Question

In an industry with inverse demand curve pequals420minus2​Q, there are five ​firms, each of which has a constant marginal cost given by MCequals20. If the firms form a​ profit-maximizing cartel and agree to operate subject to the constraint that each firm will produce the same output​ level, how much does each firm​ produce? Each firm will produce qequals nothing units. ​(Enter your response as a whole​ number.)

Answer 1

Answer: 20 units.

Explanation:

Given that,

Inverse demand curve: P = 420 - 2Q

There are five firms and each of the firm has a constant marginal cost.

Marginal cost (MC) = 20

Profit maximizing output is produced by the firms is at a point where the marginal cost is equal to marginal revenue.

P = 420 - 2Q

Total revenue(TR) = PQ

                              = 420Q - 2$Q^{2}$

Differentiating TR with respect to 'Q'

Marginal revenue(MR) = 420 - 4Q

MR = MC

420 - 4Q = 20

Q = $\frac{400}{4}$

Q = 100

Therefore, output produced by the industry is 100 units.

Per-firm production = $\frac{Total\ Production}{Number\ of\ firms}$

                                 =  $\frac{100}{5}$

                                 = 20 units

Hence, each firm produces 20 units.