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PS3 - b How many dresses and hats is she going to...

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UCLA Economics 11 – Fall 2009 Professor Mazzocco Problem Set 3 Due by October 22 before 9:00am in Room 8271 1) Suppose that an individual with income I cares about two goods, X and Y. The price of the two goods is P x and P Y . The individual has the following utility function: U(X,Y) = X (1 + Y) a) Find the Marshallian (uncompensated) demand for X and Y. Are X and Y normal or inferior goods? b) Find the Hicksian (compensated) demand for X and Y. c) What is the minimum expenditure necessary to achieve a utility level of U= 72 with Px=4 and P Y =2? 2) Britney is very fashionable. When she buys a new dress (D), she also needs to buy a hat (H) to match that dress and vice-versa. So, she views the two goods as perfect complements. The price of a dress is \$10, the price of a hat is \$5, and she has \$45 to spend. a) Write down a utility function that represents Britney’s preferences over dresses and hats.
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Unformatted text preview: b) How many dresses and hats is she going to consume? (Hint: the first order conditions will not help; draw the budget constraint and the indifference curves and look at the highest one that intersects the budget constraint) c) What is Britney’s indirect utility? 4) Suppose that an individual with income I cares about two goods, X and Y. The price of the two goods is P x and P Y . The individual has the following utility function: 1 , Y X Y X U a) Find the Marshalian(uncompensated) demand for X and Y. b) Find the Hicksian (compensated) demand for X and Y. c) Find the indirect utility of this individual in terms of prices and income. d) Find the expenditure function in terms of level of utility and prices....
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