Question

Question 1

Part A

Consider the market for fixies in Somerville. (A fixed-gear bicycle (or fixed-wheel bicycle) is a bicycle that has no freewheel, meaning it cannot coast, because the pedals are always moving when the bicycle is in motion. They are popular among hipsters in Cambridge.) The supply side of the market is perfectly competitive and is composed of fixie producers, who each have a long run cost curve C(q)=2q+5q^2. The demand side of the market comprises all the hipsters who live in Somerville (since they do not have fixies yet, their travel costs are really high so they only buy their fixies in Somerville). Market demand is Q^d=8.5−2p. Afraid that all commercial real estate in Somerville is going to be taken over by fixies producers, the mayor of Somerville caps the maximum number of firms to 25.

What is the long run equilibrium price in the market for fixies?

p=

What is the total quantity demanded?

Q^d=  

What is the total quantity supplied?

QS=  

What is the quantity produced by each firm? (Assume, contrary to fact, that you can produce fractions of fixies in Somerville.)

q=  

What is the profit earned by each firm?

π=  

Part B

Elections in Somerville are coming up. The mayor decides to try and win some votes from hipsters. After hearing their complaints about how the price of fixies is too high, he introduces a price ceiling equal to 2.5 (but he keeps the maximum number of licenses set at 25).

What is the quantity produced by each firm?

What is the profit that each firm earns?

What is the total quantity demanded?

What is the total quantity supplied?

What is the equilibrium quantity transacted?

Under a price ceiling equal to 2.5, what is consumer surplus?

CS= ?

What is producer surplus?

PS= ?

Show this in a graph.

What happens to total welfare?

a.The effect on total welfare is ambiguous

b.Total welfare is lower than before

c.Total welfare is unchanged

d.Total welfare is higher than before

  

Suppose instead implementing of a price ceiling, the mayor decides to increase the number of licenses for fixie producers to 70.

What is the quantity produced by each firm?

What is the profit that each firm earns?

What is the total quantity demanded?

What is the total quantity supplied?

What is consumer surplus under the new number of licenses for fixie producers?

What is producer surplus?

Show this in a graph.

(The graph is not graded. It is for your understanding.)

Is total welfare higher or lower than in the case where the number of firms is capped at 25 and there is no price cap?

a.The effect on total welfare is ambiguous

b.Total welfare is lower than before

c.Total welfare is unchanged

d.Total welfare is higher than before

Answer 1

PART A

i)

Equilibrium condition is MC = P

Market supply would be , multiply this q by 25(number of firms)

Longrun equilibrium arises where Q^d = Q^s

Therefore, longrun equilibrium where market fixes price is $3

ii)

Substitute the value of p in the above equation -

iii)

Substitute the value of p in the above equation

iv) To find q

Therefore, quantity produced by each firm is q = 0.1

v) To Find profit using formula -

Therefore , profit is 0.05 for each firm.

PART B

i)

Substitute p as 2.5 now

Therfore, total quantity demanded is 3.5

ii)

Substitute value of p as 2.5

Therfore, total quantity suplied is 1.25

iii) Quantity produced by each firm is -

iv) Profit that each firm earn -

Therefore, profit for each firm is .0125

v) There is no equilibrium quantity at this situation . We have Shortage at this situation

vi)

From the graph above -

Consumer surplus =

vii) Producer surplus is -

viii)

Earlier Total welfare before price ceiling is

Total welfare after pprice ceiling is , from part (vi) and (vii)

Therfore, total surplus has declined after price ceiling

Hence , option b is correct