Question
Verify the properties for the Marshallian demand function in the following propostion generated by the Cobb-Douglas utility function.Proposition4.1 : Suppose that u(.) is a continuous
Verify the properties for the Marshallian demand function in the following propostion generated by the Cobb-Douglas utility function.Proposition4.1 : Suppose that u(.) is a continuous utility function representing a locally nonsatiated preference relation >= ,then the Marshallian demand function x(p,Y) possess the following properties: (i) Homogeneity of degree zero in (p,Y). In other words, x(ap,aY)=x(p,Y) for any p,Y and scalar a.(ii) Walras' law : px= Y for all x is member of x(p,Y)(iii) Convexity uniqueness : if >= is convex, so that u(.) is quasiconcave , then x(p,Y) is a convex set . Moreover, if >= is strictly convex, so that u(.) is strictly quasiconcave, then x(p,Y) consists of a single element.
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