Question

Let the following schedule represent the production function for a firm where I is investment and Y is future output. (I'm scared this won't line up properly. If that happens, just associate the first I value with the first Y value and the last with the last etc.)

I               1               2                 3                 4                 5                 6                7                  8                9

Y             4               6                 7.7            9.2             10.5          11.7         12.85        13.95       15

How much will this firm invest if the real interest rate is 5%?

How much will they invest if the real interest rate is 15%?

(Answers are integers.)

- i'm sorry, that why I'm very confused about this question too. that is all information of my teacher posted :(

Answer 1

One way to look at this problem could be to calculate the marginal output from investment, and see if it makes sense at the two rates of interest. Pls see table below.

When the interest rate is 5% it makes sense to go all the way to the 9th unit of investment since the marginal output is 1.05, i.e., 105% of investment.

When the interest rate is 15%, it makes sense to stop at the 7th unit of investment because for 8th and 9th, the marginal output is less than 115% of investment (115% is investment plus interest).

I	Y	MI	MY
1	4.00
2	6.00	1	2.00
3	7.70	1	1.70
4	9.20	1	1.50
5	10.50	1	1.30
6	11.70	1	1.20
7	12.85	1	1.15
8	13.95	1	1.10
9	15.00	1	1.05