The water pump company has succeeded in introducing a water pump that saves electricity, is easy to install, and is durable (guaranteed). Its high quality has given the company an early edge in the local and national markets, but the entry of highly skilled competitors may occur within the next 3 years. Assume that the income and expense relationship of the company is as follows: TR = 22000Q - 15.6Q2 MR = dTR / dQ = 22000 - 31.2Q TC = 300000 + 4640Q + 10Q2 MC = dTC / dQ = 4640 + 20Q Where TR is income (in thousands of rupiah), Q is quantity (in units), MR is marginal income (in thousands of rupiah), TC is total cost, including a risk-adjusted normal rate of return on investment (in thousands of rupiah), and MC is the marginal cost (in thousands of rupiah). a. Compute: the profit-maximizing price-output combination. b. Compute: long-run equilibrium high-price / low-output. c. Compute: long-run low-price / high-output equilibrium

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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The water pump company has succeeded in introducing a water pump that saves electricity, is easy to install, and is durable (guaranteed). Its high quality has given the company an early edge in the local and national markets, but the entry of highly skilled competitors may occur within the next 3 years. Assume that the income and expense relationship of the company is as follows:

TR = 22000Q - 15.6Q2

MR = dTR / dQ = 22000 - 31.2Q TC = 300000 + 4640Q + 10Q2

MC = dTC / dQ = 4640 + 20Q

Where TR is income (in thousands of rupiah), Q is quantity (in units), MR is marginal income (in thousands of rupiah), TC is total cost, including a risk-adjusted normal rate of return on investment (in thousands of rupiah), and MC is the marginal cost (in thousands of rupiah).

a. Compute: the profit-maximizing price-output combination.

b. Compute: long-run equilibrium high-price / low-output.

c. Compute: long-run low-price / high-output equilibrium

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