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Unformatted text preview: Kata Bognar kbognar@ucla.edu Economics 142 Probabilistic Microeconomics UCLA Fall 2009 6 Trading StateContingent Goods  Risk Sharing Readings. Chapter 78. Concepts. Markets for state contingent goods. Risk sharing, feasibility, individual rationality, Pareto efficiency. Market equilibrium for state contingent goods, state prices. Asset prices, CAPM. 6.1 Example In the previous section we discussed individual behavior in the presence of risk. The terms of possible trade was given, i.e. price and returns of the assets, price of the insurance, gamble and we were interested in individual behavior. Next we analyze exchange between individuals in case of risk. We refer to trading risky assets as risk sharing and and we look into how the terms of trade arise. In our society, there are several institution through which people can share risks. There are individual contracts, financial markets, social institutions like family, social security, etc. We will model some of those using the model of markets, which must be familiar from Economics 11. We provide predictions about prices and quantities traded and emphasize welfare properties of these market, as well as problems if markets to share risks are missing. To start, consider the following example. Suppose that there are two travelers. Traveler 1 keeps her $100 in a safe place while traveler 2 does not so she may get mugged with probability 1/2. Also suppose that traveler 2 cannot eliminate the chance of being mugged and cannot even reduce this probability. Label the state in which traveler 2 does not get mugged as state 1 and the state in which traveler 2 gets mugged as state 2. We can expect an exchange, so that traveler 1 helps out traveler 2 in case she gets mugged. Traveler 2s situation is very risky so likely she is willing to give up a large sum of money in expectation to reduce this risk. 1 On the other hand traveler 1 does not face any uncertainty to start with so by the local risk neutrality she is willing to take some risk if her expected payoff sufficiently increases by that. There are many possible agreements between the two travelers. One possible contract to sign before the uncertainty is resolved is the following: traveler 2 gives $50 to traveler 1 if traveler 2 is not mugged (in state 1) traveler 1 gives $25 to traveler 2 if traveler gets mugged (in state 2). 1 How much exactly she is willing to give up depends on the level of her risk aversion. 1 How much money each traveller will have after signing this agreement? Initially, traveler 1 faces a riskyfree that is $100 in state 1 and $100 in state 2 while the endowment of traveler 2 is $100 in state 1 and 0 in state 2. After signing the contract, traveler 1 has $150 in state 1 and $75 in state 2 and traveler 2 has $50 in state 1 and $25 in state 2....
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 Fall '09
 Bognar
 Microeconomics

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