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.

5. Verify the properties for the Marshallian demand function in the following proposition generated by the Cobb-Douglas utility function. Proposition 4.1: Suppose that u(.) is a continuous utility mction representing a locally nonsatiated preference relation ?, then the Marshallian demand function 1'60, 19 possess the following properties: (i) Homogeneity of degree zero in (p,Y). In other words, x(ap, (IV) = x(p, Y) for any p, Y and. Scalar or. (ii) Walras' law: p.x = onr all x e x(p, Y). (iii) Convexity uniqueness: if F is convex, so that u(.) is quasiconcave, then x(p, Y) is a convex set. Moreover, if 2! is strictly convex, so that u(.) is strictly quasiconeave, then x(p, Y) consists of a single element