Firms 1 and 2 produce an identical product and serve the market described by the demand P=100-Q, where Q=Q1+Q2. Firms compete by choosing their output levels. Firm 1’s
total cost function is TC(Q1)=100+20*Q1. Firm 2’s total cost function is TC(Q2)=100+10*Q2.
The market demand and cost structure are common knowledge, and Firm 2 moves first.
a. How many units of output will each of the firms produce in equilibrium? (5 points)
b. What is the equilibrium price and equilibrium profit of each firm? (3 points)
c. Now assume that firms compete by setting prices rather than quantities and can change
their prices in finely divisible (infinitely small) increments. Firm with the lowest price
gets all the market, and firms split the market if there is a tie. Find the equilibrium market
price(s), and market quantity in this game and explain your result. (3 points)
d. What are the individual firms’ output levels and profits in Part c? (2 points)
e. Will your answers in all parts above change if the firms were to move simultaneously
rather than sequentially? If so, please provide the new prices, quantities, and profits
where appropriate. (6 points)