Lottery Econ term for uncertain money outcome. Gives probability(m) for all money outcomes. Let m...

 

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• Lottery – Econ term for uncertain money outcome. Gives probability(m) for all money outcomes. Let m represent money (wealth) here State of the world Possible realization of a random variable, like your health state or wealth Insurance – Something that reduces variance of m Premiums – What you pay for the policy - in both healthy and sick states • Actuarially fair premium - Premium that just exactly covers costs of payouts on average • Loading Fees - Costs for the insurance company (normal profits, advertising, administration) on top of actuary costs Certainty equivalent – Amount x that makes you just indifferent between a particular lottery and getting x for sure Expected value of money lottery – E(m) = E m*Pr(m) (weighted average outcome of the money lottery) Expected utility E(U) – E(U) =EU(m)*Pr(m), utility of an uncertain outcome. This is at the core of theories about decision under certainty It does not equal U(E(m)) (utility of the expectation of the lottery) Exercise 2 You have $100 in wealth. You know that you face some risk (a 10% chance) of having an adverse medical event that will cause you to spend your entire wealth ($100) on healthcare. If you don't have that adverse medical event, you will retain your entire wealth. a) Describe the money lottery you face in terms of all of the possible states of the world, your wealth in those states, and the probability of each State of the World Probability Wealth State 1 (healthy) State 2 (sick) b) Find the expected value of the money lottery you face. c) Find the expected utility of the money lottery you face. Assume that the utility function is defined by U(x) = x1/2, Why didn't you need to know U(x) for part a? • Lottery – Econ term for uncertain money outcome. Gives probability(m) for all money outcomes. Let m represent money (wealth) here State of the world Possible realization of a random variable, like your health state or wealth Insurance – Something that reduces variance of m Premiums – What you pay for the policy - in both healthy and sick states • Actuarially fair premium - Premium that just exactly covers costs of payouts on average • Loading Fees - Costs for the insurance company (normal profits, advertising, administration) on top of actuary costs Certainty equivalent – Amount x that makes you just indifferent between a particular lottery and getting x for sure Expected value of money lottery – E(m) = E m*Pr(m) (weighted average outcome of the money lottery) Expected utility E(U) – E(U) =EU(m)*Pr(m), utility of an uncertain outcome. This is at the core of theories about decision under certainty It does not equal U(E(m)) (utility of the expectation of the lottery) Exercise 2 You have $100 in wealth. You know that you face some risk (a 10% chance) of having an adverse medical event that will cause you to spend your entire wealth ($100) on healthcare. If you don't have that adverse medical event, you will retain your entire wealth. a) Describe the money lottery you face in terms of all of the possible states of the world, your wealth in those states, and the probability of each State of the World Probability Wealth State 1 (healthy) State 2 (sick) b) Find the expected value of the money lottery you face. c) Find the expected utility of the money lottery you face. Assume that the utility function is defined by U(x) = x1/2, Why didn't you need to know U(x) for part a?

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a In state 1 the condition is healthy Thus there is no loss of wealth in this state Since the probab... View the full answer