Risk and Insurance Activity:

Kelly is a farmer with zero wealth. She can either plant rice or cotton. If she plants cotton, Kelly earns an income of $1600 if the weather is GOOD, and $0 if the weather is BAD. If she plants rice, Kelly will have an income of $900 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. Kelly's utility function is ()=3*sqrt(c), and c is the value of consumption. Follow these informations to answer the following questions.

Kelly:

1. What is theExpected Value of Consumptionofplant riceandplant cotton?
2. What is theExpected Utilityofplant riceandplant cotton?
3. What is theCertainty Equivalent of consumptionofplant riceandplant cotton?
4. What is theRisk Premiumofplant riceandplant cotton?

Kelly's cousin Xinda is a farmer who faces the same choice as Kelly does, but he has wealth of$200 which he will add to his income from farming in his consumption. Coincidentally, he has the same utility function as Kelly: ()=3*sqrt(c), wherecis the value of consumption. Answer the following questions for Xinda.

Xinda:

1. What is theExpected Value of Consumptionofplant riceandplant cotton?
2. What is theExpected Utilityofplant riceandplant cotton?
3. What is theCertainty Equivalent of consumptionofplant riceandplant cotton?
4. What is theRisk Premiumofplant riceandplant cotton?
5. What type of risk preferences does Xinda have?
6. Which crop will Xinda choose to plant?
7. What is the effect of Xinda's wealth on his crop choice?

A new cotton mill has opened in a nearby town, and they have decided to offer an insurance contract to cotton farmers in the area.At the beginning of the season, farmers pay a premium of $480. If the weather is GOOD, the insurance will pay nothing to the farmer. If the weather is BAD, the insurance will pay an indemnity payment of $1600 to the farmer. Think that cotton mill's insurance agents have perfect information about the farmer's activity choice (means they can enforce a contract that requires the farmer to choose cotton).

1. What is the cotton mill's expected profit from this contract?
2. What are the expected utilities for planting cotton with insurance for Kelly and Xinda?
3. IfKellyis now choosing betweenplanting cotton without insurance,planting rice, andplanting cotton with insurance, what will she choose?
4. IfXindais now choosing betweenplanting cotton without insurance,planting rice, andplanting cotton with insurance, what will she choose?