Question

Suppose that the market demand curve for scooters is given by P = 300 - 5Q, where P is the price and Q is total industry output. Suppose that the industry has four firms. Each firm has a constant marginal cost of $50 per scooter. Suppose that four firms want to maximize their total profit and divide it between them. What is the total number of scooters, Q, in this case?

Answer 1

Answer:

The total number of scooters is 10

Explanation:

Total profit is maximized where Marginal Revenue (MR) = Total Marginal Cost

= 50 + 50 + 50 + 50 = $200

TR = P × Q = (300 - 5Q) × Q = 300Q - 5Q²

So, MR = $\frac{d(TR)}{dQ}$ = 300 - 2(5Q) = 300 - 10Q

Now, MR = 200 gives,

300 - 10Q = 200

So, 10Q = 300 - 200 = 100

So, Q = $\frac{100}{10}$

So, Q = 10