Microeconomics Practice Problems. Please provide a step by step solution to help me understand.

1. Consider a preference represented by u(:r;, y) = maiden y]. (a) Is this preference wellbehaved? (b) Suppose the price of x is 1 and the price of y is 2. If a person, whose utility function is specied above, has income of 20, how much of x and y will this person choose to maximize their utility? 2. Suppose Dion's preferences are represented by a (151,332) = %JH%E3 (a) Find the marginal utilities of 3:1 and 3:2 (b) Show that Dion's utility function belongs to a class of functions that are known to be wellbehaved and strictly convex. (c) Find the AIRS. ((1) Write down Diongs budget. constraint. (e) Write down the tangency condition needed to nd an Optimal con sumption bundle for wellbehaved preferences. (f) Using the equations you wrote in (c) and (d): nd Diorfs ordinary demand functions for goods 1 and 2 (in other words, nd out. how much Alex will consume of good 1 as a function of p1, p2, and In, and how much Alex will consume of good 2 as a function of p1, p2, and rr1). (g) Suppose that m = 100,101 = 2 and p2 = 3. How much of good 1 will Alex choose to consume? How much of good 2 will Alex choose to consume