Question

A 5-member cartel faces an industry demand curve given by P = 190 - 0.2Q. Each member of the cartel can produce at a constant marginal cost of MC = $10. All members of the cartel initially agree to restrict output to 90 units per firm (or 450 units total), but then one firm in the cartel cheats and doubles their own output to 180 units. This causes the profit of the cheating firm to increase by $ , ___________ and the profit of each of the 4 non-cheating members to decline by $ .__________

Answer 1

There are 5 members in the cartel.

Each member produces 90 units.

So, total production is 450 units.

P = 190 - 0.20Q

P = 190 - (0.2 * 450)

P = 190 - 90 = 100

The price is $100 per unit

Calculate profit of each firm -

Profit = [Price * Quantity produced] - [MC * Quantity produced]

Profit = [$100 * 90] - [$10 * 90] = $9,000 - $900 = $8,100

So,

In cartel, each firm will make profit of $8,100.

Now, a firm cheats and increase its production by 90 units.

So, new total production is 540 units.

Demand curve is as follows -

P = 190 - 0.20Q

P = 190 - (0.2 * 540) = 190 - 108 = $82

The new price would be $82 per unit.

Calculate the profit of cheating firm -

Profit = [Price - MC] * Quantity produced

Profit = [$82 - $10] * 180 = $72 * 180 = $12,960

The profit of cheating firm is $12,960.

By cheating, the firm has increased its profit by ($12,960 - $8,100) $4,860

Calculate profit of non cheating firm -

Profit = [Price - MC] * Quantity produced

Profit = [$82 - $10] * 90 = $72 * 90 = $6,480

The profit of non cheating firm is $6,480

So, due to cheating, the profit of each of the remaining firms has decreased by ($8,100 - $6,480) $1,620

Thus,

This causes the profit of the cheating firm to increase by $4,860 and the profit of each of the 4 non-cheating firms to decline by $1,620.