Consider the insurance problem from class in which an agent with wealth w dollars has a chance 7 € (0, 1) of incurring a loss of dollars, where 0 < l< w. She can purchase insurance at a price q € (0, 1) per unit, up to a maximum of l units. Unlike the problem from class, there is a "deductible" d with 0 < d < l. If the agents buys x units of insurance with x >d, then the insurer pays her x-d dollars if the loss occurs; if the agent buys x units of insurance with x ≤ d then the insurer pays her nothing if the loss occurs. (a) Carefully sketch this problem in (wg, w)-space (where, as in class, wg denotes the decision-maker's wealth if the loss does not occur, and w, her wealth if it does).
Consider the insurance problem from class in which an agent with wealth w dollars has a chance 7 € (0, 1) of incurring a loss of dollars, where 0 < l< w. She can purchase insurance at a price q € (0, 1) per unit, up to a maximum of l units. Unlike the problem from class, there is a "deductible" d with 0 < d < l. If the agents buys x units of insurance with x >d, then the insurer pays her x-d dollars if the loss occurs; if the agent buys x units of insurance with x ≤ d then the insurer pays her nothing if the loss occurs. (a) Carefully sketch this problem in (wg, w)-space (where, as in class, wg denotes the decision-maker's wealth if the loss does not occur, and w, her wealth if it does).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the insurance problem from class in which an agent with wealth w dollars has a
chance 7 € (0, 1) of incurring a loss of dollars, where 0 < l< w. She can purchase insurance
at a price q € (0, 1) per unit, up to a maximum of l units. Unlike the problem from class,
there is a "deductible" d with 0 < d < l. If the agents buys x units of insurance with x > d,
then the insurer pays her x-d dollars if the loss occurs; if the agent buys x units of insurance
with x ≤d then the insurer pays her nothing if the loss occurs.
(a) Carefully sketch this problem in (wg, wo)-space (where, as in class, wg denotes the
decision-maker's wealth if the loss does not occur, and w, her wealth if it does).
(b) Write the optimization problem describing the agent's choice of insurance if she is an
expected utility maximizer with von Neumann-Morgenstern utility u(x). You do not
have to solve this problem.
(c) Suppose the agent is risk averse and the deductible is small enough so that if the price
is actuarially fair, it is not optimal for the consumer to buy no insurance. How does
the highest price at which the consumer is willing to buy x = l units compare to the
actuarially fair price (i.e. is it higher, lower, or the same)?
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