Economics expected theory

Alvin and Bobbi each have wealth equal to $100, and each is presented with the same investment opportunity. If the investment is successful then the individual will have wealth equal to $1000. If the investment is a failure then the individual will have wealth equal to $0. The probability of success is 0.10.
Alvin and Bobbi must choose independently whether to make the investment or not. Use expected utility theory to answer the following questions. In this problem all utility functions are defined in terms of wealth, W.
(a) Alvin’s preferences are described by the utility function U = W.
Assuming Alvin acts to maximize utility, will Alvin choose to make this investment? Answer: Yes/No/She is Indifferent
(b) Bobbi’s preferences are described by the utility function U ( W ) = W.
Assuming Bobbi acts to maximize utility, will Bobbi choose to make this investment? Answer: Yes/No/He is Indifferent

Now suppose the investment opportunity changes such that the new probability of success is 0.5. All other details remain the same.
(c) Alvin’s preferences are described by the utility function U = W.
Assuming Alvin acts to maximize utility, will Alvin choose to make this investment? Answer: Yes/No/she is Indifferent
(d) Bobbi’s preferences are described by the utility function U ( W ) = W.
Assuming Bobbi acts to maximize utility, will Bobbi choose to make this investment? Answer: Yes/No/she is Indifferent
(e) Compare your responses in parts (a) and (c). Does Alvin change his behavior? Why or why not? Explain and write.
(f) Compare your responses in parts (b) and (d). Does Bobbi change her behavior? Why or why not? Explain.

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