A while ago, Lucky Luke became a farmer and now he plants corn. The utility he derives from the revenue of his crop depends on the weather of that year, and assumes the form: U (Cg, Cb)= πg·Cg^2+πb·Cb^2, where Cb is the crop level in a bad year, Cg in a good year and πg is the probability of having good weather year. Assume that the probability of having good weather is 0.6 and that a good crop is worth 100 while a bad one is worth 25.

 

1. derive Lucky Luke’s expected utility from the crop.

2. the “Dalton’s Insurance Company” proposes the following contract to Lucky Luke: “if you pay us 40 regardless of the weather we will insure you with the 75 that you loose in a bad weather year”. Should Lucky Luke accept the Dalton’s offer? Why?

 

请各位高手略展小才了，我都在这道题上绕一天了，怎么做呀这到底...  谢谢各位了！！！