Question

Two farmers decide to work together and diversify their crops. One farmer will grow rice, and the other farmer will grow potatoes. The two farmers gather data on their yields of rice and potatoes over the past four years and compile it in the table below:

Crop	Yield from year 1	Yield from year 2	Yield from year 3	Yield from year 4
Rice	5	3	8	4
Potato	9	17	0	14

(a) What is the expected yield of rice in year 5? What is the expected yield of potatoes in year 5?

(b) Do rice and potato appear to have a positive or negative covariance? Does this mean rice and potato are a good, or bad choice for diversification? (you do not need to calculate the covariance to answer this question)

Answer 1

Going by the average yield in four years

Expected yield of rice in year 5 = (5 + 3 + 8 + 4) / 4 = 5

Expected yield of potatoes in year 5 = (9 + 17 + 0 + 14) / 4 = 8

The yields of rice aand potatoes seem to have a negative covariance because they are inversely related an increase in the yield of rice corresponding has a decrease in the yield of potatoes and vice versa.

The diversification of planting rice and potatoes is a bad choice because the total yield would be better without diversification.