1 c 2 c s ii show that 1 y s and 2 y s interpret

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1 c 2 c s (ii) Show that 0 1 > y s and 0 2 < y s . Interpret these results. This is a Partial Equilibrium Model. The household’s problem is: + λ + = 2 2 2 ) 5 . 0 ( 2 2 1 2 1 5 . 0 2 5 . 0 1 y y c c c c L . The first order conditions are: 0 c 0 0.5 - 1 1 = λ = c L (Equation 1) 0 2 c ) 5 . 0 ( 0 0.5 - 2 2 = λ = c L (Equation 2) (3 points) 0 2 2 0 2 1 2 1 = + = λ y y c c L (Equation 3) From the first two first-order conditions (i.e., from (1) and (2)), we obtain: 2 1 0.5 - 2 -0.5 1 2 c ) 5 . 0 ( c c c = λ λ = Using this result in the third first-order condition: + = + 2 2 2 1 2 2 y y c c + = 2 3 2 2 1 * 1 y y c (2 points) + = 2 3 2 2 1 * 2 y y c (2 points) ( 2 1 * 3 1 y y s = ) (2 points) It is obvious that 0 3 1 1 * > = y s (2 points) 0 3 1 2 * < = y s (2 points) 7
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Izmir Univery of Economics I. Hakan Yetkiner Department of Economics http://homes.ieu.edu.tr/~iyetkiner/ 6 . ( 15 Points ) An unexpected invention makes supersonic transportation substantially cheaper. This invention is expected to raise overall productivity both in the current period and in the future period. What will happen to current values of N , I , C , Y , w , and r ? UU Discuss and illustrate . ) ( r N s d N s Y d Y (3 points) (3 points) ) , ( 1 ↑⇒ + + Y r Y N z s d (3 points) ) , ( 2 ↑⇒ + + Y r Y I z d d (3 points) It is more likely that . If so, then . ) , ( Y r s N In sum, when Î , , , . (3 points) ) , ( 2 1 z z C I N w (With some explanation) 8
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Izmir Univery of Economics I. Hakan Yetkiner Department of Economics http://homes.ieu.edu.tr/~iyetkiner/ 7 . ( 10 Points ) The government announces that a decrease in government expenditure will occur next year. What effect will this have on the current values of aggregate output, employment, real wage, the real interest rate, consumption, and investment? Discuss and illustrate . ) ( r N s d N s Y d Y (3 points) (3 points) ) , ( 2 ↑⇒ ↑⇒ Y r N we G s ) , ( 2 ↑⇒ + + Y r Y C G d d (3 points) . Since , then . ?) , ( Y r ) ( r + s N In sum, when Î , , , . (1 point) ) ( 2 G
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  • Summer '09
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