A monopolist faces the demand curve q = 90 - p/2, where q is the number of units sold and p is the price in dollars.He has quasi-fixed costs, C, and constant marginal costs of $20 per unit of output.Therefore his total costs are C + 20q if q > 0 and 0 if q = 0.What is the largest value of C for which he would be willing to produce positive output?

A) $3,200
B) $2,560
C) $4,800
D) $20
E) $3,840

Question

Nikki Pecina · Accepted Answer

Final Answer : A, Explanation :  Explanation:The monopolist will produce positive output if and only if p > 20. The revenue function is R = pq = 90p - p^2/2. The profit function is pi = R - C - 20q = 90p - p^2/2 - C - 20(90 - p/2) = 50p - p^2/2 - C. The profit-maximizing quantity is q = 45 - p/4. Substituting this into the profit function, we get pi = 50(45 - p/4) - (45 - p/4)^2/2 - C = 2250 - 25p + p^2/8 - C. The profit-maximizing price is p = 40. Substituting this into the profit function, we get pi = 2250 - 25(40) + 40^2/8 - C = 1600 - C. The monopolist will produce positive output if and only if 1600 - C > 0, which implies that C < 1600. The largest value of C for which the monopolist would be willing to produce positive output is therefore $1,600.

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