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

Info icon This preview shows page 1. Sign up to view the full content.

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.
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern