Economia V; Instructor: Marco Del Negro

Problem set 10

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.
Some economists believe that as the baby-boomers start to retire, the sum of private and government savings will decline in the US from 16% of GDP to about 13% of GDP. Assume that everything else remains unchanged.
Answer the following questions:
a) What will the effect of this reduction in saving be on the steady state growth rate of total output, of capital, and of productivity? Explain briefly.
b) What will the effect of this reduction in saving 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.