Question

 

Suppose there are two firms, Firm 1 and Firm 2, who produce identical goods. Together, they face the following market demand.

Q=140-P

Assume both firms have a marginal cost of 20, so MC=20.

a. Monopoly: If the two firms could collude and act like a monopoly, what is the total quantity produced and what is the price?

b. Bertrand Competition with Identical Goods: Now assume that the firms simultaneously choose their price. What is the quantity produced and at what price?

c. Cournot Competition with Identical Goods: Now assume that the firms simultaneously choose their quantity. What is the total quantity produced and at what price?

Answer 1

As they collude and act as a monopoly and accori=ding to profit maximizing condition of a monopoly a firm should Produce that quantity at which MR = MC

Here MC = 20

MR = dTR/dQ = d(PQ)/dQ = 140 - 2Q

=> 140 - 2Q = 20

=> Q = 60 and hence P = 140 - Q = 80

Hence,  total quantity produced = 60 and price = 80

(b) Suppose Firm1 charges price greater than MC then Firm 2 will charge price just below Firm 1 and greater than MC and by doing that It will have all the market share and hence Firm 1 will not charge Price > MC = 20. Similarly Firm 2 will also not charge Price > 20. Now It is straightforward that No firm will ever charge Price < MC because it will result in Loss.Hence Now Firm 1 will left with P = MC = 20. Corresponding to that Firm 2 cannot charge P > MC because then his quantity sold = 0 and Hence He will also charge Price = MC = 20.

Hence Both are charging Price = MC = 20

Hence Q = 140 - P = 120

Hence  total quantity produced = 120 and price = 20