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Homework answers / question archive / Consider the following cassava yield response functions to potassium (K) input in Cambodia Using traditional varieties: Y = 2,000+100K-0
Consider the following cassava yield response functions to potassium (K) input in Cambodia
Using traditional varieties:
Y = 2,000+100K-0.3K(squared)
MPP = 100 – 0.6K
Using the new cassava variety:
Y = 2500 + 160K – 0.4K(squared)
MPP = 160 – 0.8K
Y is yield of cassava (kg/ha), K is kg of potassium, and MPP is marginal physical product. Assume that the price of one kg of potassium costs 160 Riel and one kg of cassava sells for 4 Riel (where Riel is the Cambodian currency).
A farmer using traditional varieties, will choose what level of potassium to maximize profit?
a) 100
b) 50
c) 150
d) 10
e) 0
Computation of the level of potassium to maximize profit:-
MPP with traditional method = 100 - 0.6K
Marginal revenue product, MRP = MPP * Price of cassava
MRP = (100 - 0.6K) * 4
= 400 - 2.4K
The profit will be maximized when MRP = Cost of Potassium
400 - 2.4K = 160
2.4K = 400 - 160
K = 240 / 2.4
= 100 Kg
Producing 100 Kg of potassium will maximize the profit.
Correct option is a) 100