There are two movie theaters in the town of Harkinsville:
Modern Multiplex, which shows first-run movies, and Sticky Shoe, which shows
movies that have been out for a while at a cheaper price. The demand for movies
at Modern Multiplex is given by while the demand for movies at Sticky Shoe
prices are in dollars and quantities are measured in hundreds of moviegoers.
Modern Multiplex has a per-customer cost of $4, while Sticky Shoe has a per
customer cost of only $2.
(a) From the demand equations alone, what indicates
whether Modern Multiplex and Sticky Shoe offer services that are substitutes or
(b) Write the profit function for each theater in terms
of PSS and PMM. Find each theater’s best-response rule.
(c) Find the Nash equilibrium price, quantity, and profit
for each theater.
(d) What would each theater’s price, quantity, and profit
be if the two decided to collude to maximize joint profits in this market? Why
isn’t the collusive outcome a Nash equilibrium?