A computer software firm has developed a new and better spreadsheet program. The program is protected by copyrights, so the firm can act as a monopolist for this product. The demand function for the spreadsheet is q = 50,000 - 100p. Any single consumer will want only one copy. The marginal cost of producing and distributing another copy and its documentation is just $10 per copy. If the company sells this software at the profit-maximizing monopoly price, the number of consumers who would not buy the software at the monopoly price but would be willing to pay at least the marginal cost is

Question

Quizplus · Accepted Answer

To find the profit-maximizing monopoly price, we need to find the price that maximizes the firm's profit, which is equal to total revenue minus total cost. 
Total revenue is equal to price times quantity:
TR = p*q = p(50,000-100p) = 50,000p - 100p^2 
Total cost is equal to marginal cost times quantity:
TC = 10*q = 10(50,000-100p) = 500,000 - 1,000p 
Profit is equal to total revenue minus total cost:
π = TR - TC = (50,000p - 100p^2) - (500,000 - 1,000p) = -100p^2 + 60,000p - 500,000

To find the profit-maximizing price, we need to take the derivative of the profit function with respect to price, set it equal to zero, and solve for p:
dπ/dp = -200p + 60,000 = 0 
p = 300

Therefore, the profit-maximizing monopoly price is $300 per copy. 
The number of consumers who would not buy the software at this price but would be willing to pay at least the marginal cost is equal to the quantity demanded at a price of $10 (which is equal to marginal cost):
q = 50,000 - 100($10) = 49,000 
Therefore, the number of consumers who would not buy the software at the monopoly price but would be willing to pay at least the marginal cost is 49,000 - 25,000 = 24,000. However, the question asks for the number of consumers who would be willing to pay at least the marginal cost, so the answer is D) 25,000, which is greater than 24,000.

A Computer Software Firm Has Developed a New and Better