MR = ∂TR / ∂Q = $60 – $0.01QMC = ∂TC / ∂Q = $5 + $0.001Q
A.Setup a spreadsheet for output (Q), price (P), total revenue (TR), marginal revenue (MR), total cost (TC), marginal cost (MC), total profit (π), and marginal profit (Mπ). Establish a range for Q from 0 to 10,000 in increments of 1,000 (i.e. 0, 1000, 2000, …, 10,000). Presto Products
Units of Output ($)Price
($)Total Revenue ($)Marginal Revenue ($)Total Cost ($)Marginal Cost ($)Total Profit ($)Marginal Profit ($) 06006088,0005-88,00055
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?
Total profit is maximized at a price-output combination of P = $35 and Q = 5000. MR = MC and the total profit is maximized at $49,000.
Total revenue is maximized at a price-output combination of P = $30 and Q = 6000. MR = 0 and total revenue is maximized at $180,000.
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. Profit-Maximizing:
Solve Q at MR = MC
60 – 0.01Q = 5 + 0.001Q