3) Suppose that you have estimated the following output function where L is labor and K is capital: Y = K14[V/ (23 Points) 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. Note that this material is covered in Chapter 5. 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. (5 Points) Y=K1/41 1/2 Y=811 4L1/2 = 31 1/2 Profit Function 1=40Y - 10L - 1 * 81 = 40(3L' 2)-10L-81 Maximzing profit with labor: dn/dL = 60L-12-10=0 6L-1/2=1 L=18 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. (5 Points) Y=811/4181/2=12.73 c) Calculate the profit given the optimal number of employee given the answer in #3b. (4 Points) Profit= P * Y -wh- th = 40*12.73 -10*18 - 81= 509.2-180 - 81 =248.2d) At What number of employees would you maximize output but not lose money? This requires a calculation. (4 Points) PY-WL-K= 0 =120L 2/3/ e) If the Wage Rate Rose to $12.50, what would be the possible outcomes to L, P, and Profit? (5 Points) If the Wage rate increase the only possible outcome for profit would be for it to decrease. L the number of employees could go up or down depending on other factors within the market. P could also increase or decrease depending upon other factors impacting supply and demand