Question

41.4 A market has an inverse demand func- tion p = 100 – 2Q and four firms, each of which has a constant marginal cost of MC = 20. If the firms form a profit-maxi- mizing cartel and agree to operate subject to the constraint that each firm will produce the same output level, how much does each firm produce?

Answer 1

Answer:

Inverse demand function P= 100- 2 Q and four firms

constant marginal cost of MC = 20.

the firms form a profit maximizing cartel and agree to operate subject to the constraint that each firm will produce the same output level.

The inverse demand function of the market is given as P = 100 - 2Q and it is also given that there are four firms in total facing same constant marginal cost (mc) of $20.

now , if they decide to form a cartel then they would collectively produce the quantity at which the combined (or) market's MR equals the MC , where MR is the first differentiation of the TR . Mathematically ,

MR = 100 - 4 Q, and the equilibrium condition is :

100-4 Q = 20

Q = 20

Now , since it is given hat all firms produce the same amount hence a single firm produces a quantity of 5 units (i.e $\frac{20}{4}$ )

Note: MR is obtained by first differentiation of TR with respect to q , as shown below :

TR = p* q

= q* (m -aq)

= m * q -a*q*q

MR = $\frac{dTR}{dq}$

= m - 2aq.