Question

Problem 4 [23 marks]
Consider a profit-maximising firm that has the good fortune of being a monopolist. The firm sells output in a domestic market and exports to a foreign market as well. The domestic market demand curve given as ??(?) = 20 − 2?? and the foreign market demand curve is given as ??(?) = 20 − ??. Total output is ? = ?? + ??. The monopolist faces a cost function given by ? = 1 2 ?2 + 20.

a) Derive the firm’s marginal cost and average cost functions and draw these on a diagram. Clearly label the axes and the curves. [3 marks]
b) Derive the firm’s marginal revenue functions. Draw the marginal revenue and the market demand functions on the diagram. Clearly label the curves. [4 marks] Note: If it is easier, you may use separate graphs for the domestic market and the foreign market.
c) Without doing any calculations, will it be optimal for the monopolist to sell its output at the same price in both markets? Explain. [1 mark]
d) Write down the profit maximisation problem faced by the monopoly. What output will be supplied to each market? What price will the monopolist will charge in each market? Clearly label these output levels and prices on your graph. [6 marks]
e) What type of price discrimination is this monopolist using? Explain. [1 mark]
f) What profits will the monopoly make? [2 marks]
Now assume that consumers in the domestic and foreign markets are able to purchase output online, meaning they can order it from either the domestic or foreign market and pay the same price. Hence ?? = ?? = ?.
g) Derive the total market demand faced by the monopolist. [1 mark]
h) What price should the monopolist now set for its output? What quantity will it sell to each market? [4 marks]
i) Will the monopoly’s profits be higher, lower or equal to its profits before the internet? Justify your answer. [1 mark]

Answer 1