Individuals in the non-group market have an illness probability of p, which is uniformly distributed between...

 

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Individuals in the non-group market have an illness probability of p, which is uniformly distributed between 0 and 1. The individuals have access to a competitive insurance market that is regulated to offer a homogenous product. We can treat this as a single insurance product that will always break even. The expected cost of insuring an individual with an illness probability p is given by Cp-p300. The utility that a consumer will illness probability p receives from purchasing insurance at premium r is given by U-p900-r. The utility they receive from purchasing no insurance at all is 0. 1. Now suppose we implement an "individual mandate that issues a fine of 300 dollars to any individual that does not purchase insurance. In the model, assume that this means that the utility from not purchasing insurance is Uno insurance--300. In this case, for an arbitrary value r, which consumers will buy insurance? 2. Now that the individual mandate is in place, what is the average cost of insurance given some value of r? 3. What is the equilibrium premium with the individual mandate in place? 4. Using intuition from the model we just worked through, explain why the model predicts that the individual mandate both increases the number of insured individuals and decreases the equilibrium premium. (In other words, explain the economics of the differences in your answers for parts 2-5 and parts 6-8). Individuals in the non-group market have an illness probability of p, which is uniformly distributed between 0 and 1. The individuals have access to a competitive insurance market that is regulated to offer a homogenous product. We can treat this as a single insurance product that will always break even. The expected cost of insuring an individual with an illness probability p is given by Cp-p300. The utility that a consumer will illness probability p receives from purchasing insurance at premium r is given by U-p900-r. The utility they receive from purchasing no insurance at all is 0. 1. Now suppose we implement an "individual mandate that issues a fine of 300 dollars to any individual that does not purchase insurance. In the model, assume that this means that the utility from not purchasing insurance is Uno insurance--300. In this case, for an arbitrary value r, which consumers will buy insurance? 2. Now that the individual mandate is in place, what is the average cost of insurance given some value of r? 3. What is the equilibrium premium with the individual mandate in place? 4. Using intuition from the model we just worked through, explain why the model predicts that the individual mandate both increases the number of insured individuals and decreases the equilibrium premium. (In other words, explain the economics of the differences in your answers for parts 2-5 and parts 6-8).

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1 With the individual mandate in place any consumer with illness probability p higher than p 600 will purchase insurance to avoid the fine of 300 doll... View the full answer