# 1. Suppose that an individual has a utility function U(c) = c1/2. They have 400 dollars. With…

1.Suppose that an individual has a utility function U(c) = c1/2. They have 400dollars.With probability 0.1 they get sick, which results in complete loss of their wealth(their wealth becomes 0.a.What is their expected wealth?What is their expected utility? How much wouldthey being willing to pay for insurance which would fully cover the cost of being sick if theybecome ill?b. Now suppose there is a second individual who has the same wealth, and gets sick toa similar degree (loses all of their money if they get sick), but who gets sick with probability.5.What is their expected wealth?What is their expected utility? How much wouldthey being willing to pay for insurance which would fully cover the cost of being sick if theybecome ill?c.Suppose an insurance company can’t tell the difference between individuals 1 andindividual 2.What is the expected cost of insuring individual 1 (hint: how much wealthdoes the insurance company expect to lose)? The expected cost of insuring individual 2? Ifthe insurance company believes that individual 1 and individual 2 are equally likely to applyfor insurance, what is the expected cost of insurance (hint: just use the law of expected valueone more time)?d. If the insurance company offers the averaged plan at cost (which you just calculated),are both individuals willing to purchase the plan? Is this an example of adverse selection, ormoral hazard, or neither? Is the equilibrium a pooling equilibrium or separating equilibrium.2. Suppose you are interested in assessing the value of a statistical life for individuals.You find a dataset on risk and wages. You consider running the following OLS regression.wagesi= ß0+ ß1fatal_riski+ ui.Fatal_risk ranges from 0 to 100 in this example.a. Theoretically, do we expected ß1to be positive or negative? Why?1b.Calculate the VSL by using ß1and the implied compensation associated with achanging fatality risk from 0 to 100.c.What is a potential pitfall of using ß1to calculated the necessary compensation togo from a 0 to 100 percent risk of fatality (hint, how much variation in fatality risk are welikely to observe in the data)?3.a.Based on Ruhm’s paper on recessions and health, what are the age group wheremortality has the strongest percentage response to an increase in the unemployment rate?b.What are Ruhm’s conclusions about potential mechanisms that could explain thenegative relationship between aggregate unemployment and mortality? What do you thinkanother mechanism might be and what data would you use test your hypothesis?4. Stata StuffUse HW2_Data from blackboardIn this file there are the following variables:fat_risk – which is the fatality risk per FTE (hence going from 0 to 1 represents goingfrom 0 to 100 percent fatality risk).occ – description of occupationwages – average hourly wagesearnings – average yearly earningseducation_req – description of the minimumeducational requirement for the job (“N”=none,”H”=High School, “C”=college).First create a series of dummy variables for the different educational requirements (theeasiest way is “tab education_req, gen(ed_)” which will a series of dummy variables ed_1,ed_2, etc. for all of the different unique values for education_req).2a.Estimate the regressionwages=ß0+ ß1fat_risk + ß2ed_1 + ß2ed_2 + ui(you can actually put any two of the three dummy variables for education, but Statawon’t let you put all three because of multi-colinearity).What is the estimated value ofß1? Because this refers to hourly wages, to find the implied value of a statistical life, youmust multiply ß1by a measure of the number of hours in a year (try 2080, which is 40*52).After multiplyingˆß1by 2080, what is the implied VSL?b. An alternative way to estimate a VSL would be on the regressionearnings=ß0+ ß1fat_risk + ß2ed_1 + ß2ed_2 + uiWhat is the estimated VSL based on this regression?c. This approach to a VSL is also called the hedonic approach, and it relies on comparingrisks for occupations after controlling for differences. What other controls might also beimportant determinants of wages or earnings, and how might their exclusion bias the currentestimates?5. Please use the Table Below for problem 3.ItemCaloriesHealthyPricePrice Per 100 CaloriesSnickers27101.39Fuji Apple7211.10Doritos255403.68Broccoli15411.50Savoy Cabbage12211.79Skippy Cream Peanut Butter475004.36Chicken of the Sea (Tuna)10011.693a. Fill in the Column of Price per 100 Calories.b.What is the average price per 100 calories for healthy foods (foods with a 1 in thehealthy column) vs. unhealthy foods (foods with a 0 in the unhealthy column).c.If you run a regression with price per 100 calories as the dependent variable andhealthy (the 0/1 variable as a regressor), what is the estimated coefficient on healthy?Ifyou assume heteroskedastic standard errors, is it statistically different from zero?d. What’s a compelling reason people might consume unhealthy food despite the healthrisks, based on the data above? Would we expect consumption of unhealthy food to varyby income even if there are differences in prices? Why or why not?6.a. Consider a utility function where Utility in period t if a person exercises is 2, andutility in period t+1 if they exercise is 8.On the other hand if they don’t exercise, theirutility in period t is 6, and their utility in period t+1 is 4. Consider two scenarios. If theperson has discounts geometrically across future utilities, with ß = .8, how does the personfeel about exercising today. What about exercising 7 days from now?b. Alternatively, suppose an individual hyperbolically discounts, so the discount factorapplied to period t is11+t. How does the person feel about exercising today? What aboutexercising 7 days from now? Does this person have time-consistent or time-inconsistentchoices?4

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