Question

Assume that the market for bottled polar iceberg water is perfectly competitive, with market inverse demand given by ? ?(?) = 50 − 0.005?, price measured in dollars per bottle, and ? measured in hundreds of bottles. The short-run marginal cost curve for a typical bottled polar iceberg water producing firm is ??? (?) = 5 + 0.025?? , with ??? in dollars per bottle and ?? in hundreds of bottles. 1.a. If there are 50 identical firms, determine the industry supply function. 1.b. What is the market equilibrium quantity of bottled polar iceberg water, and what is the equilibrium price? 1.c. At this output level, what is the typical firm's producer surplus? 1.d. What is consumer surplus?

Answer 1

(1.a)

A single firm's short run supply function is its MC function, therefore

Firm's supply function: P = 5 + 0.025q

There are 50 firms, so industry output (Q) = 50 x q

q = Q/50

P = 5 + (0.025 x Q/50)

P = 5 + 0.0005Q (Industry supply function)

(1.b)

In market equilibrium, market demand equals market supply.

50 - 0.005Q = 5 + 0.0005Q

0.0055Q = 45

Q = 8,182 (hundreds) (Considering integer value only for number of bottles)

P = 50 - (0.005 x 8,182) = 50 - 40.91 = $9.09

(1.c).

q = Q/50 = 8,182/50 = 164 (hundreds) (Considering integer value only for number of bottles)

From MC function, when Q = 0, P = 5 (Vertical intercept of MC curve)

Producer surplus = Area between MC curve and price ($' hundreds) = (1/2) x (9.09 - 5) x 164 = 82 x 4.09

= 335.38

(1.d)

From demand function, when Q = 0, P = 50 (Vertical intercept of demand curve)

Consumer surplus = Area between demand curve curve & price ($ hundred) = (1/2) x (50 - 9.09) x 8,182 = 4,091 x 40.91

= 167,362.81 (Total market CS)