class practical

Three-stage production function
Wheat production function for Denmark
Y Wheat yields in tons per ha
X1 Nitrogen fertiliser application in kg per ha
PF Y = aX1 + bX1^2 + CX1^3
a 0.02
b 0.005
c -0.00007
y = 0.02X1 + 0.005X1^2 -0.00007X1^3

Questions
1. Compile a table and graph for the TPP for Nitrogen fertiliser application between 0-100 kg. / ha (use intervals of 5kg)
2. Mathematically determine the level of Nitrogen application at which output (wheat yields) is at its maximum level

Quadratic formula
x = (‐B ‐ SQRT(B^2 ‐ 4*A*C))/(2*A).

Question1

NitrogenX1 TPP
0 0.0
5 0.2 TPP
10 0.7 10.0
15 1.2
20 1.8 5.0

25 2.5
Maize yield t/ha




0.0
30 3.2 0 20 40 60 80 100 120

35 3.8 -5.0
40 4.3
-10.0
45 4.6
50 4.8 -15.0
55 4.6
-20.0
60 4.1
N fertilizer application kg/ha
65 3.2
70 1.9
75 0.1
80 -2.2
85 -5.2
90 -8.7
95 -13.0
100 -18.0



Question 2
y = 0.02X1 + 0.005X1^2 -0.00007X1^3
a' 0.02
b' 0.01
c' -0.00021