Question: Suppose that you have estimated the following output function where L is labor and K is capital: Y = K 1/4 L 1/2 You know

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 (K). The price of the output is $20 (y).

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? Calculate the profit given the optimal number of employees and at what number of employees would you maximize output but not lose money.

Show the calculus.

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