Question 4 Suppose individuals have different health levels H, where H is distributed discretely between 0 and 9, with equal numbers of individuals with each H. The marginal cost of medical care depends on an individual's health H, and is characterized by the function MC=10,000-1,000*H (notice that a higher value of H corresponds to a healthier person). Individuals are risk averse, there is a single insurance plan available for purchase, and individuals have utility functions for this insurance plan that result in a risk premium equal to RP=9,000-1,000*H. Insurers do not know an individual's H. a) Write down the equation describing the demand function for this insurance plan. (Hint: the demand function should express willingness to pay for insurance as a function of H). b) Write down the equation describing the average cost function of the insurer. (Hint: since the MC function is linear, the AC function is also linear. If you find any two points along the line you can figure out the equation for the line.) c) Draw a graph containing the demand function, MC function, and AC functions. For each function indicate the values of the vertical intercepts on the left (H=0) and right (H=9) sides of the graph. d) What is the equilibrium price p* of the insurance plan in this market? e) Which consumers will purchase the insurance plan in equilibrium? (Your answer should depend on H.) f) Calculate the size of the deadweight loss from adverse selection in the insurance market. Now suppose an individual insurance mandate is imposed that forces all consumers to purchase insurance. g) What will the insurance mandate do to the equilibrium price of insurance? h) Which types are worse off under this mandate? Which types are made better off? Suppose now that individuals either have to buy insurance or else pay a tax penalty of $3000 (similar to the former ACA insurance mandate). i) Which types would rather pay the tax penalty? Careful: this will change the equilibrium price. Assume that individuals who are indifferent between the tax penalty and purchasing insurance choose to purchase insurance. i) How large is the deadweight loss from adverse selection in the market under this policy? k) What is the smallest mandate tax penalty that will completely eliminate the deadweight loss from adverse selection in this market