Contribution of Capital in Growth - Assignment Example

Contribution of Capital in Growth1) The GDP after 88 years will be computed by the this model; fv=pv (1+r)n fv Hare: 30000(1+0.03)88 = $404386.85Tortoise: 30000(1+0.01)88 = 72011.5 2)parametersTwenty years agopresent% changeouput100001300030%labour250003250030%capital20000000023000000015%Contribution of capital in growth; ak(∆k/k)*100% =( 0.3*0.15) 100% = 4.5%Contribution of labor in growth; an (∆N/N)*100% = (0.7*0.3)100% = 21%Productivity growth will be ∆A/A = ∆Y/Y – (aK ∆K/K +aN ∆N/N) = 30%-(4.5% +21%)=4.

5 %When an= ak = 0.5 Contribution of capital in growth; ak (∆k/k)*100% =( 0.5*0.15) 100% = 7.5%Contribution of labor in growth; an (∆N/N)*100% = (0.5*0.3)100% = 15%Productivity growth will be ∆A/A = ∆Y/Y – (aK ∆K/K +aN ∆N/N) = 30% -(7.5% +15%)=7.5 %.yearKNOutput(Y = K0.3N0.7)Capital-labor ratioProductivity per workeraN (Y/N)12001000617.035431.9222501000659.754461.8332501250771.295539.9043001200791.704554.19b)yearKNOutput(Y = K0.2N0.8)Capital-labor ratioProductivity per workeraN (Y/N)12001000728.785538.0222501000757.884606.3032501250905.975724.7843001200909.434727.54 4a) At steady state sAF(k) = (n+d) k ; 0.16(554k0.36) = (0.01+0.04)k88.64k0.36 = 0.05k => 88.64/0.05 =k0.64 => k =119132.76. Quantity of capital per worker =119132.76.Output per worker, Y=554k0.

36 =>554(119132.76).36=37228.95 b) Our A will be 554*10%+ = 609.4Quantity of capital per worker, k = 0.16(609.4k0.36) = (0.01+0.04) k =>97.504k0.36=0.05k97.504/0.05 =k0.64 => k=138263.30Output per worker will be; Y =554(138263.30)0.36 = 39279.35 5 a) such destruction would not have long term effect to capital per worker as well productivity per worker since it would be short lived the invisible hand would restore the equilibrium at the steady state this has been the case with many regions of the world where countries accelerate at a higher pace to build their capital stock after suffering a devastating calamity. b) In the short run output will grow at a lower rate than growth of labor force since there is little capital stocks per person this situation is short-lived.

Capital per worker would be 119132.67*90% =107219.403.Output per worker will be Y= 554(107219.403)0.36= 35843.316Capital output ratio =107219.403/ 35843.316 =2.99:1.Growth of capital would be; {(119132.76 - 107219.403)/ 107219.403}*100% = 11.11%. d) Reason why Germany and Japanese GDP grew very fast is because the buildup of capital was growing exponentially providing more capital person and thus increasing productivity, the invisible hand works to bring equilibrium at the steady state.6 a) Increase in capital depreciation reduces capital labor ration and reduces the output per worker since capital per worker and with less output consumption also declines and thus in the long-run the capital stock must grow at the same pace with the labor force in order to have a constant capital labor ratio, un reducing output and consumption. b) In such a model, the growth rate of output is ∆y/y =(sA –n - d), and therefore arise in depreciation cause a reduction in an economies output and since the growth rate of capital is a function of such depreciation and since they are negatively relate increase in depreciation decreases capital stock.

And since consumption is relative to output a decrease in output impacts in a similar way to consumption as they are positively related. Therefore it can be seen that increase in depreciation will reduce the capital stock in the long run reducing capital, capital output per worker and finally consumption.7 a) At steady state the optimum capital is utilized and since the government takes up all the units produced. The labor force utilizes all the capital available which the government takes up as indicated by point A.

Also at this point the government saves nothing since it utilizes everything in purchasing the entire output.b) increase in government purchases will cause an increase in productivity per worker but since the capital is a function of depreciation capital at the disposal of the workers will decrease in the long run causing a reduction in the output per worker and consequently a reduction in consumption an increase in “g” cannot even match the growth of population or labor force of an economy.

Optimal purchases of the government cannot be zero as there must be some level of government purchasing.Reference:Marc Nervole. Business and Economics: Estimation and Identification of Cobb Douglas Production Function. London: Stanford University Press, 1965.Print.