Sally's utility function can be described as U(C,8) = C%S*% where C is dishes of Chocolate ice cream and S is strawberry sorbet. The price of a dish of chocolate ice cream is 2 and the price of a sorbet is $3. Sally has 536 to spend on ice cream and sorbets per month. (a) Calculate Sally's marginal rate of substitution of chocolate ice cream for sorbets. (b) Calculate Sally's optimal consumption bundle by setting the marginal rate of substitution equal to the price ratio of chocolate ice cream and sorbets. {c) Draw your solution to part (b) above. Be sure to label axes, intercepts and quantities. {d) Using a LaGrangian multiplier function, calculate Sally's optimum consumption bundle given her budget constraint. (e) Using a LaGrangian multiplier function, show that Sally's optimum consumption bundle does not change when she minimizes her spending subject to consumption of the bundle of chocolate ice cream and strawberry sorbet that you calculated in part (a) above. (f) (i) Sally'sincome remains $36 and the price of sorbets remains $3, but the price of a dish of chocolate ice cream increases to $3.00. How many chocolate ice cream and strawberry sorbets will Sally now purchase if she is maximizing her utility subject to her income constraint? (i) Are chocolate ice cream and strawberry sorbets substitutes or complements in Sally's preferences? How do you know? (iii) Draw Sally's price-consumption line for chocolate ice cream and strawberry sorbets. Put chocolate ice cream on the horizontal axis when you draw your graph. (iv) Derive Sally's demand curve for chocolate ice cream from your price-consumption line. {g) (i) The price of a dish of chocolate ice cream stays at $2 and the price of strawberry sorbets stays at $3, but Sally's income increases to $45. How many chocolate ice creams and strawberry sorbets will Sally now purchase if she is maximizing her utility subject to her income constraint? (i) Are chocolate ice cream and strawberry sorbets normal or inferior goods in Sally's preferences? How do you know? (iii) Draw Sally's income-consumption curve for chocolate ice cream. (iv) Draw Sally's Engel curve for chocolate ice cream