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Problem Set 4

# Problem Set 4 - 2 Laura’s utility function is U(X,Y =...

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UCLA Economics 11 Fall 2010 Professor Mazzocco Problem Set 4 Because of the midterm this problem set will not be graded and you do not have to turn it in. However, solving the following exercises is an excellent practice for the midterm. 1) An individual, who has income I, cares only about two goods: X and Y. Their prices are P X and P Y , respectively. The individual’ s utility function is U(X,Y) = X a Y 1-a with a=1/4. a) Find the Marshalian (uncompensated) demands for X and Y. b) Find the Hicksian (compensated) demands for X and Y. c) Suppose that I=30, P X =P Y =2. Compute the total effect, the substitution effect, and the income effect generate by a small change in price (Hint: use the Slutsky equation presented in class).
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Unformatted text preview: 2) Laura’s utility function is U(X,Y) = ln(X) + 2Y . Her income is denoted by I and the prices by P X and P Y . In addition, we suppose that I>P y . a) Find the Marshalian (uncompensated) demands for X and Y. b) Using the Marshallian demand functions, calculate the income elasticity of demand for each good. c) Using the Marshallian demand functions, calculate the price elasticity of demand for each good, i.e., e X,PX and e Y,PY . 3) John’s utility function is U (X,Y) = min{βX,ρ Y}. His income is denoted by I and the prices by P X and P Y . a) Find the Marshalian (uncompensated) demands for X and Y. b) Show that the income elasticity of demand for X and Y is equal to 1....
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