9781118041581

a. In the short run, the firm has an installed capacity of machine

hours per day, and this capacity cannot be varied. Create a

spreadsheet (based on the example below) to model this production

setting. Determine the firm’s profit-maximizing employment of labor.

Use the spreadsheet to probe the solution by hand before using your

spreadsheet’s optimizer. Confirm that MRPLMCL.

K 50

222 Chapter 5 Production

AB C D E F G H I

1

2 OPTIMAL INPUTS

3 Output 136.0

4 Price 10.0

5 Labor 20.0 Capital 50.0

6 MPL 1.600 MPK 1.000 MR 10.00

7 Revenue 1360.0

8 MRPL 16.0 MRPK 10.0

9 MCL 10.0 MCK 20.0 Cost 1200.0

10 Ave Cost 8.8

11

12 Profit 160.0

13

b. In the long run, the firm seeks to produce the output found in

part (a) by adjusting its use of both labor and capital. Use your

spreadsheet’s optimizer to find the least-cost input amounts. (Hint:Be

sure to include the appropriate output constraint for cell I3.)

c. Suppose the firm were to downsize in the long run, cutting its use of

both inputs by 50 percent (relative to part b). How much output

would it now be able to produce? Comment on the nature of returns

to scale in production. Has the firm’s profitability improved? Is it

currently achieving least-cost production?

S2. A second firm’s production function is given by the equation

Input prices are $36 per labor unit and $16 per capital unit, and P $10.

a. In the short run, the firm has a fixed amount of capital, K 9. Create

a spreadsheet to model this production setting. Determine the firm’s

profit-maximizing employment of labor. Use the spreadsheet to probe

the solution by hand before using your spreadsheet’s optimizer.

b. Once again, the firm seeks to produce the level of output found in

part (a) by adjusting both labor and capital in the long run. Find the

least-cost input proportions. Confirm that MPL/PLMPK/PK.

Q12L.5K.5.

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