(a)
The ratio of per capita
(a)
Explanation of Solution
The Solow economy is a steady state economy where the level of investment and the level of
In the case of Country U and Country S, the ratio of per capita GDP can be calculated when there is no change in TFP or in the rate of depreciation across countries. The key equation used in this case is as follows:
The value of the depreciation and TFP does not change and that means the only value and changes will be the investment rates for the two economies. The equation can be enlarged as follows:
It is identified that Country S has more investment than Country U, and it means that Country S would be richer than Country U. The difference in the per capita GDP between Countries U and S is calculated to be 14.1 percent than Country U’s level. Similarly, the difference between Country U and all other countries can be calculated and the table can be completed as follows:
Country | Investment rate | Ratio of per capita GDP relative to Country U in steady state (percent) |
US | 24.7 | - |
Switzerla | 32.1 | 14.1 |
Hokong | 26.2 | 3.1 |
Fran | 25.0 | 0.6 |
Jap | 29.0 | 8.3 |
South Kore | 35.0 | 19.0 |
Argentin | 16.0 | -19.5 |
Mexic | 21.1 | -9.2 |
Thailan | 26.4 | 3.4 |
Indi | 23.3 | -2.9 |
Keny | 11.1 | -33.3 |
Ethiopi | 10.4 | -36.4 |
(b)
The ratio of per capita GDP relative to Country U’s steady state with TFP differences.
(b)
Explanation of Solution
When there is difference in TFP of the economy, the equation would change as follows:
It is identified that Country S has more TFP than Country U, and it means that Country S would push the steady-state level higher than Country U’s level by 18 percent. Similarly, the difference between Country U’s and all other countries can be calculated and the table can be completed as follows:
Country | Investment rate | TFP | Ratio of per capita GDP relative to Country U in steady state with TFP differences (percent) |
US | 24.7 | 1.000 | - |
Switzerla | 32.1 | 1.022 | 17.8 |
Hokong | 26.2 | 0.835 | -13.0 |
Fran | 25.0 | 0.688 | -34.9 |
Jap | 29.0 | 0.680 | -36.0 |
South Kore | 35.0 | 0.711 | -31.7 |
Argentin | 16.0 | 0.534 | -55.6 |
Mexic | 21.1 | 0.438 | -67.1 |
Thailan | 26.4 | 0.381 | -73.2 |
Indi | 23.3 | 0.240 | -80.3 |
Keny | 11.1 | 0.178 | -91.4 |
Ethiopi | 10.4 | 0.102 | -96.3 |
(c)
The percentage gap between the steady-state income ratio and the ratio in 2014.
(c)
Explanation of Solution
The income ratio of Country S is 114.7 percent, whereas the steady-state level with TFP differences is 117.8. Therefore, the gap between the current position and the steady state position can be calculated as follows:
Thus, it shows that Country S is slightly below its steady state position. Similarly, the gap between the current and the steady state position for other countries can be calculated and tabulated as follows:
Country | Investment rate | TFP | Ratio of per capita GDP relative to US in steady state (percent) | Ratio of per capita GDP relative to US in steady state with TFP differences (percent) | Gap between current and steady state level |
US | 24.7 | 1.000 | - | - | - |
Switzerla | 32.1 | 1.022 | 14.1 | 17.8 | 2.70 |
Hokong | 26.2 | 0.835 | 3.1 | -13.0 | -15.62 |
Fran | 25.0 | 0.688 | 0.6 | -34.9 | -35.23 |
Jap | 29.0 | 0.680 | 8.3 | -36.0 | -40.90 |
South Kore | 35.0 | 0.711 | 19.0 | -31.7 | -42.61 |
Argentin | 16.0 | 0.534 | -19.5 | -55.6 | -44.84 |
Mexic | 21.1 | 0.438 | -9.2 | -67.1 | -63.77 |
Thailan | 26.4 | 0.381 | 3.4 | -73.2 | -74.08 |
Indi | 23.3 | 0.240 | -2.9 | -80.3 | -79.71 |
Keny | 11.1 | 0.178 | -33.3 | -91.4 | -87.11 |
Ethiopi | 10.4 | 0.102 | -36.4 | -96.3 | -94.18 |
(d)
The countries ranked based on the transition dynamics.
(d)
Explanation of Solution
The countries that have higher differences between the current state and the steady-state level would grow faster and when the countries reach close to their steady-state level, the economic growth would be slower and slower. This is suggested by the transition dynamics in the economy. The ranking will be in reverse order, which means that the economy with the highest growth rate will be Country E and least growth will be Country U.
Want to see more full solutions like this?
