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a monopolist has a total cost function TC= 5Q^2- 2Q+ 100. the inverse demand function for...

a monopolist has a total cost function TC= 5Q^2- 2Q+ 100. the inverse demand function for the monopolist is P= 10 - Q. what is the optimal price for the monopolist.

a. 6
b.7
c.8
d.9

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Answer #1

Option (d).

TC = 5Q2 - 2Q + 100

Marginal cost (MC) = dTC/dQ = 10Q - 2

Profit is maximized when Marginal revenue (MR) = MC.

P = 10 - Q

Total revenue (TR) = P x Q = 10Q - Q2

MR = dTR/dQ = 10 - 2Q

10 - 2Q = 10Q - 2

12Q = 12

Q = 1

P = 10 - 1 = 9

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