Question

The Missing Link Chain-Link Fence Company is trying to determine how many chain-link fabricating machines to buy for its factory. If we define a chainlink fence of some specified length to be equal to one unit of output, the price of a new fabricating machine is 60 units of output, and the price of a one-year-old machine is 51 units of output. These relative prices are expected to be the same in the future. The expected future marginal product of fabricating machines, measured in units of output, is 165-2K, where K is the number of machines in use. There are no taxed of any sort. The real interest rate is 10% per year.

(a) What is the user cost of capital? Specify the units in which your answer is measured.
(b) Determine the number of machines that will allow Missing Link to maximize its profit.
(c) Suppose that Missing Link must pay a tax equal to 40% of its gross revenue. What is the optimal number of machines for the company?

Answer 1

Step-by-step explanation:

What is given:

The price of a new fabricating machine - 60

The price of a one-year-old machine - 51

The real interest rate is 10% per year

Marginal product of fabricating machines 165-2K (K - desired number machines)

If calculate the depreciation, (60-51)/51 = 15%

a) Find user cost of capital

User cost of capital is the sum of interest rate and depreciation cost multiplied by the price of new machine

= 60*(0.10+0.15) = 15 units

b) Determine the number of machines that will allow Missing Link to maximize its profit

165-2K=15

2K = 150

K = 75 machines

c)

Suppose that Missing Link must pay a tax equal to 40% of its gross revenue. What is the optimal number of machines for the company?

165-2K = 15/(1-0.4)

165-2K=14/0.6

165-2K=25

2K=140

K=70 macines