Question

3) Suppose that you have estimated the following output function where L is labor and K is capital:

Y = K^1/4L^1/2

                                                                                                                       

You know that the current price of labor is $10 and capital cost is $1 per per machine (capital).

You currently use 81 units (machines) of capital. The price of the output is $20

As we compete both internationally and within markets, the challenge of wages and technology create a balancing act relative to the capital/labor ratio. In addition, rising interest rates increase the cost of capital, both explicit and implicit.

You can either do this using calculus or an excel spreadsheet—both work. If you use calculus, show your work; if you use a spreadsheet, please submit the spreadsheet.

1. How many employees (L) will you hire to maximize profit?

2. Given a fixed level of capital (K=81), and a price of $20 per unit of output, what is the level of output you will produce?

3. Calculate the profit given the optimal number of employee given the answer in #3b.

4. At What number of employees would you maximize output but not lose money?

Answer 1