Simple power production function: finding the profit maximising level of input
Onkruid production function: Y = 2.39 X1 ^ 0.25
b 0.25
A 2.39
v R45 Price of a kg organic fertiliser
p R850 Price of a ton onkruid
TFC v*X1
TVP p*2.39X1^0.25
Mathematically derive the profit maximising level of input
TVP = P*TPP
П = TVP - TFC
П = pAX1^b - vX1
Profit function of onkruid production = П = p*2.39X1^0.25 - vX1
b 0.25
A 2.39
v 45
p 850
dП /dX1 = 0
(bpAX1^b-1) - v =0
bpAX1^b-1 = v --> MRP = MC
x1^b-1 = v/bpA
X1 = (v/bpA)^(1/(b-1))
X1 = ((45/(0.25*850*2.39))^1/(0.25-1)
Onkruid production function: Y = 2.39 X1 ^ 0.25
b 0.25
A 2.39
v R45 Price of a kg organic fertiliser
p R850 Price of a ton onkruid
TFC v*X1
TVP p*2.39X1^0.25
Mathematically derive the profit maximising level of input
TVP = P*TPP
П = TVP - TFC
П = pAX1^b - vX1
Profit function of onkruid production = П = p*2.39X1^0.25 - vX1
b 0.25
A 2.39
v 45
p 850
dП /dX1 = 0
(bpAX1^b-1) - v =0
bpAX1^b-1 = v --> MRP = MC
x1^b-1 = v/bpA
X1 = (v/bpA)^(1/(b-1))
X1 = ((45/(0.25*850*2.39))^1/(0.25-1)
