Marco Del Negro, Economia 5

Problem Set 8

1) Abel and Bernanke, numerical problem 2, pg 214
Over the past twenty years an economy's total output has grown from 1000 to 1300, its capital stock has risen from 2500 to 3250, and its labor force has increased from 500 to 575. All measurements are in real terms. Calculate the contributions to economic growth of growth in capital, labor, and productivity:
a) assuming that $\alpha_=0.3$,
b) assuming that $\alpha_=0.5$.
2) The following question should be answered using the Solow growth model with population growth.
Many demographers predict that the US will have zero population growth in the twenty first century, in contrast to average population growth of about 1 percent in the twentieth century.
a) What will the effect of this slowdown in population growth be on the steady state growth rate of total output, of capital, and of productivity? b) What will the effect of this slowdown in population growth be on the steady state levels of the capital-to-labor ratio, output-per-worker, and per-capita consumption?
c) Describe graphically the evolution of the capital-to-labor ratio from the old steady state to the new steady state.
d) What will the effect of this slowdown in population growth be on the Golden Rule level of the capital stock.
3) Abel and Bernanke, analytical problem 1, pg 215
According to the Solow growth model, how would each of the following affect consumption per worker in the long run (that is, in steady state)? Explain:
a) the destruction of a portion of the nation's capital stock in war
b) a permanent decrease in the rate of immigration (which raises the overall population growth rate)
c) a permanent increase in energy prices
d) a temporary rise in the savings rate
e) a permanent decrease in the fraction of the population in the labor force (the population growth rate is unchanged)
4) Abel and Bernanke, analytical problem 2, pg 215
An economy is in a steady state with no productivity change. Because of an increase in acid rain, the rate of capital depreciation rises permanently. Determine the effects on steady state capital per worker, output per worker, and consumption per worker. Is the long run growth rate of the total capital stock affected? If so, in what way?