Question 2: Choice and Demand with Special Utility Functions. (30 pts) Consider the following utility function: u(x1,x2)=2ln(x12)+x2. (a) What kind of preferences are these? Find the MRS and sketch 3 indifference curves (no need to be precise, but make sure to label the utility level). (5 pts) (b) Suppose that m=24,p1=1 and p2=4. Use method 1 from class to solve for x1 and x2. Sketch your optimal points in a graph with the budget set and an indifference curve going through your optimal point. Hint: this is a special utility function so your answer may seem strange. Remember that xi must be a function of at least some of the variables p1,p2 and m.xi cannot however be a function of xj (the other good). (10 pts) (c) Consider an increase in income m=32. Derive the new optimal bundle and draw a graph with the new bundle, the budget set and an indifference curve passing through it. (10 pts) (d) Is there a difference in quantities between the bundles in (b) and in (c)? Briefly explain while referring to the demand functions. (5 pts) Question 2: Choice and Demand with Special Utility Functions. (30 pts) Consider the following utility function: u(x1,x2)=2ln(x12)+x2. (a) What kind of preferences are these? Find the MRS and sketch 3 indifference curves (no need to be precise, but make sure to label the utility level). (5 pts) (b) Suppose that m=24,p1=1 and p2=4. Use method 1 from class to solve for x1 and x2. Sketch your optimal points in a graph with the budget set and an indifference curve going through your optimal point. Hint: this is a special utility function so your answer may seem strange. Remember that xi must be a function of at least some of the variables p1,p2 and m.xi cannot however be a function of xj (the other good). (10 pts) (c) Consider an increase in income m=32. Derive the new optimal bundle and draw a graph with the new bundle, the budget set and an indifference curve passing through it. (10 pts) (d) Is there a difference in quantities between the bundles in (b) and in (c)? Briefly explain while referring to the demand functions. (5 pts)