6

 AEB 6933
 Spring 1995
 Exercise FA5

 Factor x Factor


In the procedure used in Exercise FA4, we could determine the best
combination of N and P to use, but would need to make successive
approximations to determine the most profitable combination of the two
for any price combination. In order to be more "precise" a
mathematical production function incorporating both amendments can be
calculated by regression. The form we will use here is quadratic
(with an NP interaction term).

1. In a spreadsheet, set up the data in the following form:

 N P N2 P2 NP Y
 0 0 0 0 0 400

 50 0 2500 0 0 1240

 100 0 10000 0 0 3630

 150 0 22500 0 0 3760

 0 25 0 625 0 790

 50 25 2500 625 1250 2580
  .
 etc. etc. etc. etc. etc. etc.

By using all the data, you should have 96 (8 X 12) rows. Calculate
the production function Y = f(N,P,N2 P2,NP) by blocking the first five
columns as independent variables in the regression menu. In the
output, the coefficients are in the same order as the columns.

2. Determine mathematically, for what quantities of N and P,
production is maximized. How much maize is produced with these
quantities of N and P? Do these values correspond with your graph
from Exercise FA4? Explain any differences.

3. Using the same prices as before, find mathematically the
quantities of N and P which maximize profit. How much maize is
produced at this level of fertilizer use? Do these quantities fall on
the expansion path from your graph from Exercise FA4? Explain any
differences.