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WeekofFeb02

# WeekofFeb02 - x = 1 = 4 p y = 1 and p z = 2 and Bob&s...

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W3211 Spring 2009 Professor Vogel Recitation for the Week of February 02, 2009 1. U ( x;y ) = y + ln x , I = 12 , p x = 2 , and p y = 3 . (a) Solve for the MRS . Is it deminishing? (b) Solve the the optimal ( x ;y ) . 2. U ( x;y ) = y + ln x , and suppose that I > p y > 0 and p x > 0 . (a) Solve for the elasticity of demand for y , the income elasticity of demand for y , and the cross-price elasticity of y . (b) Solve for the elasticity of demand for x , the income elasticity of demand for x , and the cross-price elasticity of x . (c) As income increases, what happens to consumption of x (as long as I > p y )? Why is this? To understand this, graph U x p x and U y p y . U ( x;y ) = x 2 = 5 y 3 = 5 , his income is \$10 , p x = 1 , and p y = 2 . Suppose that the price of x increases to p x = 2 . (a) Calculate the substitution e/ect. (b) Calculate the income e/ect. change in prices? U ( x;y;z ) = x 1 = 2 y 1 = 2 (1 + z ) 1 = 2 . The prices are p
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Unformatted text preview: x = 1 = 4 , p y = 1 , and p z = 2 and Bob&s income is 2 . (a) Solve for optimal x and y if z = 0 . (b) Show that any choice that results in z > reduces utility from that above. (c) Why is z = 0 optimal here? 5. Problem 5.2 in the text. 6. On Monday the price of a slice of pizza is \$2 and a coke is \$1 . At these prices Jane spends her \$30 of lunch money to purchase 11 slices of pizza and 8 cokes for her kids. On Friday the prices of pizza and coke are reversed so the price of a slice is \$1 and the price of a coke is \$2 . At these prices Jane uses her \$30 to purchase 10 slices of pizza and 10 cokes. Assuming that her (and her kids&) preferences have not changed between Monday and Friday, are her utility maximizing choices consistent with Jane (and her kids) having rational preferences? Brie±y explain your answer....
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