Question #18c40

1 Answer
Jul 29, 2015

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]}