Answered

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You are the manager of a firm that sells its product in a competitive market at a price of $40. your firm's cost function is c = 60 4q2. Your firm's maximum profits are?

Sagot :

Firm's maximum profits are 40

Profit = revenue - cost

Revenue = price x quantity = 40 x quantity

Cost = 60 + 4 x quantity x quantity

So you have:

P = 40 x Q - 60 - 4 x Q x Q

To get the maximum value for P with respect to Q, differentiate and set it to 0.

That is, set dP/dQ = 0 and solve for Q.

Since P(Q) is quadratic, dP/dQ is linear, so solving dP/dQ = 0 is easy and there is one solution.

Q=5

revenue = 5 x 40 = 200

cost = 60 + 4 x 5 x 5 = 60 + 4 x 25 = 160

Profit = 200 - 160 = 40

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