ii) Imposing a 20% tax on Peter and transferring any revenue (minus the loss) to Paul. Which policy would the government prefer if it had a Utilitarian social welfare function? What about a maxmin social welfare function? Explain how these social welfare functions differ in how they weight each member of society. 3. (30 marks) Annie and Jeff both have an income of $50 000, and identical utility functions U i (y i ) = y i 0.5 where i denotes either Annie or Jeff and y is their individual income. Suppose Annie has a 20% chance of being unemployed next year and losing $20 000 in income. Jeff has a 10% change of being unemployed next year and losing $20 000 in income. a) What are Annie and Jeff’s expected utilities if they are unable to purchase insurance? b) What are the actuarially fair premiums for Annie and Jeff if they are able to purchase insurance to cover their entire loss? What are their expected utilities with these insurance policies? c) Suppose Annie and Jeff must enter into a joint insurance contract where each pay a premium of $3000 and receive full insurance if they become unemployed. Calculate their expected utility under this insurance policy. Would either of them choose to opt out of this insurance policy if they had a choice? ********
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