+ 100% Question 2. (13 marks) Consider a household that faces a risky prospect. Its initial prospects is (e14, e24; 8) = (100, 200; 0.25) The household ranks prospects according to the expected utility of the gamble defined using the cardinal utility function u(x) = In(x). i ) (4 marks) An insurance provider wishes to offer contracts to the household. Assume to start that the firm knows that the probability of loss (state 1) for the household is 8 = 0.25. Find the household's optimal choices (x1 4, x24) if it is able to purchase actuarily fair insurance that reflects their true probability of loss (state 1). ii ) (2 marks) What is the size of the insurance benefit (b), and the premium (p) for each household type implied by your answer in i)? iii) (4 marks) Suppose the insurance thinks the household is more prone to loss, specifically that its probability of the loss state is 0.4. If the firm offers actuarily fair insurance using this assessment, find its optimal choice (x14, x24 ). iv ) (3 marks) Illustrate the household's optimal choice in iii) in a sketch of its indifference curves and budget line