Homework for Macroeconomics (1) (due March 17th)
Q1
Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is y=6k0.5, where y is output per worker and k is capital per worker. The depreciation rate of capital is 14% per year.
a. Households consume 90% of income and save the remaining 10% of income. There is no government. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?
b. Suppose that the country wants to increase its steady state value of output per worker. What steady-state value of the capital-labor ratio is needed to double the steady-state value of output per capita? What fraction of income would households have to save to achieve a steady-state level of output per worker that is twice as high as in Part (a)
Q2
This problem adds the government to the Solow model. Suppose that a government purchases goods in the amount of g per worker every year; with N, workers in year t, total government purchases are g*Nt. The government has a balanced budget so that its tax revenue in year t, Tt equals total government purchases. Total national saving, St=s*(Yt-Tt), where Yt is total output and s is the saving rate.
a. Graphically show the steady state for the initial level of government purchases per worker. b. Suppose that the government increases its purchases per worker. What are the effects on the steady-state levels of capital per worker, output per worker, and consumption per worker? Does your result imply that the optimal level of government purchases is zero?
Q3
This problem asks you to do your own growth accounting exercise. Make a table of annual growth rates of real GOP, the capitals stock, and civilian employment (自己去网上找，国家统计局数据、世行数据……..都可以，时间长度自选，不少于10年即可). Use C-D model, Y=A*KαL(1-α), assuming α=0.3.
a. Find the growth rate of Technology (A) for each year.
b. Graph the contributions to overall economic growth of capital growth, labor growth, and technology growth for each year. Try to describe their behavior during the data period.
