Question

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?

p∗ = (1,000+c)/2

(b) What is the equilibrium quantity sold by Bubble Up?

D(p∗) = (1,000−c)/2

(c) What is the equilibrium price charged by the producer Perry Air?

c∗ = 500.

(d) What is the equilibrium quantity sold by Perry Air? D(c∗) = 250.

(e) What are the profits of Bubble Up?

πb = (500−250)(750− 500) = 2502.

(f ) What are the profits of Perry Air? πp = 500 · 250.

(g) How much consumer's surplus is generated in this market?

CSe =2502/2.

(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? 10 × 2502.

(i) Suppose that Perry Air does this. What will be the new price and

quantity for mineral water? p∗ = 500 and D(p∗) = 500.

(j) What are the profits of the new merged firm? πp = 5002.

(k) What is the total amount of consumers' surplus generated? How does

this compare with the previous level of consumers' surplus?

CSi = 5002/2 > CSe.

I dont understand part e - k especially part e where does formula come from please help

Answer 1