Microeconomic theory : A Mathematical Approach by james henderson

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By james henderson

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They are derived from the consumer's risk behavior and are valid for predicting his choices as long as he maximizes expected utility. They are derived by presenting him with mutually exclusive choices ; therefore, it is meaningless to attempt to infer from the utility of event A and the utility of event B the utility of the joint event A and B. Von Neumann-Morgenstern utilities possess some, but not all, the proper­ ties of cardinal measures. Let the utilities of three alternatives be UA 10, UB = 30, and Uc = 70.

The law of diminishing marginal productivity con­ cerns the relative quantities of · the inputs and is not applicable if both inputs are increased. The entire productivity analysis may be applied to variations of X2 with x1 as the parameter. ,X�) - f(XIX�) x12 = O If a fraction equals zero, its numerator must equal zero : XI/I(xi,xg) - f(xx,xg} = 0 Moving the second term to the right, and dividing through by 0 f1(X11X2) = f(xi,x�) XI x1, -­ MP and AP are equal at the point of maximum AP if such a point exists.

Such comparisons do not imply, however, that the consumer would prefer to have C over B to B over A, since the chosen alternative must have the highest utility number. Interpersonal comparisons of utility are still impossible. However, the construction of von Neumann-Morgenstern utilities does permit (1) the complete ranking of alternatives in situations characterized by certainty, (2) the comparison of utility differences by virtue of the above cardinal property, and (3) the calculation of expected utilities, thus mak­ ing it possible to deal with the consumer's behavior under conditions of uncertainty.

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