Suppose Baldwin and Steinway are the only producers of baby blue baby grand pianos. They each have constant marginal costs of $1,000 per piano. Market demand is Q = 100 P/100 and total quantity supplied is the sum of each company's supply: Q = qB + qS.

a) Suppose Baldwin announces its production of pianos, qB, first.

i-How many pianos should Steinway produce given some qB?

ii-How many pianos should Baldwin produce?

iii-What will be the price and total supply of pianos?

b) Now suppose they must decide their output simultaneously.

i-How many pianos should Steinway produce given some qB?

ii-How many pianos should Baldwin produce given some qS?

iii-Plot those best response functions.

iv-What will be the price and total supply of pianos?

c) Finally suppose the two manufacturers can collude and form a cartel that shares profits and production evenly.

i-How many pianos should they produce together and what price will they charge? Calculate their profits.

ii-If Steinway breaks the cartel in secret (Baldwin produces the cartel quantity) how much will Steinway choose to produce? Calculate the new price and profits for each firm.

iii-Why might Steinway choose not to break the cartel. (Give an argument about profits, not violent reprisals.)