utility maximization

1. Suppose Mary's utility function for avocados (a) and blueberry muffins (b) is given by U(a, b) = a bl-" (economists call this a "Cobb-Douglas" utility function) such that a E (0, 1). The price of one avocado is Pa, the price of one blueberry muffin is po and Mary has Y to spend. (a) (10 points) Write down the budget constraint and solve for the optimal bundle a*, b* in terms of Pa, Pb and Y. (b) (10 points) Suppose Y, po are fixed constants, then calculate the elasticity of demand for avocados. Calculate also the cross-price elasticity of avocados with respect to the price of blueberry muffins. Are the two goods complements or substitutes in utility? What about in demand? 2. (a) (4 points) Suppose David is making care packages. Each one requires exactly one avocado and one blueberry muffin ((fractional care packages are ok). All he cares about is the total number of care packages. Draw a few indifference curves to represent these preferences. (b) (6 points) Suppose David also has Y to spend on care packages with avocados and blueberry muffins. Write David's demand for avocados and blueberry muffins in terms of Pa, pb and Y