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

Y = 2K^3/4L^1/8

(23 Points)

You know that the current price of labor is $13 and capital cost is $1 per per machine (capital).

You currently use 81 units (machines) of capital.The price of the output is $60

NOTEYOU CAN USE EITHER K=81 OR K=64 ON EVERY ANSWER (BOTH ARE FINE). WHILE IT WAS DESIGNED TO CHANGE THE NUMBER, IT IS ALL RIGHT IF YOU ANCHOR YOUR ANSWER TO ONE NUMBER. HOWEVERYOU NEED TO SHOW YOUR WORK.

Using calculus or an Excel spreadsheetboth work. If you use calculus, show your work; if you use a spreadsheet, please submit the spreadsheet. Note that the number of employees may include fractions (part-time workers and products in millions)

1. Given a fixed level of capital (K=81), and a price of $60 per unit of output (output is represented by Y), how many employees (L) will you hire to maximize profit?This requires a calculation. (5 Points)

1. Given a fixed level of capital (K=81), and a price of $60 per unit of output, what is the level of output you will produce? This requires a calculation. (5 Points)

1. Calculate the profit given the optimal number of employee given the answer in #2a. (4 Points)

1. At What number of employees would you maximize output but not lose money? This requires a calculation and may be a fraction (part time workers). (4 Points)

1. If the Wage Rate rises to $16.25, what would be the possible outcomes to L, P, and Profit? This requires a calculation (5 Points)