Handout 3 Key - ; 000 2 K + N , N = 8 ; 750 + 2 K , 2 N =...

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Econ 3140 Fall 2009 Handout #3 Answer Key 1. Recall the formula of Future value, FV = PV (1 + i ) n , where FV is future value, PV is present value, i is the nominal interest rate, and / n is the number of period that the interest compound. Also, recall the formula for after tax interest rate: i tax = i (1 ± t ) (a) $955 : 06 = [$1000 (1 : 08)^5] & 0 : 65 (b) $837 : 51 = $650 [1 + (0 : 08 & 0 : 65)]^5 (c) $117 : 55 = $955 : 06 ± $837 : 51 2. With a tax rate on interest income is 30% . (a) 2001: 3 : 5% = 0 : 05 & 0 : 7 2002: 2 : 8% = 0 : 04 & 0 : 7 2003: 4 : 2% = 0 : 06 & 0 : 7 (b) Nominal: $1108 : 67 = $1000 1 : 035 1 : 028 1 : 042 Real: $923 : 89 = $1108 : 67 (120 = 100) (c) Nominal: $108 : 67 = $1108 : 67 ± $1000 Real: $14 : 80 = $923 : 89 ± $1000 (110 = 100) = $923 : 89 ± $909 : 09 . 3. MPK = 10 ; 000 ± 2 K + N , and MPN = 50 ± 2 N + K . The price of capital is $5000 , the real interest rate is 10% , and capital depreciates at a 15% rate. The real wage rate is $15 . (a) uck = ( r + d ) pk = 0 : 25 $5000 = $1250 (b) Setting w = MPN gives 15 = 50 ± 2 N + K , 2 N = 35 + K . Setting uc = MPK gives 1250 = 10
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Unformatted text preview: ; 000 2 K + N , N = 8 ; 750 + 2 K , 2 N = 17 ; 500 + 4 K . Setting 17 ; 500 + 4 K = 35 + K gives 3 K = 17 ; 535 , which yields K = 5845 . Then N = 2940 4. C d = 3000 2000 r + 0 : 10 Y I d = 1000 4000 r (a) Recall the formula that S d = Y C d G , 5000 [3000 2000 r +0 : 10 Y ] 1000 , 500 + 2000 r . Setting S d = I d gives 500 + 2000 r = 1000 4000 r , which can be solved to get r & = 0 : 0833 . (b) Plugging this value of r & into the equations for consumption and investment gives C & = 3333 , I & = 667 , and S & = 667 . (c) Follow the same steps as above with the new equation for desired consumption to get: r & = 0 : 05 , C & = 3200 , I & = 800 , and S & = 800 . 1...
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