Question 2

[40 points] Consider the Solow growth model with population growth but no technological progress studied in class. To refresh your memory, the evolution of the capital to labor ratio k_i,t according to this model studied is:
$k_{t+1}=\frac{1-\delta}{1+\lambda}k_{i,t}+\frac{sA}{1+\lambda}k_{t}^\alpha$
where s is the savings rate, $\delta$ is depreciation, and $\lambda$ is the rate at which population grows.
According to some econmists, demographic trends in industrialized countries indicate that the rate of growth of population in those countries has permanently declined. Answer the following questions:
a) What will the effect of this reduction in population growth rate be on the steady state growth rate of total output, total capital, and of productivity? Explain briefly.
b) What will the effect of this reduction in population growth rate be on the steady state levels of the capital-to-labor ratio, output-per-worker, and per-capita consumption? Explain briefly.
c) Describe graphically the evolution of the capital-to-labor ratio from the old steady state to the new steady state.