II. Numerical and analytical problems (40 points) A company is trying to determined how many machines to buy for its factory. If the price of a new machine equals 50 units of output, and the price of a one-year-old machine is 40 units of output. The expected future marginal product of machine, measured in units of output, is 200-2K, where K is the number of machines in use. The real interest rate is 10% per year (1) (5 points) What is the user cost of capital? Specify the units in which your answer is measured. (2) (5 points) Determine the number of machines that will allow the company to maximize its profit. (3) (10 points) Suppose that the company must pay a tax equal to 50% of its gross revenue. What is the optimal number of machines for the company? (4) (20 points) Please use the capital stock determining diagram to analyze how the usage of capital stock will change when: (i) the real interest rate increased. (ii) the marginal product of capital increased