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Scenario: Two Identical Firms
Two identical firms make up an industry in which the market demand curve is represented by Q = 5 000 - 4P,where Q is the quantity demanded and P is the price per unit.The marginal cost of producing the good in this industry is constant and equal to $650.Fixed cost is zero.
-(Scenario: Two Identical Firms)Use Scenario: Two Identical Firms.When the firms collude and produce the profit-maximizing output,what is the profit earned by each firm if they split production equally?

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First, we need to determine the profit-maximizing output when the firms collude. This occurs where the total industry output is produced at the point where marginal revenue (MR) equals marginal cost (MC). Since there are two identical firms, each firm would produce half of the total output.

To find the profit-maximizing output, we first need to find the market price by solving the demand equation for P:

Q = 5 000 - 4P

4P = 5 000 - Q

P = (5 000 - Q)/4

If each firm produces half of the total output, then each firm's output would be:

Q/2 = (5 000 - 4P)/8

Since the marginal cost is constant at $650:

MC = $650

To find each firm's profit, we need to calculate total revenue (TR) and total cost (TC), and then subtract TC from TR:

TR = P x Q/2

TC = MC x Q/2

Profit = TR - TC

Profit = (P x Q/2) - (MC x Q/2)

Substituting in the values we have found:

P = (5 000 - Q)/4 = (5 000 - 4(Q/2))/4 = 1 250 - Q/2

P = 1 250 - Q/2

P = $1 250 - (5 000/2) = $1 250 - 2 500 = $-1 250

This result implies that the market price is zero when each firm produces half of the total output. Since the marginal cost is positive, each firm would incur a loss if they each produce half of the total output. Therefore, the firms would not earn any profit in this case, i.e., their profit would be zero.

However, we know that collusion is illegal and unlikely to occur in a competitive market. In a competitive market, each firm would independently choose its own profit-maximizing level of output, and the market price would be determined by the intersection of the market demand curve and the sum of the two firms' marginal cost curves.

At the profit-maximizing output level chosen by each firm in the competitive market, each firm would earn a positive economic profit. To find the profit earned by each firm in this case, we need to find the equilibrium output level and market price in the competitive market.

Since each firm is identical, we can find the equilibrium output for one firm and then double it to get the total industry output. To find the output level that maximizes profit for one firm, we need to set the firm's MR equal to its MC:

MR = 5 000 - 8Q = MC = 650

5 000 - 8Q = 650

4Q = 3 350

Q = 837.5

Thus, the equilibrium output for one firm is 837.5 units, and the total industry output is 1 675 units. To find the market price, we need to substitute the equilibrium output into the demand equation:

Q = 5 000 - 4P

1 675 = 5 000 - 4P

4P = 3 325

P = $831.25

Each firm produces 837.5 units at a price of $831.25. To find each firm's profit, we use the following equation:

Profit = (P - MC) x Q

Profit = ($831.25 - $650) x 837.5

Profit = $15 156.25

Therefore, each firm would earn a profit of $15 156.25 if they independently choose their profit-maximizing level of output in a competitive market. Doubling this amount gives a total profit of $30 312.50 for the industry. However, since collusion is illegal and unlikely to occur, this is not a realistic outcome.

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