1) Insurance and social policy You are making an app with a 5% chance of making
ID: 1201886 • Letter: 1
Question
1) Insurance and social policy
You are making an app with a 5% chance of making a ton-load of money, and 95% chance of earning nothing. Your utility is the square root of income (Utility = Y1/2); you will have $10,000,0001/2 happiness if your app succeeds but 01/2 happiness if it fails.
a) (2 points) What is the expected value of your app? How much money can you expect to make? What is your utility at that income (if you know that your income will be the expected value of your app)?
Note that in EXCEL, the square root function is “=X^.5” for the number X
b) (1 point) What is your expected utility from your app? (Note: this is the weighted average of utility when the app succeeds and when it fails where the weight is the probability of success.)
c) (2 points) Why do people buy insurance? How can insurance companies profit? What happens to expected utility when people can buy insurance at a fair market price?
d) (2 points) What is moral hazard and what is adverse selection. How do these affect insurance markets? Give examples from the marketing of veterinary insurance. Would you expect markets with moral hazard and adverse selection to provide the optimal amount of veterinary insurance at an efficient price?
Explanation / Answer
a) What is the expected value of your app? How much money can you expect to make? What is your utility at that income (if you know that your income will be the expected value of your app)?
Ans:- The expected value of the app is $500000 which is the chance times the value of success plus the chance times the value of the failure. In this case, it is (0.05 * $10,000,000) + (0.95 * $0) = $500000. My utility at that income is square root of $500000 which is approximately $707.10
Note that in EXCEL, the square root function is “=X^.5” for the number X
b) What is your expected utility from your app? (Note: this is the weighted average of utility when the app succeeds and when it fails where the weight is the probability of success.)
Ans:- My expected utility from my app is the chance times the utility of option one plus the chance times the utility of option two. In this case, (0.05 * square root $10,000,000) + (0.95 * square root $0) which is around $3162.28.
c) Why do people buy insurance? How can insurance companies profit? What happens to expected utility when people can buy insurance at a fair market price?
Ans:- People buy insurance because it guarantees them the same utility or better than without insurance. Insurance companies can profit by selling plans to customers who are less likely to make claims, or customers who have more stable income. Expected utility would increase when people can buy insurance at a fair market price because the insurance protects them from uncertainty.
d) What is moral hazard and what is adverse selection. How do these affect insurance markets? Give examples from the marketing of veterinary insurance. Would you expect markets with moral hazard and adverse selection to provide the optimal amount of veterinary insurance at an efficient price?
Ans:- Moral hazard is the phenomenon where consumers will only buy insurance when they will need it. For example, people will only buy health insurance when they know they are going to be sick. Adverse selection is the tactic that insurance companies adopt to counteract moral hazard. They screen their potential customers and “cherry pick” and “lemon drop” so that they can maximize the profits. They only sell insurance to those who are less likely to need it. Moral hazard and adverse selection make the health insurance markets have more asymmetric information and be less efficient. Consumers are trying to buy insurance only when they need it while insurance companies try to sell insurance only to those who don’t need it. When insurance companies have to pay claims then they will increase their premiums to cover their increased expenses. Markets with moral hazard and adverse selection are not likely to provide optimal insurance at an efficient price. Instead, the insurance companies will likely provide insurance only at a high price or not at all.
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