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 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.)