5. Individual Health Insurance Mandates and Adverse Selection Consider a market for health insurance similar to the one depicted below that we discussed in class. Demand curve Price AC curve SA Quantity Suppose individuals have different health levels H, where H is distributed uniformly between 0 and 9. The marginal cost of medical care depends on an individual's health H, and is characterized by the function MC=1000+1000*H (notice that a higher value of H corresponds to a sicker person, with higher marginal costs, so the left edge of the graph corresponds to the sickest person with H=9, and the right edge of the graph corresponds to the healthiest person with H=0). Individuals are risk averse, there is a single insurance plan available for purchase (as in the Akerlof model, NOT the R-S model), and individuals have utility functions for this insurance plan that result in a risk premium equal to RP=1000*H. a) [2 points] 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) [2 points] 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) [3 points] Draw a graph similar to the one above containing the demand function, MC function, and AC functions. For each function indicate the values of the vertical intercepts on the left (H=9) and right (H=0) sides of the graph. d) [2 points] What is the equilibrium price p* of the insurance plan in this market? e) [2 points] Which consumers will purchase the insurance plan in equilibrium? (Your answer should depend on H.)