Question

1. (2.5 marks) In the market of cars, there are two firms operating. The Industry Demand Curve

is a function of the outputs being produced by both firms, and is given as: P = 240–(X1+X2),
where X, and X2 are the outputs of Firm 1 and Firm 2 respectively. The Total Cost faced
by Firm 1 is TC1 = 20.X1 and by Firm 2 is TC2 = 20X2. Each firm maximizes its own profit
by choosing its own output, while taking the output of the other firm as given. Write down
the profit function of each firm, and find the level of output for each firm that will maximize
its profit. What are the corresponding levels of prices and profits for each firm?​

Answer 1

For each firm, the output level to maximize profit is 220 unit when the output of the other is 0.

The corresponding price level of each firm: P = 20

The corresponding profit for each firm: 4,400

Step-by-step explanation:

1. Firm 1:

- TC1 = 20 x X1 => MC1 = 20

- Revenue of firm 1 for X1 unit: P x X1 => MR = P

Firm 1 maximizes profit when MR = MC => P = 20

With P = 20. the demand function => X1 + X2 = 220 => X1 = 220 - X2

X1 maximizes when X2 is the minimum at 0.

If X2 = 0 => X1 = 220 => Profit of firm 1: P x X1 = 20 x 220 = 4,400

2. Firm 2:

Similarity, Firm 2 maximizes profit when MR = MC => P = 20

X2 maximizes when X1 is the minimum at 0.

If X1 = 0 => X2 = 220 => Profit of firm 2: P x X2 = 20 x 220 = 4,400