Self-Test Problems

# Self-Test Problems - Chapter 2 Basic Economic Relations...

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-1- Chapter 2 Basic Economic Relations SELF-TEST PROBLEMS & SOLUTIONS ST2.1 Profit versus Revenue Maximization. Presto Products, Inc., manufactures small electrical appliances and has recently introduced an innovative new dessert maker for frozen yogurt and fruit smoothies that has the clear potential to offset the weak pricing and sluggish volume growth experienced during recent periods. Monthly demand and cost relations for Presto's frozen dessert maker are as follows: P = \$60 - \$0.005Q TC = \$100,000 + \$5Q + \$0.0005Q 2 MR = TR/ Q = \$60 - \$0.01Q MC = TC/ Q = \$5 + \$0.001Q A. Set up a table or spreadsheet for Presto output (Q), price (P), total revenue (TR), marginal revenue (MR), total cost (TC), marginal cost (MC), total profit ( π ), and marginal profit (M π ). 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. Using the Presto table or spreadsheet, 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? Why? At what price/output combination is total revenue maximized? Why? C. Determine these profit-maximizing and revenue-maximizing price/output combinations analytically. In other words, use Presto's 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? ST2.1 SOLUTION A. A table or spreadsheet for Presto output (Q), price (P), total revenue (TR), marginal revenue (MR), total cost (TC), marginal cost (MC), total profit ( π ), and marginal profit (M π ) appears as follows:

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-2- Presto Products, Inc. Profit vs. Revenue Maximization -\$150,000 -\$100,000 -\$50,000 \$0 \$50,000 \$100,000 \$150,000 \$200,000 \$250,000 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Units of Output (Q) Dollars Total Revenue Total Cost Total Profit Maximum Revenue Maximum Profit Units Price Total Revenue Marginal Revenue Total Cost Marginal Cost Total Profit Marginal Profit 0 \$60 \$0 \$60 \$100,000 \$5 (\$100,000) \$55 1,000 55 55,000 50 105,500 6 (50,500) 44 2,000 50 100,000 40 112,000 7 (12,000) 33 3,000 45 135,000 30 119,500 8 15,500 22 4,000 40 160,000 20 128,000 9 32,000 11 5,000 35 175,000 10 137,500 10 37,500 0 6,000 30 180,000 0 148,000 11 32,000 (11) 7,000 25 175,000 (10) 159,500 12 15,500 (22) 8,000 20 160,000 (20) 172,000 13 (12,000) (33) 9,000 15 135,000 (30) 185,500 14 (50,500) (44) 10,000 10 100,000 (40) 200,000 15 (100,000) (55) B. The price/output combination at which total profit is maximized is P = \$35 and Q = 5,000 units. At that point, MR = MC and total profit is maximized at \$37,500. The price/output combination at which total revenue is maximized is P = \$30 and Q = 6,000 units. At that point, MR = 0 and total revenue is maximized at \$180,000. Using the Presto table or spreadsheet, a graph with TR, TC, and π as dependent variables, and units of output (Q) as the independent variable appears as follows:
-3- C. To find the profit-maximizing output level analytically, set MR = MC, or set M π = 0, and solve for Q. Because MR = MC \$60 - \$0.01Q = \$5 + \$0.001Q 0.011Q = 55 Q = 5,000 At Q = 5,000, P = \$60 - \$0.005(5,000) = \$35 π = -\$100,000 + \$55(5,000) - \$0.0055(5,000 2 ) = \$37,500 ( Note : This is a profit maximum because total profit is falling for Q > 5,000.) To find the revenue-maximizing output level, set MR = 0, and solve for Q. Thus, MR = \$60 - \$0.01Q = 0 0.01Q = 60 Q = 6,000 At Q = 6,000, P = \$60 - \$0.005(6,000) = \$30 π =T R - T C = (\$60 - \$0.005Q)Q - \$100,000 - \$5Q - \$0.0005Q 2 = -\$100,000 + \$55Q - \$0.0055Q 2 = -\$100,000 + \$55(6,000) - \$0.0055(6,000 2 )

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-4- = \$32,000 ( Note : This is a revenue maximum because total revenue is decreasing for output beyond Q > 6,000.) D.
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## This note was uploaded on 09/25/2011 for the course BSAD 314 taught by Professor Staff during the Spring '10 term at SUNY Canton.

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Self-Test Problems - Chapter 2 Basic Economic Relations...

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