Problem
Suppose that you have estimated the following output function where L is labor and K is capital:
Y = 2K1/4L1/2
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 $40
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. Note that number of employees may include fractions (part time workers and product in millions)
A. Given a fixed level of capital (K=81), and a price of $40 per unit of output (output is represented by Y), how many employees (L) will you hire to maximize profit? This requires a calculation.
B. Given a fixed level of capital (K=81), and a price of $40 per unit of output, what is the level of output you will produce? This requires a calculation.
C. Calculate the profit given the optimal number of employee given the answer in (B).
D. At What number of employees would you maximize output but not lose money? This requires a calculation.
E. If the Wage Rate Rose to $12.50, what would be the possible outcomes to L, P, and Profit?