A major software developer has estimated the demand for its new personal finance software package to be Q = 1,000,000P^-^1.40 while the total cost of the package is C = 100,000 + 20Q. If this firm wishes to maximize profit, what percentage markup should it place on this product?

Question

Quizplus · Accepted Answer

To maximize profit, the firm should set marginal revenue (MR) equal to marginal cost (MC). The demand function is Q = 1,000,000P^-1.40, which implies P = (1,000,000/Q)^(1/1.40). The total cost function is C = 100,000 + 20Q, so MC = 20. Solving for MR = MC gives the optimal price. The percentage markup is calculated as (P - MC)/MC * 100%. Solving this gives a markup of approximately 250%.

A Major Software Developer Has Estimated the Demand for Its