Question

3. Consider an industry with market demand characterized by: P = 6300 - 32. Suppose the market is currently served by a large collection of firms all with constant marginal costs: MC = 4200. (a) 2 points What will be the initial price in this market? (b) 6 points Suppose one firm is able to innovate and drive their own costs down to MC = 3600. What price and quantity would this firm want to set to maximize profits as a single-price monopolist if it were to have the market to itself? (c) 8 points Suppose one firm is able to innovate and drive their own costs down to MC = 3600. What price and quantity will this firm actually set and what are the firm's profits? Is this a large or small innovation? (d) 8 points Given that there's a large collection of firms in the market and given that one firm has innovated to reduce its costs, what will be the output and profits of this innovating firm when it chooses to practice first degree price discrimination after having driven its costs down to MC = 3600?

Answer 1

a.)

The condition in which this market is working is perfect competition, and hence the equilibrium conditions are obtained by equating the marginal cost to the marginal revenue. In a perfectly competitive market, the Price is the AR which is the MR as well.

We have -

6300 -38 - 4200

2100 3Q

2100 700 3

b.)

For a monopolist, the quantity is found by equating MC and MR and the price is found by plotting that quantity back into the AR equation

$TR = AR \times Q = 6300Q - 3Q^{2}$

$MR = \frac{d}{dQ}(TR) = 6300-6Q$

Given MC = 3600

Hence we get -

$6Q=2700$

$Q=\frac{2700}{6}=450$

$P=6300-3(450)=4950$