Question

4. The market demand for pizza in a small town is estimated to be P 250 20 This market is served by two firms: 1 and 2. Firm 1 has costs of TC1 20q1 while firm 2 is more cost efficient, with costs of TC2 10q2 (16 marks total) a. If the two firms set prices and compete à la Bertrand, what is the (4 marks) (2 marks) equilibrium price of pizza? What is the output for each firm? b. What profit does each firm make? c. In a hypothetical scenario, suppose firm 1 did not exist - so firm 2 operates as a monopolist and serves the entire market. What is the monopoly price, output and profit of firm 2 under this scenario? 4 marks) d. Under asymmetric cost Bertrand competition, the more efficient firm serves the entire market. How is this different to firm 2 operating asa monopolist? Explain why the profit for firm 2 that you have previously (6 marks) calculated in parts b) and c) are different.

Answer 1

a..)

Bertrand model says that firms in market compete on prices and tend set price and output where P = MC.

P = 250 – 2Q

TC1 = 20Q

TC2 = 10Q

Firm 1 cost is larger than cost of firm 2. Thus, firm 1 is inefficient. It will not stay in market.

MC2 = 10

Equilibrium:

P =MC

250 -2Q = 10

240 = 2Q

Q = 240/2

= 120

P =10

Output of firm 1 = 0

Output of firm 2 = 120

b)                  

Profit of firm 1 = 0

Profit of firm 2 = TR – TC

= 10*120 -10*120

= 0

c)

Monopolist condition for profit maximization; MR = MC

P = 250 - 2Q

TR = P *Q

= 250Q – 2Q^2

MR = 250 – 4Q

MC = 10

MR = MC

250 – 4Q =10

240 = 4Q

Q = 240/4

= 60

P= 250 – 2(60)

= 250 – 120

= 130

Profit = TR – TC

= 60*130 – 10*60

= 7200

d)

Monopoly market maximizes the profit of firm. Firm profit is positive in case of monopoly market but in case of two firms model where one firm is inefficient, profit is zero. Firm can behave like monopoly in such market as it would incentivize entry of new firm.