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# The Production Function and Cost Analysis

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1. The attached table summarizes the short-run production function for your firm. Your product (Q) sells for \$50 per unit, labor (L) costs \$5 per unit, and the rental price of capital (K) is \$25 per unit. Lastly, assume capital and labor are used only in whole units, i.e. it is not possible to use 1.37 units of capital or labor, but instead 1,2, 3, etc. units are used. Complete the following table, and then answer the accompanying questions.
a. Fill in the missing values in the above table.
b. Which inputs are fixed inputs? Which are the variable inputs? Explain.
c. How much are your fixed costs at an output of 10? Show your calculations.
d. What is the cost of producing 2 units of output? Show your work.
e. How many units of the variable input should be used to maximize profits? Explain.

2. You hire an intern from Southern University to help you analyze your production process, and she uses your historical cost records to estimate that your total cost function is C(Q) = 100 + 2Q + 3Q^2. Using this equation, answer the following and show your logic and calculations.
a. How much is your firm’s profit or loss at an output of zero? Explain.
b. With the above cost equation, average total costs (ATC), first decline as output increases, and then begin to rise. Assuming output occurs in whole units, i.e. 1, 2,3,… at what output does the low point of ATC occur and what is the ATC at that output? Show your calculations.
c. What is the variable cost of an output of 50?
d. What are Average Fixed Costs (AFC) at a production level of 10?

3. Suppose the new leadership in Congress decides to repeal some of the tax breaks granted to large businesses during the past several years. If investment tax credits granted earlier are either repealed or eliminated, what impact will the repeal have on the exporting of jobs to foreign countries? Explain using isoquant/icocost theory.

4. You are the manager of USA 800, a small telemarketing company. Your company owns its own building and rents part of it as temporary storage for \$10,000 per month. USA 800 has been asked to do a new telemarketing campaign for Ford motor company, but accepting this campaign will require it to use all the rented space. What is the opportunity cost of accepting the offer to work for Ford?