Re: MICro: cost curves for two plants

Posted by Amit Goyal on Jun 05, 2013; 1:57pm
URL: http://discussion-forum.276.s1.nabble.com/MICro-cost-curves-for-two-plants-tp7581776p7581799.html

Consider 2 firms facing dd curve P=50-5q where q =q1+q2. The firms' cost functions are
C1=20+10q1 and
C2=10+12q2
a)Suppose that both firms have entered the industry what is the joint profit maximizing level of output?
Joint profit maximizing level of output is given by the following condition:
MC of the firm with lower marginal cost = MR
10 = 50 - 10 Q, this gives us
Q = 4
How much will each firm produce?
Firm 1 will produce 4 units and Firm 2 will produce 0 units.
How would your answer change if the firms have not yet entered the industry?
If the firms have not entered the industry fixed cost is not sunk cost. Only one of the two firms will enter. Firm 1 will produce 4 units if it enters and makes a profit of 30(4)-20-10(4) = 60.
Firm 2 will produce 3.8 units if it enters and makes a profit of 32(3.8) - 10 - 12(3.8) = 66
In this case, its more profitable for the firm 2 to enter and produce 3.8 units.