Question

Imagine an area that has one dominant industry of cassava growing. Cassava is a low-risk crop that has an 80% chance of having a good harvest giving a farmer an income of 100 dollars and a 20% chance of a poor harvest giving a farmer zero dollars. Buying cassava clippings necessary for planting costs the farmer 50 dollars.

i.   What are the expected profits of growing cassava?
ii. Suppose some households do not have any assets or cash necessary to pay the investment cost for planting cassava, what is the maximum interest rate a farmer will be willing to pay a bank assuming they have limited liability and are risk-neutral?
iii. Would a lender be willing to lend at this interest rate?

Answer 1

i. The expected payoff for a farmer will be 0.8*(100) + 0.2*(0) = 80 dollars
The cost of planting is 50 dollars
Expected profit will be 80 - 50 = 30 dollars

ii. The investment of 50 dollars today is expected to give a profit of 30 dollars in the future, i.e. the investment grows to 80 dollars.
If we let i to be the maximum interest rate that the farmer will be willing to pay, then

50(1+i) = 80
1+i = 1.6
i = 0.6 or 60 per cent

iii. Yes, any lender would be willing to pay at high interest rate such as 60 percent.