Question

Suppose the demand function is given by P = 100-0. 02Q , and total cost is...

Suppose the demand function is given by P = 100-0. 02Q , and total cost is TC = 5Q . Find

the marginal revenue function, profit maximizing quantity, profit maximizing price and draw

a fully labelled diagram. [5]

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Answer #1

P = 100 -0. 02Q

TR = P*Q = 100Q - 0.02Q^2

Marginal Revenue Function, MR = dTR/dQ = 100 - 0.04Q

Profit = TR - TC = 100Q - 0.02Q^2 - 5Q

Profit = 95Q - 0.02Q^2

First order condition:

dProfit / dQ = 0

95 = 0.04Q

Q = 2375 : profit maximizing quantity

P = 100 - 0.02*2375 = 52.5 : profit maximizing price

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