Task 6 Optimal Choice A powerful tool for analyzing and predicting the behavior of homo sapiens (but also for capuchin monkeys') is indifference curve analysis that incorporates the 'equal bang for your buck' rule. This analysis strictly separates considerations concerning tastes from budgetary considerations. Preferences (= tastes) are represented by indifference curves. Affordable consumption bundles are represented by the budget set. The frontier of this budget set is called the budget constraint. Indifference curve analysis assumes that an individual selects that particular consumption bundle in the budget set that lies on the highest indifference curve (in other words, an individual chooses his/her mostly preferred consumption bundle that he/she can afford). The selection of the optimal consumption bundle satisfies a restatement of the 'equal bang for your buck rule where the marginal rate of substitution is equal to the relative price. Apart from the traditional application to typical consumption goods, a broader interpretation of a good allows its applications to scenarios such as the allocation of time between labor and leisure or intertemporal consumption decisions. Assume that there are two goods in the world: apples and bananas. Say that Natalie has a utility function for these goods of the following type, where XA denotes the quantity of apples and xB the quantity of bananas ax . Vx = (x Vx)n Do the following: a) Draw the indifference curves that are defined by the utility function (2-3 curves). Make sure to include an indifference curve that is defined by a utility level of 2,500. b) What is the marginal rate of substitution when Natalie consumes 50 apples and 50 bananas? What is the marginal rate of substitution between these two goods when Natalie consumes 50 apples and 100 bananas? c) If the unit prices of the apples and the bananas are 3 EUR and 4 EUR, respectively, what bundle of apples and bananas would Natalie buy with her income of 100 EUR? d) Previous exam question: Sarah's utility function is given by Er. Ix (xx)n Her budget is 72. The price for good 1 is 4 and the price for good 2 is 12. Which amounts of good 1 and good 2 will she buy? MacBook Air 000