Problem 1: Firm A is the dominant firm in a market where industry demand is given by Qd = 48-4P. There are four “follower” firms, each with long-run marginal cost given by MC= 6 + Qf. Firm A’s long run marginal cost is 6.
a. Write the expression for the total supply curve of the followers (qs) as this depends on price. (Remember, each follower acts as a price taker.)
b. Find the net demand curve-facing firm A. Determine A’s optimal price and output. How much output do the other firms supply in total?
Problem 2: Suppose instead that the firms in Problem 9 compete by setting quantities rather than prices. All other facts are the same. It is possible to rewrite the original demand equations as P1= [150-(2/3)Q2] – (4/3)Q1 and P2= [150 – (2/3)Q1] –(4/3)Q2. In works, increases in the competitor’s output lowers the intercept of the firms’ demand curve.
a. Set MR1=MC to confirm the firm 1”s optimal quantity depends on Q2 according to Q1 = 45-.25Q2. Explain why an increase in one firms’ output tends to “deter” production by the other.
b. In equilibrium, the firms set identical quantities: Q1-Q2. Find the firms’ equilibrium quantities, prices and profits.
c. Compare the firms’ profits under quantity competition and price competition (problem 9). Can you provide an intuitive explanation for why price competition is more intense (i.e. leads to lower equilibrium profits)?
Problem 3: Two firms produce differentiated products. Firm 1 faces the demand curve Q1 = 75 –P1 + .5P2. (Note that a lower competing price robs the firm of some, but not all sales. Thus price competition is not as extreme as in the Bertrand model.) Firm 2 faces the analogous demand curve Q2 = 75-P2 + .5P1. For each firm, AC=MC = 30.
a. Confirm that firms 1’s optimal price depends on P2 according to P1= 52.5 + .25P. (Hint” set up the profit expression Profit1= (P1-30)Q1 = (P1-30) (75-P1 + .5P2) and set Mprofit = profit1/P1 =0 to solve for P1 in terms of P2. Alternatively, set MR1= MC and solve for Q1 and then P1 in terms of P2.
b. Explain why a lower price by its competitor should cause the firm to lower its own price.
c. In equilibrium, the firms set identical prices: P1=P2. Find the firms’ equilibrium prices, quantities and profits.