Consider the following competitive market for insurance. There are two states of the world: good G and bad B. Consumers have wealth £500. If the bad state occurs their wealth is reduced by £200. Consumers are expected utility maximisers, with common utility func- tion u(x)=√√x. There are two types of consumers: high risk types H and low risk types L. Consumers know their own types, but firms cannot distinguish between different types of consumers. The probabilities that H and L types find themselves in the bad state are PH = 0.5 and PL = 0.4. It is estimated that 70% of the population are low risk. Firms are expected profit maximisers that offer consumers state-contingent contracts c = (CG, CB) in exchange for their endowment e = (eg, eg). Determine the equilibrium set of contracts.

Consider the following competitive market for insurance. There are two states of the world: good G and bad B. Consumers have wealth £500. If the bad state occurs their wealth is reduced by £200. Consumers are expected utility maximisers, with common utility func- tion u(x)=√√x. There are two types of consumers: high risk types H and low risk types L. Consumers know their own types, but firms cannot distinguish between different types of consumers. The probabilities that H and L types find themselves in the bad state are PH = 0.5 and PL = 0.4. It is estimated that 70% of the population are low risk. Firms are expected profit maximisers that offer consumers state-contingent contracts c = (CG, CB) in exchange for their endowment e = (eg, eg). Determine the equilibrium set of contracts.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider the following competitive market for insurance. There are two states of the world:
good G and bad B. Consumers have wealth £500. If the bad state occurs their wealth is
reduced by £200. Consumers are expected utility maximisers, with common utility func-
tion u(x) = Vx. There are two types of consumers: high risk types H and low risk types
L. Consumers know their own types, but firms cannot distinguish between different types
of consumers. The probabilities that H and L types find themselves in the bad state are
Pu = 0.5 and p = 0.4. It is estimated that 70% of the population are low risk. Firms are
expected profit maximisers that offer consumers state-contingent contractsc = (cg, Cg) in
exchange for their endowment e = (eg, eg). Determine the equilibrium set of contracts.

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Step 1: Explain competitive market

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Step 2: Expected consumer utilities for each state

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Step 3: Market clearing condition

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Step 4: Solve for equilibrium contract and premium

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