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

Given

MCi=5+0.025qi

In perfect competition, a firm sets its output level such that P=MCi

So, supply curve of a perfectly competitive firm is given by

P=MCi=5+0.025qi

or

P=5+0.025qi

40P=200+qi

qi=-200+40P

a)

Since there are 50 firms in the market, Industry supply is given by

Qs=50qi=50*(-200+40P)=-10000+2000P

b)

Given P=50-0.005Q

or

200P=10000-Q

or Q=10000-200P

Set Quantity demanded = quantity supplied for equilibrium

10000-200P=-10000+2000P

2200P=20000

P=100/11

Quantity demanded=10000-200*(100/11)=8181.82

Quantity supplied=-10000+2000*(100/11)=8181.82

Equilibrium price=$100/11 per bottle

Equilibrium quantity=8181.82 hundred bottles or 818182 bottles)

c)

Let us see at what price supply becomes zero

Qs-10000+2000P=0

or P=$5

Producer surplus =1/2*((100/11)-5)*(8181.82-0)=$16735.54 hundred or $1673554

Producer surplus of each firm=1673554/50=$33471.08

d)

Let us see the price where quantity demanded is zero

P=50-0.005Q=50-0.005*0=$50

Consumer surplus=1/2*(8181.82-0)*(50-(100/11))=$167355.41 hundred or $16735541