Question

A firm has a monopoly in the market for match boxes. In order to produce Q match boxes, it

costs the firm C(Q) = 2Q2

.

(a) Find the marginal cost of producing a match box for this firm. (2 marks)

(b) The demand for match boxes is Q =12 − 0.25P. Find the level of output that maximizes the

firms’s profits. What price is the firm charging? (4 marks)

(c) What level of output and price would maximize total surplus in the match box market? Hint:

Find competitive market output level and price. (3 marks)

(d) What is the deadweight loss from monopoly power of the firm?​

Answer 1

Monopoly MC = 4Q , Profit maximising output Q = 4 , Profit maximising Price P = 32

Step-by-step explanation:

• C (Q) = 2Q^2

Marginal Cost MC = d C / dQ = 4Q

• Q = 12 − 0.25P

P = (12 - Q) / 0.25

P = 48 - 4Q

TR = PQ = 48Q - 4Q^2

Marginal Revenue MR = d TR / dQ = 48 - 8Q

• Producer equilibrium at Marginal Revenue MR = Marginal Cost MC

48 - 8Q = 4Q

12Q = 48

Q = 4

P = 48 - 4Q = 48 - 16

P = 32