Question

1. Tom is a farmer. Tom grows wheat. The quantity that he produces is determined by the following production function:

Y=10I^1/2

Where “I” stands for investment and is the quantity of wheat that he plants and Y stands for output and is the total amount of wheat he harvests. (Recall that the ½ exponent means square root.)

a. Now imagine that in year 1 Tom plants 1 unit of wheat and then each year after that Tom plants half of the wheat that he produced in the previous year. Fill in the following table giving the amount of wheat he plants and harvests in each year. (I got you started.)

Year                         Investment (Planted)                            Output (Harvested)

1                                                1                                                                 10           

2                                                5

3

4

5

6

7

b. Plot these points on a graph with Year on the horizontal axis and Output (Y) on the vertical axis. Make your vertical axis go from 0 to 100. Draw a smooth curve between these points.

Answer 1

(a) We have Y= 10(I)^1/2

Where I is investment and Y is output

Year	Investment	output
1	1	10
2	10/2=5	10 (5)1/2= 22.3~22*
3	22/2= 11	10(11)1/2=33.1~33*
4	33/2 = 16.5 ~16*	10(16)1/2= 40
5	40/2 = 20	10(20)1/2 = 44.7~45*
6	45/2= 22.5 ~23*	10(23)1/2=47.9~ 48*
7	48/2=24	10(24)1/2= 48.9~49*

* --> approximate values are taken

( b) Following icture shows the graph for the above table