ps3 - goods ( y ) is $1 per unit. (a) For each price p x...

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ECO 310, Fall 2007 Problem Set 3: Consumer Theory Due in class on October 16 Question 1 For each of the following utility functions over two goods, ±nd the Marshallian demand, the Hicksian demand, and the expenditure function. (a) U ( x, y )= x . (b) U ( x, y )= xy x + y . (c) U ( x, y ) = min( x, y ). (d) U ( x, y ) = max( ax, ay ) + min( x, y ), where 0 <a< 1. Question 2 Let U ( x, y )=( x + y ) 2 . Find the Marshallian demand, the Hicksian demand, the indirect utility function and the expenditure function. Verify the Slutsky equation and Roy’s Identity. Question 3 Della Driver’s utility is a function U ( x, y ), where x denotes her consumption of gallons of gasoline per week, and y stands for her consumption of all other goods in the economy, measured simply by the amount spent (measured in $, the currency unit) on these other goods. U ( x, y ) = ln( x ) + 9 ln( y ) . Della’s income is $1000 per week. In addition to facing a budget constraint, she is not allowed to buy more than 40 gallons of gasoline. The price of “other
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Unformatted text preview: goods ( y ) is $1 per unit. (a) For each price p x for gasoline, how much will Della buy? (b) How much gasoline will Della buy if p x = 2? What is her marginal rate of substitution of other goods for gasoline at this point? Is it greater or less than the price? Give an economic intuition for this result. (c) How much gasoline will Della buy if p x = 3? What is her marginal rate of substitution of other goods for gasoline at this point? Is it greater or less than the price? Give an economic intuition for this result. (d) Suppose that the price of gasoline is p x = 2, but that a black market in gasoline opens up, where she can buy additional quantities (above 40 gallons) for $3 a gallon (while continuing to buy the ration of 40 gallons at the legal price of $2). How much gasoline will she buy on the black market? 1...
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