Modeling risk and smoking: consider a basic model of risk-taking where an individual weighs
the decision to smoke given the potential risk of contracting lung cancer. Conditional on
smoking, our individual contracts lung cancer with probability /span>. I
1. Modeling risk and smoking: consider a basic model of risk-taking where an individual weighs the decision to smoke given the potential risk of contracting lung cancer. Conditional on smoking, our individual contracts lung cancer with probability rt. If the smoker does not contract lung cancer, they end life with their maximum potential wealth. If they do contract lung cancer, they must pay the associated medical costs. In both cases their utility is equal to U = 311/2, where 3/ represents their level of wealth. Finally, individuals can forgo taking the risk and just abstains from smoking, if they do this they are guaranteed not to get lung cancer but receive a utility payo (regardless of their wealth) of only: U (abstain) = 40. a. Graph the relationship between wealth and utility. [Just graph 4 or 5 points, you can stop at wealth equals to $3,600] [Draw a nice large graph because you will use it later.] Does it exhibit risk aversion? How can you tell? b. Susan has $2,500 in wealth. If she gets lung cancer she'll use $1,600 in medical care. On your graph, indicate Susan's outcome when sick (S) and when healthy (H) and draw her expected utility line. c. Suppose Susan has a 25% chance of getting lung cancer (1 in 4). [f Susan decides to smoke what is her expected utility? Show your work. [Hint be sure to plug utility if sick (not wealth if sick) into the formula] d. Given Susan's expected utility in part c. above, will she choose to smoke? What would the value of rt have to be such that Susan is indiferent between smoking and not smoking. .0 Structure of Insurance and the Demand for Medical Care 2. Consider the following demand equation for medical services: D(p) = 100 2p a. Graph the demand curve for medical services. b. Assume that our consumer has insurance with a co-pay of $10. What is the quantity of medical services demanded? Graph the co-pay as a horizontal line and make a note of the quantity demanded and price faced by the consumer.. Suppose the true marginal cost of the medical service is $40. 0 What is the quantity of medical services that is \"overconsumed\" due to moral hazard? o What is the total value of the additional quantity of medical care consumed due to moral hazard (hint: multiply the quantity "over consumed\" by the price and subtract out the amount paid for the \"extra\" medical care by the consumer)
