Pierre considers buying K items of car insurances, which pay $1 in case of an accident, at the cost of y each. The insurance estimates the probability of an accident as 20% for the type of car Pierre is driving. His utility of consuming c is U(c) = c. Denote by ca his consumption in the case of an accident and cn his consumption in the case of no accident. In case of an accident, he will buy a new car immediately, thus his consumption reduces if he does not buy the insurance. His von-Neumann-Morgenstern Utility function is therefore U(ca, Cn) = 0.2ca + 0.8Cn. His brand-new car is worth L = $4,000 and his income is m = $4,000. What is the fair price for the insurance? Justify your finding. Find Pierre's budget constraint. Determine and interpret the slope. How much of the insurance will he buy? Give a justification. a. b. C. d. (20%) (30%) (20%) If the insurance price is fair, what can you say about Pierre's state-contingent consumption? Explain. (30%)