Homework in Statistics - Assignment Example

Assignment answers The GDP for Hare will grow more than that of Tortoise since it is 3% as compared to only 1 % of Tortoise. The higher the growth rate, the higher the GDP This formula will answer this question: x(t)=x(t0)(1+g)(t-t0) Where x (t) rep. real GDP in t years, x(t0) is real GNP in t0 years, g is the constant growth rate of real GNP between t0 years to t years. Therefore: Hare’s real GDP in year 2000 is: $5000  (1.03)50 = $21,919.50 Tortoise’s real GDP in year 2000 is: $5000  (1.01)50 = $8,223.15 2a) 20 Years Ago Today Percent Change Y 1000 1300 30% K 2500 3250 30% N 200 230 15% When aK = 0.3 and aN = 0.7 A/A  Y/Y – aK K/K – aN N/N  30% – (0.3  30%) 0.7  15%  30% – 9% – 10.5%  10.5% Capital growth contributed 9% Labor growth contributed 10.5% Productivity growth was 10.5%. (b) When aK = 0.5 and aN = 0.5 A/A  30% – (0.5  30%)(0.5  15%)  30% – 15% – 7.5%  7.5% Capital growth contributed 15% Labor growth contributed 7.5% Productivity growth was 7.5%. 3). Y=total output K/N=capital labour ratio Y/N= output per worker Year K N Y K/N Y/N 1 200 1000 617 0.20 0.617 2 250 1000 660 0.25 0.660 3 250 1250 771 0.20 0.617 4 300 1200 792 0.25 0.660 Capital labour ratio for year 1 = K/N = 200/1000 = 0.2 Capital labour ratio for year 2 = K/N = 250/1000 = 0.25 Capital labour ratio for year 3 = K/N = 250/1250 = 0.20 Capital labour ratio for year 4 = K/N = 300/1200 = 0.25 Output per worker for year 1 = Y/N = 617/1000 = 0.617 Output per worker for year 2 = Y/N = 660/1000 = 0.660 Output per worker for year 3 = Y/N = 771/1250 = 0.617 Output per worker for year 4 = Y/N = 792/1200 = 0.660 The production function presented above can be written in per-worker form because Y/N = K.3 N.7 / N =K.3/ N.3 = (K/N).3 b) Repeated with K0 .3N0.8 In this case, the same method of calculating the capital labour ratio and output per worker should be used to come up with the following; Y=total output K/N=capital labour ratio Y/N= output per worker Year K N Y K/N Y/N 1 200 1000 1231 0.20 1.231 2 250 1000 1316 0.25 1.316 3 250 1250 1574 0.20 1.259 4 300 1200 1609 0.25 1.341 However, this production function cannot be written in per-worker form because Y/N =K0.3N0.8/N = K0 .3/ N0.2. Although K/N is the same in years 1 and 3, Y/N is not the same in these years. The same is true for years 2 and 4. 4. a). In steady state, the formula is: sf(k) = (n + d)k 0.16 x 0.36k5 =( 0.01+0.04)k 0.0576k5 = 0.05k 0.0576/0.05 = k / k5 1.154=k5 k= 1.1542= 1.3=capital per worker Y=0.36k5 = 0.36 x 1.154=0.41544 x 554=230= output per worker b) Suppose A is increased by 10%, the capital per worker and ouptu per worker will increase by 10%, K= 10% x1.3=1.43 Y=10% x 230= 253 c) Yes, when A was increased by 10%, the capital to output ratio did not change and was increased by 10%. 5a). On the long run, the quantity of the capital per worker and the output per worker which had undergone changes during the natural disaster finally go back to normal, at their levels before the occurrence of the natural disaster. This is because, during the reconstruction period, they grow at a relatively higher rate which is meant to update them with the original level until they are back to normal and are constant. At the long run, all factors should go back to normal and stabilize inkling the capital per worker and output per worker. b).Immediately after the aftermath of the destruction of capital stocks through a natural disaster, measures are taken to recover the economy. Therefore, an economy undergoes a rapid recovery period which is accompanied by technological advancement. Resources are allocated towards the reconstruction of the damaged capital stock such as foreign aid and human capital. In the short run the aggregate output will grow at a higher rate than the growth rate of the labour force due to the increased savings and foreign aid which pushes the recovery of the capital growth rate back to normal. c) When the capital starts out at 90%, the capital per worker will be calculated at 90% Therefore, 1.3 x90%= 1.17 The growth rate will be 0.13/1.17=11.1%. d) After world war two, the real GDP in Germany and Japan grew steadily due to the period of technological advancement and reconstruction. During the recovery period, the technology in these countries grew at a faster rate leading to the faster growth of effective labour which is translated into their real GDP. 6. With the rise in depreciation, the equilibrium steady-state capital-labour ratio declines.as a result, output per worker becomes lower and that leads to lower consumption of the same worker. This is based on the assumption that the capital-labour ratio is not very high in that an increase in k can reduce consumption of the worker. On the long run, there are no effects on the growth rate of the total capital stock. This is due to the fact that, in the long run, the capital stock should grow at the same rate as the labor rate growth is and therefore the capital-labour ratio remains constant. 7a) The government purchases per worker are indicated by IS at the inintial time, as the government purchases more, the IS curve shifts to IS2 curve which goes up and further to the right of the curve. This shows the increase in both the government spending and also the increase in the interest rate of the government revenue. b). if the government increases g, it will lead to reduction in the savings of the government and therefore capital per worker increases due to increased savings, output per worker will decreases, while consumption per worker is increased. Work cited David Andolfatto. Macroeconomic Theory and Policy, Department of Economics, Simon Fraser University 2006. Read More