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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

Economics

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

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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

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