Sandra Lives in the Pacific Northwest and Enjoys Walking to and from Work

Essay

Sandra lives in the Pacific Northwest and enjoys walking to and from work during sunny days. Her utility is sharply diminished if she must walk while it is raining. Sandra's utility function is
U = 1,000 I₁ + 250 I₂ + 1 I₃ where I₂ = 1 if she walks and there is no rain and I₁ = 0 otherwise, I₂ = 1 if she drives to work and I₂ = 0 otherwise, and I₃ = 1 if she walks and it rains and I₃ = 0 otherwise. Sandra believes that the probability of rain today is ³/₁₀. Given her beliefs, what is her expected utility from walking to work? What is her expected utility from driving to work according to her beliefs? If Sandra maximizes her expected utility according to her beliefs, will she drive or walk to work? Sandra missed the weather report this morning that stated the true probability of rain today is ⁴/₅. Given the weather report is accurate, what is Sandra's true expected utility from walking and driving to work? How much could Sandra increase her expected utility if she read and believed the weather report?