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The profit maximization

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1. John's Lawn Mowing Service is a small business that acts as a price taker (MR = P). The prevailing market price of lawn mowing is $20 per acre. John's costs are given by

total cost = .1q^2 + 10q + 50

where q = the number of acres John chooses to cut a day

a. How many acres should John choose to cut in order to maximize profit?
b. Calculate John's maximum daily profit
c. Graph these results and label John's supply curve

2. Would a lump-sum profits tax affect the profit-maximizing quantity of output? How about a tax assessed on each unit of output?

3. Universal Widget produces high-quality widgets at its plant in Gulch, Nevada for sale throughout the world. The cost function for total widget production (q) is given by

total cost = .25q^2

Widgets are demanded only in Australia (where the demand curve is given by q = 100 - 2P) and Lapland (where the demand curve is given by q = 100 - 4P). If Universal Widget can control the quantities supplied to each market, how many should it sell in each location in order to maximize total profits? What price will be charged in each location?

4. Young's theorem can be used in combination with the envelope theorem to derive some useful results

a. Show that dl(P,v,w)/dv = dk(P,v,w)/dw. Interpret this result using substitution and output effects

b. Use the result from part (a) to show how a unit tax on labor would be expected to affect capital input

c. Show that dq/dw = -dl/dP. What is the interpretation of the result?

d. Use the result from park (c) to discuss how a unit tax on labor input would affect quantity supplied

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Caledonia Products Case: Differences between goals of profit maximization and maximization of shareholder wealth; risk-return trade-off

Please see attached file.

The final stage in the interview process for an assistant financial analyst at Caledonia Products involves a test of your understanding of basic financial concepts and of the corporate tax code. You are given the following memorandum and asked to respond to the questions. Whether you are offered a position at Caledonia will depend on the accuracy of your response.

To: Applicants for the position of Financial Analyst
From: Mr. V. Morrison, CEO, Caledonia Products

Re: A test of your understanding f basic financial concepts and of the corporate tax code

Please respond to the following questions:

1. What are the differences between the goals of profit maximization and the maximization of shareholder wealth? Which goal do you think is more appropriate?
2. What does the risk-return trade-off mean?
3. Why are we interested in the cash flows rather than accounting profits in determining the value of an asset?
4. What is an efficient market and what are the implications of efficient markets for us?
5. What is the cause of the agency problem and how do we try to solve it?

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Book title: Foundations of Finance: Logic and Practice of Financial Management (6th Edition)
Author: Keown, Martin, Petty, and Scott

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