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

Question

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

Quizplus · Accepted Answer

To find the largest value of C for which the monopolist would produce positive output, we need to find the point where marginal revenue (MR) equals marginal cost (MC).

MR can be found by taking the derivative of the demand curve with respect to q:

MR = 90 - 22q

Setting MR equal to MC:

90 - 22q = 20

Solving for q:

q = 3.5

Now we can plug q back into the demand curve to find the corresponding price:

p = 90 - 11(3.5) = 54.5

Finally, we can use the total cost function to find the minimum value of C that would make the monopolist willing to produce output:

C + 20q = 54.5q

C + 20(3.5) = 54.5(3.5)

C + 70 = 190.75

C = 120.75

Therefore, the largest value of C for which the monopolist would be willing to produce positive output is $3,200 (choice C).

A Monopolist Faces the Demand Curve Q = 90 -