Suppose insurance companies can perfectly observe
the types of insurance consumers.
i. Using the numerical values provided for a, z, πL, and πH, write down the
zero-profit condition for providing insurance to type H consumers specifying
y as a function of x.
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ii. Find the values for x and y that a type H consumer will receive from an
insurance contract in the competitive insurance market. Show your work.
iii. Find the values for c and f that a type H consumer will receive from an
insurance contract in the competitive insurance market. Show your work.
iv. Using the numerical values provided for a, z, πL, and πH, write down the
zero-profit condition for providing insurance to type L consumers specifying
y as a function of x.
v. Find the values for x and y that a type L consumer will receive from an
insurance contract in the competitive insurance market. Show your work.
vi. Find the values for c and f that a type L consumer will receive from an
insurance contract in the competitive insurance market. Show your work.
vii. Construct a well-labeled diagram with x on the horizontal axis and y on the
vertical that graphically shows how the equilibrium values of x and y are
determined for both types of consumers.
(b) Asymmetric information. Now suppose that insurance companies cannot observe
the types of insurance customers.
i. Find the values for x and y that a type H consumer will receive from an
insurance contract in a separating equilibrium (assuming that one exists).
You do not have to show your work.
ii. Find the values for x and y that a type L consumer will receive from an
insurance contract in a separating equilibrium (assuming that one exists).1
Show your work.
iii. Let nH and nL denote the numbers of type H consumers and type L consumers.
Suppose that nH = 100 and nL = 900. Is there a separating equilibrium
in the insurance market? Explain.
iv. Suppose that nH = 500 and nL = 500. Is there a separating equilibrium in