There are two suppliers of distilled water, called A and B. it is considered to be an homogenous good. Let Pa and Pb denote the price per litter and qA and qb the quantity sold by ?rms A and B, respectively. Suppose that municipality provides all the water for free, so ?rms don‘t bear any production cost. Formally, assume that cA = cb = 0. The inverse demand function fordistilled water is given by
P = 12 -Q/3 = 12 – (qA + q3)/3,
Where Q = qA + qb denotes the aggregate industry supply of distilled water
a) Suppose the ?rms compete in quantities (production levels). Assume that ?rm A sets its output level qa ?rst. Then, ?rm B observes qA and sets its output level qb. Compute the quantity produced by each ?rm in this two-stage game. Also, compute the resulting market price, p, and the ?rms’ equilibrium pro?t levels, for a and b (using backward induction)
b) Suppose the ?rms compete in prices. Assume that ?rm A sets its price p, ?rst. Then, ?rm B observes pa, and sets its price pb to maximize pro?ts. Solve for the equilibrium price strategies of this game.
