Agricultural Production Economics
Agricultural Production Economics – Week 1:
refresher
Please make sure that you understand the below given exercises as they will be required for
subsequent steps and are relevant for the exam. These tasks are for self-study. Brief answers
will be provided later.
I) Calculus
Recall the rules of differentiation (more rules exist):
Determine the first and second derivative of the following functions:
a) 𝑓(𝑥) = 4𝑥3 + 11
b) 𝑓(𝑥) = 2√𝑥
c) 𝑓(𝑥) = 𝑎𝑥𝑏
d) 𝑓(𝑥) = 3𝑙𝑛(𝑥)
e) 𝑓(𝑥) = 𝑥2𝑙𝑛(𝑥)
II) For which of the below functions does the law of diminishing returns hold?
a) y = 3x
b) y = x3
c) y = 6x – 0.10x2
Derive APP and MPP for the above given production functions.
Agricultural Production Economics – Week 1:
refresher
Please make sure that you understand the below given exercises as they will be required for
subsequent steps and are relevant for the exam. These tasks are for self-study. Brief answers
will be provided later.
I) Calculus
Recall the rules of differentiation (more rules exist):
Determine the first and second derivative of the following functions:
a) 𝑓(𝑥) = 4𝑥3 + 11
b) 𝑓(𝑥) = 2√𝑥
c) 𝑓(𝑥) = 𝑎𝑥𝑏
d) 𝑓(𝑥) = 3𝑙𝑛(𝑥)
e) 𝑓(𝑥) = 𝑥2𝑙𝑛(𝑥)
II) For which of the below functions does the law of diminishing returns hold?
a) y = 3x
b) y = x3
c) y = 6x – 0.10x2
Derive APP and MPP for the above given production functions.
