1. Consider a country in which Y = 200 K2/5N 3/5. Assume in this country they sa

Question

1. Consider a country in which Y = 200 K2/5N 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.

a. 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 * ).

b. 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

At steady state level of capital depreciation equals investments.

(n+d)K = sY = sF(K;L) = s 200K2/5

K/K.4 = s / (n+d)

K.6 = s  / (n+d)

K* = [s  / (n+d)]1/.6

Given: Saving(s) = 0.20; Depreciation (d) = 0.10 and population growth (n) = 0.03

Thus K* = [0.20 / (0.03+0.10)]1/.6 = 2.050

Steady state level Per capita production/output: : K2/5 = 2.050.4 = 1.332

Steady state level of per capita consumption : (1-s)Y = (1-0.20)1.332 = 1.065

(i) Now when the savings increses from 20% to 30%

K* = [0.30 / (0.03+0.10)]1/.6 = 4.029

Steady state level Per capita production/output: : K2/5 = 4.029.4 = 1.746

Steady state level of per capita consumption : (1-s)Y = (1-0.30)1.746 = 1.222

(ii) Now when the population growth decreases from 3% to 1%

K* = [0.20 / (0.01+0.10)]1/.6 = 2.708

Steady state level Per capita production/output: : K2/5 = 2.708.4 = 1.489

Steady state level of per capita consumption : (1-s)Y = (1-0.30)1.746 = 1.191

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