Question

The inverse demand curve a monopoly faces is p=130 - Q. The firm's cost curve is C(Q) = 40 +5Q. What is the profit-maximizing solution? The profit-maximizing quantity is (Round your answer to two decimal places.) The profit-maximizing price is $ (round your answer to two decimal places.)

also what is the firms economic profit?

Answer 1

Demand, P = 130 - Q

Cost, C = 40 + 5Q

The monopolist maximizes profit at MR =MC

Total revenue, TR = PQ

TR=(130 – QQ

+ TR = 130Q - Q

Differentiating TR wrt Q, we get

OTRE (1300 – Q?) do

MR= 130 – 20

Differentiating the Cost function wrt Q, we get

MC = 5

Now, equate MR to MC

130 - 20 = 5

20 = 125

Q = 62.5

P = 130 - 62.5 = $ 67.50

Profit = TR -TC = 62.5 × 67.5 - (40 + 5×62.5) = 4,218.75 - 352.5

Profit = $ 3,866.25

Profit maximizing quantity = 62.50

Profit maximizing price = $ 67.50

Profit = $ 3,866.25

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