Managerial Economics (12 Edition) by Mark Hirschey Ch. 2 Problem
ST 2.1 (Page 43 in Text Book): Profit vs Revenue Maximization
Presto Products, Inc. recently introduced an innovative new frozen dessert maker with the following revenue and cost relations.
P = $60 – $0.005Q TC = $88,000 + $5Q + 0.0005Q2
MR = ∂TR / ∂Q = $60 – $0.01Q MC = ∂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 ($)
0 60 0 60 88,000 5 -88,000 55
1,000 55 55,000 50 93,500 6 -38,500 44
2,000 50 100,000 40 100,000 7 0 33
3,000 45 135,000 30 107,500 8 27,500 22
4,000 40 160,000 20 116,000 9 44,000 11
5,000 35 175,000 10 125,500 10 49,500 0
6,000 30 180,000 0 136,000 11 44,000 -11
7,000 25 175,000 -10 147,500 12 27,500 -22
8,000 20 160,000 -20 160,000 13 0 -33
9,000 15 135,000 -30 173,500 14 -38,500 -44
10,000 10 100,000 -40 188,000 15 -88,000 -55
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
0.011Q –
Presto Products, Inc. recently introduced an innovative new frozen dessert maker with the following revenue and cost relations.
P = $60 – $0.005Q TC = $88,000 + $5Q + 0.0005Q2
MR = ∂TR / ∂Q = $60 – $0.01Q MC = ∂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 ($)
0 60 0 60 88,000 5 -88,000 55
1,000 55 55,000 50 93,500 6 -38,500 44
2,000 50 100,000 40 100,000 7 0 33
3,000 45 135,000 30 107,500 8 27,500 22
4,000 40 160,000 20 116,000 9 44,000 11
5,000 35 175,000 10 125,500 10 49,500 0
6,000 30 180,000 0 136,000 11 44,000 -11
7,000 25 175,000 -10 147,500 12 27,500 -22
8,000 20 160,000 -20 160,000 13 0 -33
9,000 15 135,000 -30 173,500 14 -38,500 -44
10,000 10 100,000 -40 188,000 15 -88,000 -55
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
0.011Q –