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 ( , )abUxy xywhere 0aand 0bare given parameters and 0xand 0ydenote the quantities of the two goods. Let pand sdenote the prices of goods xand y, respectively, and let Mdenotes the individual's wealth. a. Solve for the individual's Marshallian demand functions for the two goods, *(,, )xxpsMand *yyp. Hint: *xdoes not depend on s, and *ydoes not depend on p. b. Verify that these demand functions are homogeneous of degree zero in ( , ,)psM. c. Let ijdenote the elasticity of demand for good ,ixywith respect to price ,jps, and let iMdenote the elasticity of demand for good iwith respect to income. (i) Verify that 0xpxsxM and that 0ypysyM . (ii) Verify that 0xpyppxsypxMMM , that 0xsyspxsysy, and that 1xMyMpxsyMM .
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