Answer to Question #203782 in Economics of Enterprise for saleha

Question

John is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. John’s utility function is 𝑢(𝐶) = 5√𝐶 , where 𝐶 is the value of consumption. Use this information to fill out the table below. (Don’t forget to include the value of wealth when you compute consumption!). The PDF will round all typed numbers to two decimals; However, you should use all decimals when computing your answers.

Answer 1

Missing part of the question:

Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that requires the farmer to plant corn. Here’s how the insurance contract works. At the beginning of the year, the corn farmer pays an insurance premium of $202.5. If the weather is GOOD, Mae makes no payment to the farmer. If the weather is BAD, Mae makes an indemnity payment of $675 to the farmer.

a. If a farmer buys this insurance contract, what is Mae’s expected profit?

b. What is John’s expected utility if he plants corn with an insurance contract?

c. Which activity will John choose? (Corn without insurance, Corn with insurance, Beans)

d. What is the highest premium Mae could charge such that John would still want to buy the insurance contract?(Assume the indemnity payment remains at $675)

Solution

a.

MAE's expected profit can be calculated by :

Premium amount - (Probability of bad weather * Payment made during bad weather)

MAE's expected profit $= 202.5 - 0.3 \times675$

MAE's expected profit = 202.5 - 202.5

MAE's expected profit = $0

b.

 John’s expected utility if he plants corn with an insurance contract = {5Probability of Good weather * Earings^0.5 + Probability of Bad weather * Earning with insurance^0.5 - Premium of insurance^0.5 }

 John’s expected utility if he plants corn with an insurance contract

= 5 {0.7*675^0.5 + 0.3*675^0.5 - 202.5^0.5 }

 John’s expected utility if he plants corn with an insurance contract = $58.75

c.

 John’s expected utility if he plants corn with an insurance contract = $58.75

 John’s expected utility if he plants corn without an insurance contract = 5{Probability of Good weather * Earings^0.5 + Probability of Bad weather * Earning^0.5 }

 John’s expected utility if he plants corn without an insurance contract = 5{0.7 * 675^0.5 + 0.3 * 0^0.5 } = $90.93

 John’s expected utility if he plants beans = 5{Probability of Good weather * Earings^0.5 + Probability of Bad weather * Earning^0.5 }

 John’s expected utility if he plants beans = 5{0.7 * 451^0.5 + 0.3*451^0.5 } = $106.18

John has the same utility with and without insurance.

John will choose to plant beans as the expected utility is highest. 

d.

The highest premium Mae could charge such that John would still want to buy the insurance contract :

{ Probability of Good weather * Earings^0.5 + Probability of Bad weather * Earning^0.5 } = John's wealth - Premium

{ 0.7 * 675^0.5 + 0.3 * 0 ^0.5 } = 225 - RP

RP = $206.81

the highest premium Mae could charge such that John would still want to buy the insurance contract is $206.81