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To: gpowell who wrote (311)	11/17/2003 10:33:51 PM
From: Don Lloyd	Read Replies (1) \| Respond to of 445

gpowell, Further Notes on MRS. As decision makers move towards utility maximization, the path becomes indeterminate at points of indifference. When a decision maker faces a move to a state of higher utility, and if there is more than one state at this same higher utility, we cannot predict which state the decision maker will chose. Indifference sets are used to contain these equally preferred states and each point in the indifference set becomes an equally likely point of exchange. In addition, each state in the indifference set has a relationship with every other state in the set - this relationship is defined by the marginal rate of substitution between states. As individual decision makers become coordinated in exchange markets, it is the intersection of indifference sets that define which exchanges will occur. The utility maximization principle places a condition that the exchange will occur at points where the marginal rate of substitution of the market participants are equal. Even if utility has enough reality to be maximized, there is nothing to say that the maximum state can't be found and achieved by an exhaustive global search strategy performed over all achievable states. OTOH, there is no guarantee that the maximum state can be reached by a form of a local strategy of gradient ascent unless all possible combinations of goods including money are involved in the full dimensional step content. The maximum state may or may not be close to the second ranked state, but it need not necessarily share any goods content with it. Regards, Don