Managerial Economics (12 Edition) by Mark Hirschey Ch. 2 Problem

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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 – $0.005QTC = $88,000 + $5Q + 0.0005Q2

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
1,0005555,0005093,5006-38,50044
2,00050100,00040100,0007033
3,00045135,00030107,500827,50022
4,00040160,00020116,000944,00011
5,00035175,00010125,5001049,5000
6,00030180,0000136,0001144,000-11
7,00025175,000-10147,5001227,500-22
8,00020160,000-20160,000130-33
9,00015135,000-30173,50014-38,500-44
10,00010100,000-40188,00015-88,000-55

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 –...
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