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E C O N 2 1 5 I N T E R M E D I AT E M A C R O E C O N O M I C S SOLUTION TO ASSIGNMENT 1 I. Consumption and an Interest Tax a. Y1=Q1+(1+r)B0=Q1 Inter-temporal budget constraint: C1+C2/(1+r1)=Q1+Q2/(1+r1) C1+C2/1.1=100+220/1.1 C1+C2/1.1=300 Graphically, C2 330 300 C1 When C2=0, C1+0=300 C1=300 When C1=100, 100+C2/1.1=300 C2=220 ∴(100,220) is on the budget constraint. When C1=0, 0+C2/1.1=300 C2=330 Permanent Income Yp+Yp/1.1=300 Yp=157.1 S1=100-157.1= -57.1 (i.e. borrowing) b. After-tax permanent income 1. Ypt+Ypt/(1+r1)=(Q1-T1)+(Q2-T2)/(1+r1) Ypt(1+1/1.1)=(100-50)+220/1.1 Ypt=130.95 2. Ypt=104.76 3. Ypt=130.95 After-tax Consumption and Saving 1. 2. 3. C1=130.95 S1=50-130.95= -80.95 C2=130.95 C1=104.76 C2=104.76 C1=130.95 C2=130.95 S2=89.05 S1=-54.76 S2=60.24 S1=-30.95 S2=34.05 All the three tax policies lead to reduction in consumption of both periods. The temporary tax increase represents a temporary fall in disposable income, households trying to maintain a smooth consumption path will borrow against the future during the period of temporary high tax. Therefore, the saving in the first period is lowest among the three. For the anticipated tax increase, people’s future disposable income is lowered. People tend to reduce the borrowing so as to reduce the future debt burden and maintain a stable consumption. A permanent increase in tax reduces the disposable income for all period. So, the saving pattern would not be affected significantly. II. a. Output Growth Qt K t Lt a a 1 a 1 a Qt K t Lt a 1 a Lt Lt Lt qt k t 1 k t a a MPK=aKta-1 Lt1-a As 0<a<1, (a-1)<0. When K increases, Kta-1, and thus MPK, will decrease. When capital increase, the output, and thus the investment increase more slowly. Therefore, there must be some point where the investment level meets the need for capital replacement, that is, the steady state. Graphically, (n+d)k ska k kss And this is applicable to both Hong Kong and Costa Rica. At Steady State of Hong Kong, s HK k t (n HK d )k t a s HK 1 a kt n HK d 1 s k t ( HK ) 1 a n HK d a qt ( s HK 1 a ) n HK d Similarly, in Costa Rica, a qt ( s CR 1 a ) nCR d s n d HK 0. 2 0. 02 0. 08 CR 0. 16 0. 03 0. 08 1. 407 1. 203 2. 000 1. 455 a 0. 33 0. 5 q 0. 7 5. 040 2. 397 0. 9 512. 000 29. 144 When a is large, a little increase in capital stock gives a significant increase in output. Therefore, the little difference in saving rate and labor growth rate between Hong Kong and Costa Rica is sufficient to make a great difference in output. b. Q Q/L q a K K/L k Therefore, for all levels of L, MPK remains constant. Even if the population grows at MPK a steady state, MPK would not change. When r=0.05, MPK=r+d=0.05+0.08=0.13 Q K 1Q 0.13 3K Q 0.39 K MPK a If a=1/3, At steady state, sk a (n d )k nd s i sk a sk a 1 k k nd s( )nd s k a 1 I K I K When r=0.05, a=0.33 Therefore, in Hong Kong, Similarly, in Costa Rica, 0.03 0.08 sCR 0.282 .39 0.08 0.002 s HK 0.256 0.39 s I I /K nd Q Q/K Q/K When r=0.07, MPK=0.07+0.08=0.15 Q/K =0.15/0.33=0.45 Then, in Hong Kong, s' HK 0.02 0.08 0.222 0.45 In Costa Rica, 0.03 0.08 0.244 0.45 As interest ate increases, the cost of capital become higher. This in turn dicourages s 'CR investment. Therefore, investment rates in both countries fall. III. Deflators Nominal GDP in HK dollars = 110 x 20 + 60 x 30 = 4000 1500 0.6 2500 1000 0 .4 2500 HK wSHOES HK wHAIR Pc=0.6(20/15)+0.4(30/20) Pc=1.4 RGDP1996=2500 RGDP1997=4000/1.4=2857.14 Growth rate of RGDP=(2857.14-2500)/2500=0.143 π1997=(1.4-1)/1=0.4 The absolute purchasing power parity is hold for shoes but not for haircut is due to that the former is tradable good while the latter is non-tradable. International competition can drive to price of tradable goods to the same level. However, for non-tradable, such competition cannot be held. And thus the price might vary across countries. In Japan, Pshoes=15/0.5=30 Nominal GDP=100 x 30 + 50 x 50 = 5500 Nominal GDP in HK$=5500x0.5=2750 From this measure (exchange rate conversion), the level of output is higher in Japan. In Hong Kong, In Japan, PH/PS=20/15=1.33 PH/PS=50/30=1.67 Thus, the relative price of haircuts (non-tradable goods) is higher in Japan. Countries with non-competitive non-tradable goods sectors will generally have their ouput level exaggerated by exchange rate conversion. 3000 0.545 5500 2500 JPN wHAIR 0.455 5500 INT wSHOES .5 x.545 .5 x.6 0.573 JPN wSHOES INT wHAIR .5 x.455 .5 x.4 0.427 Price of International Basket=0.573x(30/15)+0.427x(50/20)=2.214 PPP conversion Japanese GDP in HK$ = 5500/2.214=2484.19 The actual baskets of good in Hong Kong and Japan are the same in 1996. Therefore, the value of their nominal GDP should be close. The PPP conversion provides a better method for international comparison that is more accurate that exchange rate conversion.