In the market of identical firms, the market demand function is Q=1000-1000P. The marginal cost is the same for all firms, mc=0.28.
a) Characterize what is the firm’s optimal output and price when there is a single firm in the market.
b) Characterize what is the firm’s optimal output and price when the market is perfect competition.
c) Characterize what is the Cournot Duopoly Equilibrium and firms’ best response function when there are two identical firms in the market and compete over quantities simultaneously. Show the best response functions and the Equilibrium both mathematically and graphically.
d) Characterize what is the Cournot multi-firm Equilibrium and firms’ best response function when there are n identical firms in the market. Show the best response functions and the Equilibrium both mathematically.
e) Characterize what is the Stackelberg Duopoly Equilibrium and firms’ best response function when there are two identical firms in the market and compete over quantities sequentially. Show the best response functions and the Equilibrium both mathematically.
f) Characterize what is the Stackelberg multi-firm Equilibrium and firms’ best response function when there are n identical firms in the market. Show the best response functions and the Equilibrium both mathematically.
g) Characterize what is the Bertrand Duopoly Equilibrium and firms’ best response function when there are two identical firms in the market and compete over price simultaneously. Show the best response functions and the Equilibrium both mathematically and graphically.
h) Now consider two firms in the Bertrand Competition. Each firm’s maximum output capacity is 360. That is each firm’s average and marginal cost curves are horizontal at 28 cents up to 360 units, and then the average and marginal cost curves are vertical (the cost of the next unit is infinite). With limited capacities, is the original Bertrand Equilibrium still equilibrium? Explain if an equilibrium price exists and why