Chapter 5 Solutions
Macroeconomics (Fourth Edition)
- A country's growth rate (the percentage change in output) between 2000 and 2002 was 11%, and the growth rate between 2000 and 2001 was 7%, what was the country's growth rate between 2001 and 20027 Solve the problem by first formulating an equation(s). Please, enter the answer in (with two decimal points) and UPLOAD your work and final answer in the next question.arrow_forward(a) Does the data on Cambodia's GDP per capita in the table correspond approximately to a linear function, an exponential function, or neither? Year 2010 2011 2012 2013 2014 2015 GDP/capita ($/person) 782.7 824.8 870.5 920.3 969.3 1020.9 The data approximately corresponds to Choose one ▼ (b) Find a formula to approximate G, the GDP per capita in dollars/person, as a function of time, t, in years since 2010. NOTE: Round your estimated coefficients to 3 decimal places. We have G(t) 2 (c) What is the approximate annual percent increase in per capita GDP? NOTE: Give your answer to 1 decimal place. GDP is increasing at approximately % per year.arrow_forwardHow large will Canada’s GDP be in 25 years? The answer depends on what the rate of growth in GDP will be over that 25-year period. A mathematical formula we can use for this calculation is the following: GDP2041 = GDP2016 (1 + g)25 where GDP2041 is the level of GDP in the year 2041, GDP2016 is the level of GDP in the year 2016, and g is the rate of growth in GDP. Assume that GDP in 2016 is $1000 million and assume that the value of g is 0.035 (3.5 percent per year). What will be the value of GDP in 2041? Now suppose that the value of g is 0.040 (4.0 percent per year). What will be the value of GDP in 2041 given this slightly larger rate of growth? What does this result say about the importance of policies that promote even slightly faster rates of growth in GDP?arrow_forward
- Question 2 Calculate new HDI for Egypt using the given actual values from Egypt: Actual life expectancy at birth: 73.5 Mean years of schooling: 6.4 Expected years of schooling: 12.1 GNI per capita: 5,401 How would you classify Egypt based on the NHDI you found? Click on reveal once you are done calculating NHDI (0.662) Full explain this question and text typing work only thanksarrow_forwardExplore 05 yearly data of the following indicators with respect to Pakistan in graphical as well as tabular form a) Gross Domestic Product (GDP)b) Gross National Product (GNP)c) Net National Product (NNP)d) Net Domestic Product (NDP)e) National Income (NI)f) Personal Income (PI)g) Disposable Personal Income (DPI)arrow_forwardUsing the World Bank data base, (data,worldbank.org) select four economic variables of interest and analyze those variables over the last 20 years for Caricom member countries, Dominican Replublic, Mauritius and Singapore. Examples of these variables are inflation, unemployment, Real GDP Growth, Per Capita Income, Debt to GDP, Fiscal Deficits, etc.arrow_forward
- The United Nations Development Program (UNDP) needs your help!!! The UNDP wants you to empirically explore the strength of the relationship between income per capita and measurement of human development. To answer this question, use the UNDP Data in the fifth worksheet of Problem Set 2 data “Sheet UNDP 2019 data” in the file folder on Canvas. This file contains data from 2019 for 189 countries and comes from the UNDP’s country-level data sets. To calculate the indexes, use the minimum and maximum values for Gross National Income (GNI), life expectancy at birth (LE), mean years of schooling (MYSA), and expected years of schooling (EYSC) that are provided in the Excel spreadsheet.[1] Which of the following indicators need to be log-transformed before constructing its index? Life expectancy at birth (LE) Expected years of schooling of children (EYSC Mean years of schooling of adults (MYSA) GNI per-capitaarrow_forwardFinal output in the economy is pro- duced using capital K and labor L. The production function is: Y = ĀK/ L^/5 Assume that the supply of all inputs are exogenous and equal to L and K. Perfectly compet- itive firms are price-takers and choose how much capital and labor to demand by maximizing profits. Let w and r denote the wage and rental rate of one unit of labor and capital respec- tively.arrow_forwardQuestion: The following data show the population of Turkey in the selected years between 1990 and 2020: Year 1990 1995 2000 2005 2010 2015 61 68 ? 74.1 79.1 Population (millions) 57 2020 84.1 (a) Calculate the rate of growth of the population in millions per year in the year 2020 with an error level of O(h²).arrow_forward
- The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per year. (i) Assuming that this growth rate continues, derive a model to represent the population P (in billions of people) in year t. (ii) From the model derive in (i), approximately when will the population of the world be 11.2 billion people?arrow_forwardIndia’s GDP per capita increased from $310 in 1991 to $1,489 in 2012. (i) Calculate the average annual rate of growth of the Indian economy during this period using the arithmetic average. (ii) Calculate the geometric average annual growth rate of India during this period. Explain why the number you find in (ii) differs from the result obtained in (i).arrow_forwardCountry A produces GDP according to the following equation: GDP = 5VK. The country has a depreciation rate of 8.9 %. What does this country's savings rate need to be in order to sustain a steady-state GDP of $134? %3D Put your answer into percentage form (e.g. 30.57 % not 0.3057) and then round to two decimal places. You do not need to include the % sign.arrow_forward
- Principles of Economics (12th Edition)EconomicsISBN:9780134078779Author:Karl E. Case, Ray C. Fair, Sharon E. OsterPublisher:PEARSONEngineering Economy (17th Edition)EconomicsISBN:9780134870069Author:William G. Sullivan, Elin M. Wicks, C. Patrick KoellingPublisher:PEARSON
- Principles of Economics (MindTap Course List)EconomicsISBN:9781305585126Author:N. Gregory MankiwPublisher:Cengage LearningManagerial Economics: A Problem Solving ApproachEconomicsISBN:9781337106665Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike ShorPublisher:Cengage LearningManagerial Economics & Business Strategy (Mcgraw-...EconomicsISBN:9781259290619Author:Michael Baye, Jeff PrincePublisher:McGraw-Hill Education