Question

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 ? = 0.5y²+20

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

e) Since the monopolist is charging different prices for the same product in different markets, this is an example of third degree price discrimination.

f) Profits for the monopoly are given by:

Using the values of as 0 and 5, we have:

g) Now,

New demand is given by aggregating the individual demands in two markets:

h) The monopolist's profit is given by:

The monopolist's objective is to maximize profit with respect to y:

Output in each market is given by:

i) The monopolist's profit for the above values of y and p is:

Profits where the monopolist is forced to charge the same price in both markets is lower than the profit when the monopolist is free to price discriminate. This gives further proof that a monopolist can increase his profit by indulging in price discrimination.