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...) But what determines the shape of the indifference map? Given this situation... suppose RED begins to seem less likely ? A x(BLUE) x(RED) ? E ? B you need a bigger win to pensate Indifference curves after the change change in perception rotates the contours After the change B (not A) is equivalent to E ? Distinguish goods by stateoftheworld as well as by physical characteristics etc ? Extend consumer axioms to this classification of goods ? From indifference curves get the concept of certainty equivalent ? Model changes in perceptions of uncertainty about future prospects A provisional summary on modelling uncertainty. We can: The Consumer Opportunities and Preferences Expected Utility Risk Aversion Optimisation and Comp. Statics Aggregation Welfare Modelling Uncertainty l i rtai ty The Basics (Again) Further restrictions on the structure of utility functions Three extra axioms to clarify the consumer39。s attitude to uncertain prospects For more results we need more structure ? State irrelevance: The identity of the states is unimportant ? Independence: Induces an additively separable structure ? Revealed likelihood: Induces a coherent set of weights on statesoftheworld Time for a closer look Three key axioms... Relabelling the statesoftheworld does not affect utility All that matters is the payoff in each stateoftheworld 1: State irrelevance We can see this by partitioning up the state space for ? 2: 2: The independence axiom What if we pare prospects that have the same payoff under GREEN? 0 x(BLUE) The ordering of points is identical for each plane The independence axiom Re d Bl ue Gree