Homework3 北大周黎安微观经济学作业和答案

Question 6: Growth Accounting
In the economy of Solovia, the owners of capital get two-thirds of national income, and the workers receive one-third. a) The men of Solovia stay at home performing household chores, while the women work in factories. If some of the man started work outside the home so that the labor force increased by 5%, what happen to the measured output of the economy? Does labor productivity – defined as output per worker – increase, decrease or stay the same? Does total factor productivity increase, decrease or stay the same? b) In year 1, the capital stock was 6, the labor input was 3, and output was 12. In year 2, the capital stock was 7, the labor input was 4 and output was 14. What happen to total factor productivity between the two years?
Guanghua School of Management, Peking University Intermediate Macroeconomics
Se Yan Spring 2012
Homework Assignment 3 Due on May 30 Question 1: Growth Rates
Question 3: GDP Growth Rates Data
Go to Penn World Table (http://pwt.econ.upenn.edu/php_site/pwt63/pwt63_form.php) and compute the average per capita real GDP growth rate for 10 countries between in 1971 and in 2000: you should choose 5 countries from “G7 countries” and another 5 countries should be less developed/developing countries and use “Real GDP per capita (Constant Prices: Laspeyres), derived from growth rates of c, g, i”. Briefly describe what you see in the data.
E is the
Et 1 (1 g ) Et
And the production function is changed to
Yt K t ( Et L)1
The rest of the equations are the same as in Question 3. Assume country A and B have following parameters: s 0.3, 0.36, 0.2, g 0.02 . However, country A has 100 workers and country B has 200 workers. a) Rewrite the capital accumulation equation and production function in per effective worker term. b) In period 1, suppose the aggregate capital in country A is 50 and the aggregate capital in country B is 10. Compute and plot the output per effective worker in both countries from period 1 to period 20. c) Suppose country A is in steady state initially. 10 periods later, there is a technology improvement in E such that g suddenly increase from 0.02 to 0.03. Compute the new steady state value in per effective worker term. Plot a graph with time on the horizontal axis, and output, consumption, investment and capital (in per-effective worker) on the vertical axis.
Lt 1 Lt L Yt K t Lt1 I t sYt K t 1 I t (1 ) K t
a) Show why it must be case that:
Ct (1 s )Yt
1
b) Divide Y , C , I and K by L . Denote these per-capita variables as y, c, i and k respectively. Show how the equations of the model change. c) Solve for the steady state value of the capital stock as a function of the parameters How many steady states are there? d) What is the golden rule? How dose the golden rule tell you what the saving rate should be? Show how to solve the golden rule saving rate. e) Suppose that the economy is in the golden rule steady state with optimal saving rate s g . Now assume that the saving rate drops to sl , which is lower than sg . Draw a graph with time on the horizontal axis, and output, consumption, investment and capital (per-capita) on the vertical axis. And show how these variables change over time as the economy converges to the new steady state.
Question 4: Solow Growth Model
Consider the following version of the Solow growth model. Y is the total output. K is the capital stock. L is the number of workers. I is investment. s is the fraction of output that saved. Assume L is constant over time.
Question 2: US Saving Rate
Go to the BEA web page (www.bea.gov) and get quarterly data for U.S. personal saving rate from 1980 to 2009. (Look for “Personal saving as a percentage of disposable personal income” on Table 2.1 Personal Income and Its Disposition. Be smart and download the data, NOT copy them by hand). Plot the saving rate data over time (turn in the figure only do not show the table). What do you see? Can we find saving rate data for China? If so, do the same thing for the US.
,
and s .
Question 5: Computing Solow Model (You need to use a spread sheet program like Excel to solve this question)
Consider the modified version of the Solow growth model in Question 3 with technology changed. efficiency of workers and the growth rate of E is g .
2
And show how these variables change over time as the economy converges to the new steady state. d) “It seems that the technology improvement is not a good thing for this economy, because it actually lowers the steady state capital stock, which leads to lower output.” Do you think the following statement is true or not? (Hint: plot the transition path of output per worker)
If real GDP grows at 2% a year, how many years does it take for GDP to double? ቤተ መጻሕፍቲ ባይዱhat is the general formula for the doubling of a time series that grows at x percent a year?
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