【正文】 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。 the same? Another two fruit prospects A key result And now... ? State irrelevance ? Independence ? Revealed likelihood mean that preferences must be representable as... The three key axioms... ? ?? ? ? ??( ) ( )???xpayoff in state ? revealed likelihood weight on state ? the cardinal utility or felicity function: independent of state ? additive form from independence axiom The von NeumannMenstern form of the utility function ? ?? ? ? ??( ) ( )?? ?xTHREE STATES WITH PROBABILITIES 321 , ???Utility Function ?xxU ?)(Expected Utility )()()()( 332211 ??? ??? xxxxEv ???The vNM assumptions impose structure on indifference curves ? A what39。s look at these in the 2state example... Another look at preference axioms Greed: Prospect B is preferred t