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,
Y = 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,
TC = 700 + 20y and 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. [Hint: you need to work out the perfectly competitive quantity and price. The diagram will help you work out how to calculate the DW L using the simple geometry of triangles and rectangles.]
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.
e) If the government regulates the monopolist by imposing average cost pricing, what will be the monopolist's price and quantity? Draw a diagram to illustrate your answers. Explain the problem that exists with this average cost pricing. [Note: this is a trickier part than the others, so don't worry if you can't do it. If this question came up in the exam, I would miss out e) and have a)-d), making you feel a bit better! To answer it, you have to set p = AC and solve for output. It requires solving a quadratic equation with 2 potential output levels and working out which output level is the one the monopolist would produce. The quadratic equation is a simple one, but if you are not comfortable with maths, even its mention probably sounds like a nightmare.
