Question #18c40

1 Answer
Bruno Pedron
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]}

Related questions
Impact of this question
1509 views around the world
You can reuse this answer
Creative Commons License