Profit versus Revenue Maximization. Presto Products, Inc., recently introduced an innovative new frozen dessert maker with the following revenue and cost relations:

P = $60 - $0.005QTC = $88,000 + $5Q + $0.0005Q2

MR = ∂TR/∂Q = $60 - $0.01QMC = ∂TC/∂Q = $5 + $0.001Q

A. Set up a spreadsheet for output (Q), price (P), total revenue (TR), marginal revenue (MR), total cost (TC), marginal cost (MC), total profit (π), and marginal profit (Mπ). Establish a range for Q from 0 to 10,000 in increments of 1,000 (i.e., 0, 1,000, 2,000, ..., 10,000).

B. Use the spreadsheet to, create a graph with TR, TC, and π as dependent variables, and units of output (Q) as the independent variable. At what price/output combination is total profit maximized? At what price/output combination is total revenue maximized?

C. Determine these profit-maximizing and revenue-maximizing price/output combinations analytically. In other words, use the profit and revenue equations to confirm your answers to part B.

D. Compare the profit-maximizing and revenue-maximizing price/output combinations, and discuss any differences. When will short-run revenue maximization lead to long-run profit maximization?