1. An individual has the risk of becoming sick next period, p=0.35. When sick, the individual earns income Is=3, and when healthy they earn Ih=5. In a single graph, complete questions a, b, c, d, and e. (a) Draw and label the endowment point (b) Draw and label the set of full insurance contracts (c) Draw and label the zero profit line (d) Individual has the following utility function over income next period: U=Ih(Is1). Draw the indifference curve intersecting the endowment point. Solve for and label it's intersection with the 45 degree line. (e) Will insurance contract =(4,4) constitute an equilibrium? Explain by determining whether the 3 equilibrium conditions hold. 2. Now, suppose there is another type of individual in this market, labelled frail. The probability of sickness is for frail individuals is pf=0.75 and their corresponding utility is U=Ih(Is2). Suppose 50% of the market are frail, and the other 50% have probability of sickness p=0.35 and U=Ih(Is1). (a) What is the level of utility through the endowment for frail individuals? (b) In a separate graph, plot the full insurance contract line, the zero profit lines for both types of individuals, and the indifference curves for each individual through the endowment point (Note: label graphs and be clear and neat. Illegible graphs will be market incorrect). (c) Assuming insurers are unable to distinguish individuals risk types, Does the point =(4.3,4.3) constitute an equilibrium? Explain by determining whether the 3 equilibrium conditions hold. (d) If insurers can perfectly discriminate individuals by risk type and are legally allowed to exclude one risk type from the others insurance contract, what pair of insurance contracts will be an equilibrium? (Hint: there will be a contract for frail types and a separate contract for the more robust individuals) 1. An individual has the risk of becoming sick next period, p=0.35. When sick, the individual earns income Is=3, and when healthy they earn Ih=5. In a single graph, complete questions a, b, c, d, and e. (a) Draw and label the endowment point (b) Draw and label the set of full insurance contracts (c) Draw and label the zero profit line (d) Individual has the following utility function over income next period: U=Ih(Is1). Draw the indifference curve intersecting the endowment point. Solve for and label it's intersection with the 45 degree line. (e) Will insurance contract =(4,4) constitute an equilibrium? Explain by determining whether the 3 equilibrium conditions hold. 2. Now, suppose there is another type of individual in this market, labelled frail. The probability of sickness is for frail individuals is pf=0.75 and their corresponding utility is U=Ih(Is2). Suppose 50% of the market are frail, and the other 50% have probability of sickness p=0.35 and U=Ih(Is1). (a) What is the level of utility through the endowment for frail individuals? (b) In a separate graph, plot the full insurance contract line, the zero profit lines for both types of individuals, and the indifference curves for each individual through the endowment point (Note: label graphs and be clear and neat. Illegible graphs will be market incorrect). (c) Assuming insurers are unable to distinguish individuals risk types, Does the point =(4.3,4.3) constitute an equilibrium? Explain by determining whether the 3 equilibrium conditions hold. (d) If insurers can perfectly discriminate individuals by risk type and are legally allowed to exclude one risk type from the others insurance contract, what pair of insurance contracts will be an equilibrium? (Hint: there will be a contract for frail types and a separate contract for the more robust individuals)
