Question 1. Collusion
Assume a market for a homogenous good with the following demand curve:
Q = 1000 - 10P
where Q represents total industry output.
There are two firms competing in the market, with constant and identical marginal costs of production of £30. They compete on the basis of quantity.
a) Find the Nash equilibrium quantities, prices and profits of the Cournot game.
b) Solve for quantities, prices and profits under the collusive outcome.
c) Solve for quantities, prices and profits when one firm produces the collusive output and the other deviates (or cheats).
d) Explain why the firms face a prisoners' dilemma.
Assume that the game is repeated infinitely and that each firm has a discount factor, δ = 0.5.
e) Is collusion sustained if each firm assumes that their competitor will follow the Grim Trigger Strategy?
f) Consider a ‘stick-and-carrot' strategy whereby each firm promises to punish deviation by producing an output of 500 units in the following period, but will subsequently revert to the collusive output.
i. Is collusion sustained under this strategy?
ii. Is such a strategy credible?
g) What implications do your results have for competition policy?
2. Price Discrimination
Assume that there is a single monopoly supplier of gadgets, but there are two distinct types of consumers, with the following individual demand curves:
Type α: qα = 100 - 2pα
Type β: qβ = 80 - 3pβ
There are five consumers of type α and ten of type β. All consumers are price takers. The firm's marginal cost of production is £1, and there are no fixed costs.
a) Suppose the monopolist can identify consumers according to their type. What price should the firm charge each type of consumer in order to maximize its profits? Calculate the following for each consumer, and in aggregate: (i) the firm's profits, (ii) consumer surplus and (iii) deadweight loss.
Suppose now that a law is passed which makes it illegal to offer different prices to different consumers.
b) Derive and graph the aggregate demand curve and aggregate marginal revenue curve.
c) Calculate the profit maximising uniform price, as well as the quantity, profits, consumer surplus and dead weight loss under the uniform price.
The law does not prohibit two-part tariffs, as long as they are available to all consumers. The firm decides to offer the following two pricing options:
Option A: Pay a fixed contract fee of £800 and then £5 per individual unit Option B: A fixed contract fee of £400, and a variable price per unit of £10
d) Show that these two-part tariffs are both participation compatible (i.e. that both types of consumer choose to buy) and incentive compatible (i.e. that each type chooses a different option).
e) Show that the firm prefers the two-part tariffs to the uniform price.
f) Compare social welfare and the well-being of each of the agents (firm, high valuation consumer, and low valuation consumer) under:
i. group pricing (part a),
ii. uniform pricing (parts b,c), and
iii. menu pricing (parts d,e).
Explain intuitively what drives these results?