Subject: Economics / General Economics
Winter 2017, Assignment 2
1. (30 pts) Consider the following technology: c(yi ) = yi2 + 2yi + 4.
Many …rms have access to this technology, in fact so many that there is not room for
all to pro…tably operate in the industry. The market demand for the product is given
by, P = 30 Y , where Y is the market quantity. Assume also that these …rms are
price takers, and entry / exit is costless.
(a) What is the long-run free entry equilibrium per-…rm quantity produced by each
…rm in the industry? Explain (10 pts)
(b) Do you have enough information to determine the number of …rms who operate
in such a long-run free entry equilibrium? If so, what is the number and justify
your solution. If not, explain what other information you would need. (10 pts)
(c) Is the price-taking behavioral assumption sensible for this industry? Explain (10
2. (40 pts) A monopolist has access to an industry with market demand D(p) = 24
and its cost function is c(y) = y 2 . 2p (a) Determine its pro…t – maximizing output level y and the market price p(y ). (5
(b) Calculate the monopolist’s pro…t. (5 pts)
(c) Compute the point-elasticity of demand at the pro…t maximizing output level y .
Would the monopolist ever operate at a point elasticity j"(y)j < 1? Explain. (5
(d) Suppose this monopolist is regulated to produce at that quantity where price
equals average cost. Calculate the quantity the monopolist will produce and the
price it will charge given this regulatory scenario. (5 pts)
(e) Calculate the pro…t for the monopoly if it is regulated to produce where price
equals average cost. Explain. (5 pts)
(f) Suppose this monopolist is regulated to produce at that quantity where price equals
marginal cost. Calculate the quantity the monopolist will produce and the price
it will charge given this regulatory scenario. (5 pts)
(g) Calculate the pro…t for the monopoly if it is regulated to produce where price
equals marginal cost. (5 pts)
(h) Is this is a natural monopoly? Explain. (5 pts) 1
3. (30 pts) A monopoly is facing two types of consumers. Type 1 consumer has relatively
low demand given by pL (y L ) = 4 y L and type 2 consumer has relatively high demand
given by pH (y H ) = 8 y H . The …rm’s marginal cost is M C = 0.
(a) Suppose the two types are observable and the …rm o¤ers two packages using the
two-part tari¤s pricing scheme (it charges a fee as well as a per unit price). What
quantities and fees maximize the …rm’s pro…t? Show these outcomes on graphs.
(b) Now suppose that the …rm is unable to distinguish the types, would the pricing
scheme from part (a) work if the …rm kept o¤er the same quantities y L and y H ?
(c) If the …rm is unable to distinguish between the two types, but wants to o¤er the
two di¤erent quantities you found in part (a), what fees should it charge to the
di¤erent types of consumers? (8 pts)
(d) Based on the pricing scheme used in part (c), calculate the consumer’s surplus
(for both types) and the producer’s surplus. Do we have DW L in the market? (8