400ps8-11 - ECON 400 Winter 2011 Problem Set VIII (for...

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ECON 400 Hartman Winter 2011 Problem Set VIII (for Wednesday, March 2) 1. A person's preferences over two goods can be represented by the utility function ( , ) ab Uxy xy where 0 a and 0 b are given parameters and 0 x and 0 y denote the quantities of the two goods. Let p and s denote the prices of goods x and y , respectively, and let M denotes the individual's wealth. a. Solve for the individual's Marshallian demand functions for the two goods, * (,, ) x xp sM and * y yp . Hint: * x does not depend on s , and * y does not depend on p . b. Verify that these demand functions are homogeneous of degree zero in ( , , ) psM . c. Let ij denote the elasticity of demand for good , ix y with respect to price , j ps , and let iM denote the elasticity of demand for good i with respect to income. (i) Verify that 0 xp xs xM    and that 0 yp ys yM   . (ii) Verify that 0 xp yp px sy px MMM    , that 0 xs ys px sy sy   , and that 1 xM yM px sy MM   .
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