1. There are three countries in the World: A, B, and C. Given the data in the table below for year 2050, fill in all the missing cells below, add the three columns for the year 2100 (population, gdp, gdp per capita), and calculate the average growth rate of per capita gdp for the world from 2050 to 2100. Assume per capita gdp grows at 1.5% per year for each country over this period. Use the growth formula for continuous compounding.
| country |
pop(millions) |
gdp(billions) |
gdp per capita |
projected annual population growth rate, 2050-2100 |
| |
|
|
|
|
|
|
|
|
|
| A |
1 300 |
25 000 |
|
0.05% |
| B |
5 000 |
12 000 |
|
0.50% |
| C |
3 000 |
1 000 |
|
2.50% |
| World |
9 300 |
|
|
|
2. Assume that population growth rates for each country A, B and C are as listed in the table from question 1 for the period 2050-2100. Assume α = 1/3, the investment rate is 10%, and the depreciation rate of capital stock is 4%. If annual average population growth rates had been 0.1% for A, 3.0% for B and 5.0% for C from 2000-2050, how much does the change in population growth rates from 2000- 2050 to 2050-2100 affect the steady state levels of per capita gdp for each country over the period 2050-2100 relative to the base period of 2000-2050?
3. Returns to education are given in the table below.
| years of schooling |
return per year |
| 1 - 4 |
13.40% |
| 5-8 |
10.10% |
| 9+ |
6.80% |
In country A the average person has 11 years of education, while in country B the average person has 15 years. What is the ratio of steady state incomes for these two countries?
4. For each country in the table below, calculate the share of the wage paid that is payment to human capital and payment to raw labour. Returns to years of education are given in question 3 above.
| years of school |
share of labour force |
|
country A |
country B |
| 0-Jan |
1.80% |
0.025 |
| 3 |
22.00% |
0.065 |
| 6 |
0.35 |
0.25 |
| 9 |
0.27 |
0.35 |
| 13 |
0.142 |
0.31 |
5. Consider the following data on two countries ABC and XYZ. The production function is y = Akαh 1-α where α = 0.5.
|
ABC |
XYZ |
| Output per Worker, y |
120 |
200 |
| Physical Capital per Worker, k |
12100.00% |
100 |
| Human Capital per Worker, h |
3600.00% |
81 |
a. Calculate the ratio of productivity of country ABC to country XYZ.
b. Calculate the countries' relative levels of output if all differences in output were the result of productivity
c. Calculate the countries' relative levels of output if all differences in output were the results of factor accumulation.
6. The following table provides data on the annual growth rates of output per worker yˆ, physical capital per worker kˆ, and human capital per worker hˆ. α = 25
For each country, calculate growth rates of factor accumulation and productivity. In which country does factor accumulation account for the largest share of growth? In which country does productivity account for the largest share of growth?
| Country |
Annual Growth Rate (%) |
|
yˆ |
kˆ |
hˆ |
| Algeria |
75.00% |
0.4 |
0.45 |
| Botswana |
155.00% |
1.65 |
0.47 |
| Cameroon |
1.07 |
0.95 |
0.65 |
7. Consider the one-country growth model of technology and growth that was presented in Section 8.3. Suppose that L = 1, µ = 4, and γA = 0.15. Calculate the growth rate of output per worker. Now suppose that the share of the L in R&D, γA, increases to 0.25. How many years will it take before output per worker returns to the level it would have reached had γA remained constant? Illustrate the two paths of output on a graph of y as a function of time.
8. Consider the two-country model of technology growth from Weil, section 8.3. Suppose that γA,1 > γA,2, A1 > A2, and the two countries are in steady state. Now suppose that Country 1 raises the fraction of the labour force that is doing R&D.
Draw two graphs, one illustrating the paths of productivity for both countries as a function of time, and one illustrating the paths of y for both countries as a function of time. Explain what these graphs illustrate.
9. Relationships between technology and income
a. Generate a scatter plot of growth of per capita income (gy7509) against growth of productivity (prodgrowth). Describe the pattern.
b. Generate a scatter plot of computer ownership (comp05) against per capita income growth from 2005 to 2009 (rgdpch20xx).
c. Generate a scatter plot of computer ownership (comp05) against per capita incomes in 2009 (rgdpch2009). Compare results in parts b. and c.
d. Repeat parts b. and c. above replacing computer ownership with internet usage (intuser09).
Attachment:- 1466471_2_data.xlsx