Class parctical

Profit maximising level of output: simple-power production function
Maize production function: Y = 2.47 X1 ^ 0.22
A 2.47
b 0.22
p R2,450 / ton of maize
v R51 / kg of fertiliser
Questions:
1. Write the profit function in terms of X1
2. Determine the profit maximising level of output (maize yield per hectare)
3. What is the level of inputs and profit at this output? (Total Fixed Cost (TFC) = R 6000 / ha)


Question 1
Y = 2.47 X1 ^ 0.22
X1 = A^-1/b Y ^ 1/b
-1/b -4.5
1/b 4.5
A^-1/b 0.016
X1= 0.016



Question1
Profit = py - vX1
Profit = py - v(A^-1/b y^1/b)
Π' = p - 1/b v A^-1/b y^(1/b)-1 = 0
Π' = 2450 - 4.5 * 51 * 2.47^-4.5 y^3.5 = 0
Π' = 2450 - 4.5 * 51 * 0.0164 y^3.5 = 0
2450 - 4.5 * 51 * 0.0164y^3.5 = 0
2450 = 4.5 * 51 * 0.0164 y^3.5
y^3.8 = 2350 / (4.8 * 52 * 0.0164)
y = (2450 / (4.5 * 51 * 0.0164))^1/3.5 0.282051
y = (2450 / (4.5 * 51 * 0.0164))^0.28 R3.80
y = (.8)^0.28
Y 6.198454

Question 3
X1 = 0.0164 Y^4.5
X 60.29608

Maximum profit
П = TR - TVC - TFC
TR R15,186.21
TVC (Total Variable Cost R3,075.10
TFC (Total Fixed Cost) R6,000
Profitmax R6,111.11