The residents of Seltzer Springs, Michigan, consume bottles of mineral water according to the demand function D(p) = 1, 000 − p. Here D(p) is the demand per year for bottles of mineral water if the price per bottle is p.
The sole distributor of mineral water in Seltzer Springs, Bubble Up, purchases mineral water at c per bottle from their supplier Perry Air. Perry Air is the only supplier of mineral water in the area and behaves as a profit-maximizing monopolist. For simplicity we suppose that it has zero costs of production.
(a) What is the equilibrium price charged by the distributor Bubble Up? ________.
(b) What is the equilibrium quantity sold by Bubble Up? ________.
(c) What is the equilibrium price charged by the producer Perry Air? c∗ = ________.
(d) What is the equilibrium quantity sold by Perry Air? D(c∗) = ________.
(e) What are the profits of Bubble Up? πb = ________.
(f) What are the profits of Perry Air? πp = ________.
(g) How much consumer’s surplus is generated in this market? ________.
(h) Suppose that this situation is expected to persist forever and that the interest rate is expected to be constant at 10% per year. What is the minimum lump sum payment that Perry Air would need to pay to Bubble Up to buy it out? ________.
(i) Suppose that Perry Air does this. What will be the new price and quantity for mineral water? ________.
(j) What are the profits of the new merged firm? πp = ________.
(k) What is the total amount of consumers’ surplus generated? How does this compare with the previous level of consumers’ surplus? ________.