Lesson 8 Assignment 3

Lesson 8 Assignment 3 - Marcie DeGiovine February 1 2013...

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Marcie DeGiovine 258-10-0153 February 1, 2013 – May 20, 2013 BA635 Lesson #8, Assignment #3: P = \$75 - \$0.003Q MR = Δ TR/ Δ Q = \$75 - \$0.006Q TC MC = Δ TC/ Δ Q = \$25 + \$0.004Q The company has assets of \$100,000 used for call waiting services and the utility commission has authorized a 12% return on investment. A. Calculate Black Hills' profit-maximizing price (monthly and annually), output, and rate-of-return levels. B. What monthly price should the commission grant to limit Black Hills to an 12% rate of return? (Demand for shelled almonds) (Marginal revenue from shelled almonds) (Demand for shell by-product) (Marginal revenue from shell by-product) TC = \$3,000,000 + \$6.25Q (Total cost) MC = \$6.25 (Marginal cost) Answers: A. To find the profit-maximizing level of output, we must set MR = MC where: MR = MC \$75 - \$0.006Q = \$25 + \$0.004Q 0.01Q = 50 Q = 5,000 P = \$6.25 - \$0.00025(5,000) = \$5 (Monthly price) P = \$75 - \$0.003(5,000) = \$60 (Annual price) p = TR - TC = \$60(5,000) - \$108,000 - \$25(5,000) - \$0.002(5,0002) = \$17,000 If the company has \$100,000 invested in plant and equipment, its optimal rate of return on investment is: Return on investment = \$17,000 \$100,000 = 0.17 or 17% (Note: Profit is falling Q > 5,000) B. With a 12% return on total assets, Black Hills would earn profits of: p = Allowed return Total assets = 0.120(\$100,000) = \$12,000 To determine the level of output that would be consistent with this level of total profits, consider the profit relation: p = TR - TC \$12,000 = \$75Q - \$0.003Q2 - \$108,000 - \$25Q - \$0.002Q2 12,000 = -0.005Q2 + 50Q - 108,000 0 = -0.005Q2 + 50Q - 120,000 which is a function of the form aQ2 + bQ + c = 0 where a = -0.005, b = 50 and c = -120,000 and can be solved using the quadratic equation: Q = -b √b² + 4ac 2a = -50 √50² + 4(-0.005)(-120,000) 2(-0.005) = -0.01 = 4,000 or 6,000 customers Because public utility commissions generally want utilities to provide service to the greatest possible number of customers at the lowest possible price, the "upper" Q = 6,000 is the appropriate output level. This output level will result in a monthly service price of: P = \$6.25 - \$0.00025(6,000) = \$4.75 This \$4.75 per month price for call waiting service will provide Black Hills with a fair rate of return on total investment, while ensuring service to a broad customer base.
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