hw9-07-1 - ECONOMICS 331 Mathematical Economics Kevin...

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ECONOMICS 331 Mathematical Economics Kevin Wainwright Homework Assignment 9 1. Given the utility maximization problem Max U = xy subject to B = p x x + p y y (a) Derive an expression for the Slutsky equation for x and y when p x changes. Iden- tify the income and substitution e f ects .Canyous ignthee f ects? (b) Using the Implicit function theorem (where the Hessian is also the Jacobian), f nd the comparative statics ∂x/∂B and ∂x/∂p x by using Cramer’s Rule. Compare your solutions from the implicit approach to the ones you get by di f erentiating the x ( p x ,p y ,B ) function directly. 2. The following graph is found in most economics texts and it illustrates how an economy can get outside its PPF through free trade. Solving this problem is a straight forward application of Lagrange. Figure 1: PPF u* y* x* A B Y E X E y x The Gains From Trade “Trading Line”

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hw9-07-1 - ECONOMICS 331 Mathematical Economics Kevin...

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