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(x1 + x2) where firms      produce outputs x1 and x2 , 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 Ci = Fi + cixi, so that each firm faces fixed costs Fi and constant marginal    costs xi.

You may assume that F1 < F2 and that c1 > c2 .

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(KR, LR) = min(2KR, LR) and S(KS , LS) = min(KS , 2LS). The requirements of market clearing must be fulfilled in equilibrium.

The utility functions are UF = 2ln RF + ln SF, and UG = 2ln RG + ln SG .

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

Questions with answers in red

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(x1 + x2) where firms      produce outputs x1 and x2 , 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 Ci = Fi + cixi, so that each firm faces fixed costs Fi and constant marginal    costs xi.

You may assume that F1 < F2 and that c1 > c2 .

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)

Students should realise that they are being asked to explore the model of competition in quantities, in which firms have a degree of monopoly power. The novel element of this question is the introduction of fixed costs, and good answers will note that with firm 2 having higher fixed costs, but lower marginal costs, when firm output is high enough, firm 2 has lower average costs.

Answers should demonstrate that:

- in Cournot competition, firm 2’s lower marginal cost means that it produces more than firm 1, but that it may make a smaller profit than firm 1 because of its higher fixed costs.

- when forming a cartel, firm 2’s lower marginal cost effectively means that it pays firm 1 to cease production, while meeting its fixed costs

- in Stackelberg competition, firm 1 chooses its output so that firm 2 chooses the output on its reaction function where firm 1 maximises its profits. Firm 1 can now produce more than firm 2, and make greater profits.

Good answers will consider the advantages which firm 2 possesses, arguing that while firm 1 might benefit initially from incumbency, that as market demand increases, firm 2 has the capacity to serve the market at lower average cost than firm 1. A cartel arrangement seems unlikely to survive given firm 2’s cost

advantages (and good answers may relate that to the challenge of firm 1 imposing punishment on firm 2), and if we think of fixed costs as existing in the short run only, we expect to see firm 1 having to adapt to the new competition, or leave the market.

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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(KR, LR) = min(2KR, LR) and S(KS , LS) = min(KS , 2LS). The requirements of market clearing must be fulfilled in equilibrium.

The utility functions are UF = 2ln RF + ln SF, and UG = 2ln RG + ln SG .

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)

Students should recognise the Leontief production functions, and that for market clearing in the factor markets, the output expansion paths for goods R and S intersect, giving the relative factor prices and the marginal costs of both goods. Good answers will explain that with these considerations, the production possibility frontier will consist of two linear segments, with a corner where there is full employment of resources.

Taking the ratio of marginal costs to be the marginal rate of transformation, answers should note that this is not well defined at the corner, and so will concentrate on obtaining the constrained maximum in exchange for F and G, given outputs and factor incomes. Given the form of the utility functions, 2/3 of expenditure will be on good R and 1/3 on good S

Good answers will obtain expressions for relative factor prices from the full employment condition, and hence will obtain expressions individual income, obtaining the Walrasian income as the intersection of offer curves.

3)  Begin by sketching a diagram showing in state space the endowment for a         consumer (W0 , W1), where WS is wealth in state S, with W0 > W1 . The probability