Question

A farmer has found that in a typical year they earn $75000 from their harvest. In a wet year they earn $48000, and in a drought they earn $26000. If the probability of a wet year is 0.30 and the probability of a drought is 0.20 find the mean amount this farmer will make from their harvest over a long period of years. If the farmer has the option of buying insurance for $2000 a year that pays $20000 in a year of a drought, does it make sense financially to buy the insurance? Justify.

Answer 1

1. The mean amount that this farmer will earn over a long period of years is:

$57,100

2. It makes sense financially for the farmer to buy the insurance. In a year of drought, he earns only $5,200. If he spends on insurance premium, his earnings are reduced by $2,000 to $3,200 but the insurance reimbursement will take his overall net earnings to $23,200 ($3,200 + $20,000). Incurring the insurance expense is highly justified.

Explanation:

Earnings in a typical year = $75,000

Earnings in a wet year = $48,000

Earnings in a drought = $26,000

Pro

Typical Wet Drought

Earnings $75,000 $48,000 $26,000

Probability 0.50 0.30 0.20

Expected

earnings $37,500 $14,400 $5,200

Mean earnings = $57,100

Insurance expense $2,000

Net earnings after insurance expense $3,200

Insurance Reimbursement $20,000

Net earnings $23,200