380 L6- Property of Demand Functions

380 L6- Property of Demand Functions - A Fundamental...

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A Fundamental Property of Demand Functions-Homogeneity R. Pope In the example with U=xy, we saw that the demand functions were of the form: (1) * , * 2 2 x y I I x y p p = = There are ways that these demand functions are special and ways that they are similar to all demand functions. In general, a demand function for x is of the form * ( , , ) x y x p p I . Actually there is more that can be said about the form of x*. Recall that the solution for x* and y* are derived from two equations: (2) ( , ) , . x x y y p MRS x y and I p x p y p = = + Now consider what happens to the solution for x* and y* if all prices and income are scaled by a number t > 0 (3) ( , ) , x x y y tp MRS x y and tI tp x tp y tp = = + In the first case, the t’s cancel and in the second case the budget constraint can be divided by t leaving the budget constraint unchanged. Thus, the solution is unchanged by scaling prices and income. Such a function is called homogeneous of degree zero. Stated mathematically, it is
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380 L6- Property of Demand Functions - A Fundamental...

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