(30 points) Consider an individual who consumes three goods x=(x1,x2,x3) with price p=(p1,p2,p3) and has utility function U(x). Suppose someone claims that the function e(p,u), given below, is the expenditure fuction dual to U(x) e(p,u)=h(u)(p1/2p2/2+p3),=0 (a) (5 points) State the properties an expenditure function must satisfy. (b) ( 15 points) Write down the restrictions on the function h(u), and the parameters , for the function e(p,u) given above to satisfy these properties. (c) (10 points) Now assume that the parameters are such that the given function e(p,u) is a valid expenditure function. Show how an increase in the price of good 3 affects the Walrasian demand for good 1, i.e., find p3x1(p,w) (30 points) Consider an individual who consumes three goods x=(x1,x2,x3) with price p=(p1,p2,p3) and has utility function U(x). Suppose someone claims that the function e(p,u), given below, is the expenditure fuction dual to U(x) e(p,u)=h(u)(p1/2p2/2+p3),=0 (a) (5 points) State the properties an expenditure function must satisfy. (b) ( 15 points) Write down the restrictions on the function h(u), and the parameters , for the function e(p,u) given above to satisfy these properties. (c) (10 points) Now assume that the parameters are such that the given function e(p,u) is a valid expenditure function. Show how an increase in the price of good 3 affects the Walrasian demand for good 1, i.e., find p3x1(p,w)