Suppose that a consumer's preferences are described by the following utility function: U(x)=x12x2 i) Derive the Walrasian Demands for goods 1 and 2 and list their properties. Show that indeed those properties hold true. Are the preferences convex? Show your work. ii) Are the First Order Conditions of the Utility Maximization Problem sufficient? (i.e. do they ensure that the utility function is indeed maximized?) iii) Derive their Indirect Utility Function and list its properties regarding monotonicity and convexity/concacity. Show that the property regarding monotonicity holds true. iv) Derive their Hicksian Demands for goods 1 and 2. v) Derive their Expenditure Function. Is it monotonic to the argumments it should be (i.e. the variables it should be monotonic with respect to)? Show your work. Suppose that a consumer's preferences are described by the following utility function: U(x)=x12x2 i) Derive the Walrasian Demands for goods 1 and 2 and list their properties. Show that indeed those properties hold true. Are the preferences convex? Show your work. ii) Are the First Order Conditions of the Utility Maximization Problem sufficient? (i.e. do they ensure that the utility function is indeed maximized?) iii) Derive their Indirect Utility Function and list its properties regarding monotonicity and convexity/concacity. Show that the property regarding monotonicity holds true. iv) Derive their Hicksian Demands for goods 1 and 2. v) Derive their Expenditure Function. Is it monotonic to the argumments it should be (i.e. the variables it should be monotonic with respect to)? Show your work