9781118041581

Summary 269

where L, K, and Q are measured in thousands of units. Input prices are

36 per labor unit and 16 per capital unit.

a. Create a spreadsheet (based on the example shown) to model this

production setting. (You may have already completed this step if you

answered Problem S2 of Chapter 5. An algebraic analysis of this

setting appears in this chapter’s Special Appendix.)

b. To explore the shape of short-run average cost, hold the amount of

capital fixed at K 9 thousand and vary the amount of labor from

1 thousand to 2.5 thousand to 4 thousand to 5.5 thousand to

7.5 thousand to 9 thousand units. What is the resulting behavior of

SAC? Use the spreadsheet optimizer to find the amount of labor

corresponding to minimum SAC. What is the value of SACmin?

c. In your spreadsheet, set L 9 thousand (keeping K 9 thousand)

and note the resulting output and total cost. Now suppose that the

firm is free to produce this same level of output by adjusting both

labor and capital in the long run. Use the optimizer to determine the

firm’s optimal inputs and LACmin. (Remember to include an output

constraint for cell I3.)

d. Confirm that the production function exhibits constant returns to

scale and constant long-run average costs. For instance, recalculate

the answer for part (c) after doubling both inputs.

e. Finally, suppose the firm’s inverse demand curve is given by

With capital fixed at K 9 in the short run, use the optimizer to

determine the firm’s optimal labor usage and maximum profit. Then

P 9 Q/72.

AB C D E F G H I J

1

2 COST ANALYSIS

3 Output 36

4 Price 8.50

5 Labor 1.00 Capital 9.00

6 MPL 18.00 MPK 2.00 MR 8.00

7 Revenue 306

8 MRPL 144.00 MRPK 16.00

9 MCL 36.00 MCK 16.00 Cost 180

10 Avg. Cost 5.00

11

12 Profit 126

13

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