Hula hoop fabricators cost $100 each. The Hi-Ho Hula Hoop Company is trying to decide how many of these machines to buy. HHHHC expects to produce the following number of hoops each year for each level of capital stock shown.
Number of Fabricators Number of Hoops Produced per Year
0 0
1 100
2 150
3 180
4 195
5 205
6 210
Hula hoops have a real value of $1 each. HHHHC has no other costs besides the cost of fabricators.
a. Find the expected future marginal product of capital (in terms of dollars) for each level of capita. The MPK^f for the third fabricator, for example, is the real value of the extra output obtained when the third fabricator is added.
b. If the real interest rate is 12% per year and the depreciation rate of capital is 20% per year, find the user cost of capital (in dollars per fabricator per year). How many fabricators should HHHHC buy?
c. Repeat part (b) for a real interest rate of 8% per year.
d. Repeat part (b) for a 40% tax on HHHHC's sales revenues.
e. A technical innovation doubles the number of hoops a fabricator can produce. How many fabricators should HHHHC buy when the real interest rate is 12% per year? 8% per year? Assume that there are no taxes and that the depreciation rate is still 20% per year.