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, and individuals have utility functions for this insurance plan
that result in a risk premium equal to RP=1000*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 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) 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
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 or else pay a tax of $3000.
g) What will the insurance mandate do to the equilibrium price of insurance?
h) What is the effect of the mandate on the deadweight loss from adverse selection in the market?
i) What is the smallest mandate tax penalty that will completely eliminate the deadweight loss
from adverse selection in this market?