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# Midterm+1_+Answer+Key - Midterm 1 Answer Key 1 1 dX 40 40 a...

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Midterm 1 Answer Key February 25, 2010 1. a) X*= : 4 & 100 p X = 40 p x dX & dp X = & 40 p 2 x : Jack&s consumption of X decreases with a price increase for X. Z*= (1 ± : 4) & 100 p Z = 60 p Y dZ & dp X = 0 : Jack&s consumption of Z doesn&t change with a price increase for X. b) While an increase in p x leads to a decrease in the consumption of X, there is no e/ect on either p Z or the optimal consumption Z*. The share of the budget spent on X is p X & X Y : But it is also 1- p Z & Z Y . Since the share of income spent on Z hasn&t changed, the share of income spent on X must also remain unchanged. Thus, the decrease in the units of X comsumed must exactly make up for the increased price. Thus, the change in consumption of X is entirely due to the substitution e/ect, and not the income e/ect. 2. a) Setting supply equal to demand, we ±nd: 20 + 5 p = 140 & 5 p (1) 10 p = 120 (2) p & = 12 (3) Q & = 20 + 5 ± 12 = 80 (4) b) The new supply function with a tax is Q s = 20+5( p & t ) = 20+5 p & 5 t = 20 & 10 = 5 p = 10 + 5 p: Setting our new supply function equal to demand we get: 10 + 5 p = 140 & 5 p (5) 10 p = 130 (6) p & = 13 (7) ( p & S = p & & t = 11) (8) Q & = 140 & (5 ± 13) = 75 (9) 1

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c) The new consumer price is \$13.
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Midterm+1_+Answer+Key - Midterm 1 Answer Key 1 1 dX 40 40 a...

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