverse demand function, p = a – b ( x 1 + x 2) where firms produce outputs x 1 and x 2 , selling them at the market price p . The parameters a and b are constant, but undefined. Their cost functions are also linear, with total cost C i = F i + c i x i , so that each firm faces fixed costs F i and constant marginal costs x i .

You may assume that F 1 < F 2 and that c 1 > c 2 .

Your task is to write a report in which you set out the outcome of competition between the firms in these three situations:

a) They make their production decisions simultaneously and without cooperating;

b) They make their production decisions simultaneously while seeking to maximise joint profit; and

c) They make their production decisions sequentially, with firm 1 setting output first.

In each case, you should state expressions for firm outputs, the market price, and firm profits. You should compare firm output and profits. In doing so, comment on the circumstances in which you consider that it would be reasonable to expect firm 2 to agree to cooperate with firm 1, whether by joint output setting, or by conceding market leadership.

(100 marks)

2) Consider the situation where F has an endowment, K , of capital, and G has an endowment, L , of labour. To create value from these endowments, they produce quantities of goods R and S , generating utility from consumption.

The factors of production are perfect complements in production. The production functions are:

R ( K R , L R ) = min(2 K R , L R ) and S ( K S , L S ) = min( K S , 2 L S ). The requirements of market clearing must be fulfilled in equilibrium.

The utility functions are U F = 2ln R F + ln S F , and U G = 2ln R G + ln S G .

Your task is to write a report in which you set out how F and G arrange production and consumption so that there is efficient use of factors in production, and the distribution of goods for consumption completes the Walrasian equilibrium.

You should be aware that since factor inputs are perfect complements, we do not find offer curves when analysing production. You should instead derive a market clearing condition, from which you should be able to obtain the relative price of the factor inputs, and hence the optimal distribution of goods, and then the utility achievable by both consumers, noting how this varies with the ratio of capital: labour endowments.

(100 marks)

3 ) Begin by sketching a diagram showing in state space the endowment for a consumer ( W 0 , W 1), where W S is wealth in state S , with W 0 > W 1 . The probability of state 0 is . The consumer derives utility from wealth W S , U ( W S ) = W S , where 0 < < 1.

Your task is to write a report in which you demonstrate that this consumer is risk averse. Then show that where the consumer is able to trade wealth in state 0 for increased wealth in state 1, expected wealth remains constant along a line whose slope is the odds ratio.

Then, by forming a Lagrangean function, or otherwise, show that if the consumer is offered actuarially fair insurance, she will purchase full insurance. Hence, explain how it is possible for a population whose members face identically, independently distributed risks of incurring loss in state 1 to form a mutual insurance society, which offers full, fair insurance against loss. Explain why the society might be vulnerable to moral hazard among its members.

(100 marks)