A monopolist faces the price equation P = 1,000 – 0.5Q, and cost is given as TC = 400 + 100Q +2.5Q^2.Determine the profit at the revenue maximizing level and the profit maximizing level. Compare the answers above and comment on the appropriate goal of the firm.

Answer 1

Always always always, maximize where MC=MR

Total revenue is P*Q = 1000Q- 0.5Q^2. MR is the first derivative of TR. So, MR=1000 - Q
MC is the first derivative of TC. So, MC=100 + 5Q
MC=MR is 100+5Q = 1000-Q. solve for Q. then plug the optimized Q into TC and TR to derive the profit.