1) Alice lives in a town with only one movie rental store.

Suppose Alice's demand for movie rentals per month is Q = 16 2P.

The movie store currently charges $5 per movie, but is thinking of adding a flat monthly cardholder fee, and dropping the price to $2 per rental.

At this new price, what is the largest cardholder fee that Alice will pay?

If the rental store has a constant marginal cost of $2, which strategy is more profitable?

2) A monopolist faces a demand curve given by, D = 100 p with the inverse demand curve equal to, p = 100 y and MR = 100 2y.

The monopolist's total and marginal cost functions are: T C = 700 + 20, MC = 20.

a) Calculate the monopoly output level, the monopoly price, and the profits of the firm.

b) Draw a diagram to illustrate your answers to part a). Calculate the deadweight loss from this monopoly.

c) Explain why this market might be considered to be a "natural" monopoly

d) Illustrate and explain the problem that emerges when the government regulates the monopolist by imposing marginal cost pricing.

3) Consider a simultaneous quantity choice (Cournot) game between 2 firms. Each firm chooses a quantity, q1 and q2 respectively.

The inverse market demand function is given by P(Q) = 1434 2Q where Q = q1 + q2.

Firm 1 has cost functions, T C(q1) = 3(q1)^2 and MC(q1) = 6q1

Firm 2 has cost functions, T C(q2) = 12(q2)^2 12q2 MC(q2) = 24q2 12

Each firm wishes to maximise its profit. [Note: the Cournot game is an example of the continuous strategy games we studied in the game theory topic.]

a) Set up the profit function for Firm 1 and Firm 2.

b) You know that MR1 = 1434 4q1 2q2 and MR2 = 1434 2q1 4q2. Find the best response functions for Firms 1 and 2.

c) Find the Nash equilibrium to this game.

d) Find the (1) total market quantity, (2) price, and (3) profit for each firm.