Question

Suppose a firm sells its product in a perfectly competitive industry in Dubai, where all the firms charge a price of 90 dirhams. The firm’s total costs are given by the following equation: TC = 50 + 10Q + 2Q2 (Kindly answer clearly)

a) Calculate the MC function?

b) Calculate the MR function?

c) Calculate the profit maximizing level of output for the firm?

d) Calculate the size of the profit? Show it graphically

e) Is this industry SR or LR?

Answer #1

a) TC = 50 + 10Q + 2Q^{2}

MC is the first order derivative of TC function.

MC = 10 + 4Q

b) Since in a perfectly competitive market, P = MR, So

MR = 90

c) The profit maximization condition is,

MC = P

10 + 4Q = 90

4Q = 90 - 10 = 80

Q = 80 / 4 = 20

Thus, the profit maximizing level of output for the firm is 20 units.

d) TR = P * Q = $90 * 20 = $1,800

TC = 50 + 10Q + 2Q^{2} = 50 + 10(20) + 2(20)^{2}
= 50 + 200 + 800 = 1,050

Profit = TR - TC = 1,800 - 1,050 = $750

e) This industry is SR (Short Run). Because in the short run, the firm incurs both fixed and variable cost. From thr TC function it is seen that the Fixed cost is $50. So, this industry is short run industry.

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