Question

Question #18c40

Answer 1

Profit maximization occurs when `MR = MC`. Supposing an imperfect competition market, you can use derivatives to find that each company will produce 2,500 units to maximize its profit.

Explanation:

If this is not a perfect competition market, then `P= AR != MR` . Presuming that x is the quantities the company produces and sells, then:
`P=50/sqrt(q)=MR`
Since the total revenue is `TR=P*q`, we have:
`TR=50sqrt(q)`
The marginal revenue is the derivative of the total revenue function with respect to with respect to q:
`MR=(delTR)/(del q)=25/sqrt(q)`
The marginal cost is the derivative of the total cost function with respect to q:
`MC=(delTC)/(del q)=0.5`
Equaling Marginal revenue and marginal cost:
`25/sqrt(q)=0.5`
Isolate q and solve:
`sqrt(q)=50`
`q=2,500`
The profit function for this problem would have this graph:
graph{50/sqrt(x)*x-(0.5x+500) [, 5000, -500, 1000]}