Assignment:
1.A firm is considering the purchase of a machine that is expected to generate profits of $100,000 per year. The interest rate is 3%. After seven years of operation, the firm expects to be able to sell the machine as scrap for $50,000. Should this firm undertake this investment? Explain. Now, assume that the depreciation rate on the machine is 9% per year (i.e., the profits decrease by 9% per year). Should this firm undertake this investment? Explain.
2.A firm faces the following Total Revenue and Total Cost functions:
TR = 41.5Q - 1.1Q2
TC = 150 + 10Q - .5Q2 +.02Q3
What is the profit maximizing level of output? Show all work.
3.A van conversion company has fixed capital and labor expenses of $1.2 million per year, and variable expenses averaging $2,000 per van conversion. Recent experience suggests the following annual demand for their products:
Q = 1000 - .1P
Where Q is the number of van conversions (output) and P is price.
1.Calculate the profit-maximizing output, price, and profits.
2.Assuming a parts shortage limits their output to 300 conversions per year, use the Lagrangian multiplier method to calculate the profit-maximizing output, price, and profits.
3.Calculate and interpret the Lagrangian multiplier.