# Question: 1 suppose there are two potential customers in the market...

###### Question details

1. Suppose there are two potential customers in the market. One
has demand function D_{1}(p)=10-p . The other has demand
function D_{2}(p)=20-2p. The only firm in this market has
constant marginal cost of 2.

(1) Draw the two demand curves in a graph, with price on the vertical axis and demand on the horizontal axis.

(2) (3rd-degree price discrimination) If the monopoly can identify the two consumers and charge different prices to them, what is the optimal price charged to each consumer? At the optimal prices, is there a relationship between price and elasticity of demand?

2. (2^{nd}-degree price discrimination) Given the market
as described in the above question, suppose the monopolist cannot
identify the two consumers, but he can use a single two-part
tariff.

(1)Find out the optimal fixed fee and per-unit price.

(2)Is it more profitable to serve both consumers or to serve only the one with higher demand?

3. Suppose there are two firms competing in a market. Both firms
produce identical products. Firm One is an efficient firm and has
total cost function C_{1}=5q_{1}; Firm Two is a
less efficient firm and has total cost function
C_{2}=10_{q2}_{ }. Market
demand for this product is given by Q=150-2p.

If two firms compete in quantities of production, find out the best response function of each firm and the equilibrium output level of each firm.