Week5 Handout (6pp)

Week5 Handout (6pp) - Thinking about uncertainty An...

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1 Choice under uncertainty Chapter 12 Thinking about uncertainty An individual makes a choice before knowing the state of the world in which the outcome will occur. The state of the world will determine the payoff from the act. Example: choice take my umbrella (cost of carrying umbrella) or not states of the world: rain or no rain payoffs: umbrella no umbrella rain Dry minus cost wet no rain Dry minus cost dry 2 Classic example: Insurance you have income m, and with some probability you can suffer a loss L say loss occurs because of an accident States: accident (a), probability p a no accident (na) probabilty p na p a + p na = 1 So you have a bundle (m, m L) of state-contingent commodities. 3 State-Contingent Bundle C na C a m The endowment bundle. m L C a and C na are your consumptions in the two states 4 State-Contingent Budget Constraints Now suppose you can buy insurance at the rate of per dollar insured. For each you pay, the insurer will reimburse you \$1 if the accident occurs . Buy \$K of accident insurance, pay K premium. C na = m - K. C a = m - L - K + K = m - L + (1- )K. 5 State-Contingent Budget Constraints For each you give up in state na, you get a net return of 1- in state a. Or, for each \$ /(1 ) you give up in na, you get \$1 extra in a. so suppose that C a > m L, then you must give up [ /(1- )][C a (m-L)] in the no- accident state, i.e. C na = m - [ /(1- )][C a (m-L)] C m L C na a 1 1 6

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2 State-Contingent Budget Constraints C na C a m The endowment bundle. slope   1 C m L C na a 1 1 m L m L 7 Risky consumption plans Note that contingent consumption bundles that are near one axis are more risky consumption fluctuates widely depending on which state occurs. Consumption bundles near the 45- degree line are less risky consumption doesn’t fluctuate much. So a consumer that does not like risk
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Week5 Handout (6pp) - Thinking about uncertainty An...

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