Question

1. Suppose that the total cost of producing pizzas for the typical firm in a local town is given by C(q)=2q+2q^2.
   1. What is MC?
   2. What is the competitive supply behavior of the typical pizza firm? (i.e.: how much does each firm produce?)
   3. If there are 100 firms in the industry each acting as a perfect competitor, what is the inverse supply function for the entire market?
   4. Suppose that market demand is given by Q^d=1000-50P. What is the market price in equilibrium, how much will be exchanged in the market, how much will each firm produce and what will be the profits for each firm.
   5. Given your answer in d, can you tell whether this is an equilibrium that is sustainable in the long run? If not, what do you think will happen in this market?

Answer 1

a)

C(q) = 2q + 2q²

dC(q)/dq = MC = 2 + 4q

MC = 2 + 4q

b) supply function for a typical pizza firm is given by

P = MC

P = 2 + 4q

P - 2 = 4q

q = (P - 2)/4

c) Since there are 100 firms

So market supply curve Qs = nq

= 100 (P - 2)/4

= 25(P - 2)

= 25P - 50

Qs = 25P - 50

Q + 50 = 25P

P = Q/25 + 2

Thus inverse market supply is P = Q/25 + 2

d)

Qd = 1000 - 50P

Qs = 25P - 50

Qd = Qs (Market equilibrium condition)

1000 - 50P = 25P - 50

1000 + 50 = 25P + 50P

1050 = 75P

P = 1050/75

= 14

Q = 1000 - 50(14)

= 1000 - 700

= 300

Quantity produced by each firm q = (P - 2)/4

= (14 - 2)/4

= 12/4

= 3