1. Suppose a country that is initially at a steady-state level of capital per-worker introduces a successful birth-control campaign that permanently reduces the growth rate of the population
a. Compare the initial steady state and the final steady state in terms of their:
i. levels of capital per worker and output per worker
ii. growth rates of capital per worker and output per worker
b. What can you say about the growth rates of capital per worker and output per worker during the transition between the original and the final steady states?
2. In the Solow model, population growth leads to steady-state growth in total output, but not in output per worker. Do you think this would still be true if the production function exhibited increasing or decreasing returns to scale?
3. Suppose that the production function is Y = 10(K)1/4 / (EL)3/4 and capital lasts and average of 10 years so that 10 percent of capital wears out every year. Assume that the rate of growth of population is 4 percent, the rate of technological growth is 2 percent, and the saving rate s = 0.128.
a. Derive the equation for output per effective worker y = Y/EL = f(k), where k equals the amount of capital per effective worker
b. Calculate the steady-state levels for each of the following: capital per effective worker, output per effective worker, consumption per effective worker, saving and investment per effective worker, and depreciation per effective worker
c. Now, calculate the steady-state growth rates of capital per worker, output per worker, saving and investment per worker, and consumption per worker
d. Finally, calculate the steady-state growth rates of capital, output, saving and investment, and consumption
4. The amount of education the typical person receives varies substantially among countries. Suppose you were to compare a country with a highly educated labor force and a country with a less educated labor force. Assume that education affects only the level of the efficiency of labor. Also assume that the countries are otherwise the same: they have the same saving rate, the same depreciation rate, the same population growth rate, and the same rate of technological progress. Both countries are described by the Solow model and are in their steady states. What would you predict for the following variables?
a. The rate of growth of total income
b. The level of income per worker
c. The real rental price of capital
d. The real wage