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

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Unformatted text preview: ECONOMICS 331 Mathematical Economics Kevin Wainwright Homework Assignment 9 Answer Key 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/ects. Can you sign the e/ects? L & = B & p x x & p y y = 0 L x = y & &p x = 0 L x = y & &p x = 0 x & = B 2 p x ;y & = B 2 p y ;& = B 2 p x p y Setting up the Jacobian 2 4 & p x & p y & p x 1 & p y 1 3 5 2 4 d& dx dy 3 5 = 2 4 xdp x + ydp y & dB &dp x &dp y 3 5 & & & H & & = 2 p x p y 2 4 & p x & p y & p x 1 & p y 1 3 5 2 4 d&=dp x dx=dp x dy=dp x 3 5 = 2 4 x & 3 5 dx=dp x = & & & & & & x & p y & p x & 1 & p y & & & & & & 2 p x p y = & x & & & & & p x 1 & p y & & & & 2 p x p y + & & & & & & p y & p y & & & & 2 p x p y dx=dp x = & x 1 2 p x INCOME + & & p y 2 p x SUBSTITUT: Both e/ects are negative. Now &nd @[email protected] x : From our initial set up 2 4 & p x & p y & p x 1 & p y 1 3 5 2 4 d&=dp x dx=dp x dy=dp x 3 5 = 2 4 x & 3 5 1 we can again use Cramer&s rule, substituting the d-vector into the 3rd column @y @p x = dy=dp x = & & & & & & & p x x & p x & & p y 1 & & & & & & & & & H & & @y @p x...
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hw9-07-1-KEY - ECONOMICS 331 Mathematical Economics Kevin...

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