Consider a country in which Y = 200 K^2/5N^3/5. Assume in this country they save

Question

Consider a country in which Y = 200 K^2/5N^3/5. Assume in this country they save 20% of their income, population grows at 3% per year, and depreciation of capital occurs at 10% per year. Use the Solow model. Compare the effectiveness of i) a 50% increase in the savings rate (to 30%). ii) a 67% decline in the population growth rate (to 1%), and iii) a 10% increase in productivity (to 220). That is. for each, give the percent by which it increases long-run average income (y*) and long-run average consumption (c*). Give one policy each that could be undertaken to accomplish i)-iii). Which policy has the greatest impact on long-run well-being (assuming each policy has zero costs)?

Explanation / Answer

Here A = 200, a = 2/5, s=0.2, n = 0.03. d=0.1

long run income y*=A(sA/(n+d))^1/(1-a)

long term consumption c*=(1-s)y*

So substituting vales to find y* & c*

a)

b) We can see from the rable that policy (i) is having greatestt impact on long run well-being with more than 96% change in income & 72% change in comsumption. Policy (i) can be achieved by increasing interest rate in savings. policy (ii) can be achieved by implementing various birth control program e.g. by not giving benefits to family having more than 1 child. policy (iii) can be implemented by reducing tax rates for corporates which will give them a boost in production.

Normal Condition When saving is increased to 30% Population growth rate declined to 1% Productivity increased to 220 A 200 200 200 220 a 0.4 0.4 0.4 0.4 s 0.2 0.3 0.2 0.2 n 0.03 0.03 0.01 0.03 d 0.1 0.1 0.1 0.1 y1 2804730.0 5512854.0 3705176.0 3616359.1 c1 2243784.0 3858997.8 2964140.8 2893087.3 % Change in y 96.6 32.1 22.4 % Change in c 72.0 32.1 22.4

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