Answer to Question #246838 in Macroeconomics for Garima

Question

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 fol-
lowing number of hoops each year for each level of cap-
ital stock shown .
Number of
Fabricators
0
1
2
3
4
5
6
Number of Hoops
Produced per Year
0
100
150
180
195
205
210
Hula hoops have a real value of $1 each. HHHHC has no
other costs besides the cost of fabricators.
c. Repeat Part (b) for a real interest rate of 8

Answer 1

referenced question:

1. Find the expected future marginal product of capital (MPKf) in terms of Dollars for each level of capital.
2. 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. How many fabricators should HHHHC buy?
3. Repeat part (b) for real interest rate of 8 % per year.

solution

a)MPK is the extra amount of output that is generated by using an extra unit of capital.

User cost is the cost incurred from using fixed capital such as machinery's. It is also the loss in asset value due to its use.

b. User cost can be calculated as follows:

Depreciation = 20% and rate of interest = 12% given, real value of hoops = $1

$UC = ( r + d) pK\\ = ( 0.12 + 0.20 )\times 100\\ = 0.32 \times 100\\ = 32$

MPK of 2 Fabricators is = 50 (MPK > UC)

And at 3             = 30 ( MPK < UC)

AT 3 the MPK is less it does not lead to increase in productivity, so HHHHC should 2 Fabricators.

c. when r = 8%

$UC = ( 0.08 + 0.20) \times 100\\ = 0.28 \times 100\\ = 28$

From the table we can see, for 3 Fabricator MPK = 30 > UC

While for the 4th Fabricator, MPK = 15< 28.

 

So HHHHC should buy 3 Fabricators.