Consider a monopolist that faces the following demand curve

Consider a monopolist that faces the following demand curve: P-150-Q. The total cost curve for this monopolist is given by the following TC-100+10Q+Q2. Which of the following is true? O The monopolist will set price equal to 115 and sell 35 units. O The monopolist will set price equal to 45 and sell 105 units O The monopolist will set price equal to 30 and sell 120 units. O The monopolist will set price equal to 60 and sell 90 units. O None of the above.

Solution

Option (1).

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

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

P = 150 - Q

Total revenue (TR) = P x Q = 150Q - Q²

MR = dTR/dQ = 150 - 2Q

Equating with MC,

150 - 2Q = 10 + 2Q

4Q = 140

Q = 35

P = 150 - 35 = 115