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Macroeconomics Global Edition 6th Edition Stephen D. Williamson - Solutions

9.2 How do consumers save in the two-period model?
9.1 Why do consumers save?
2. Perform the following analysis to examine the income convergence for two groups of countries:Argentina, Chile, Mexico, and Uruguay (from South America); and the Four Asian Dragons (Hong Kong, Taiwan, South Korea, and Singapore).(a) Compute the annual growth rates for every ten years from 1956 to
1. Calculate real GDP per capita and annual growth rate for all countries of the world for the year 2015. Construct a scatter plot between the growth rate of real GDP per capita and the index of human capital per person. Do you observe a positive correlation between these two variables, as
11. LO 2 In the endogenous growth model, suppose that there are three possible uses of time.Let u denote the fraction of time spent working, s the fraction of time spent neither working nor accumulating human capital (call this unemployment), and 1 - u - s the fraction of time spent accumulating
10. LO 4 Suppose there are two countries. In the rich country, the representative consumer has Hr units of human capital, and total factor productivity is zr. In the poor country, the representative consumer has Hp units of human capital, and total factor productivity is zp. Assume that b and u are
9. LO 3 Reinterpret the endogenous growth model in this chapter as follows. Suppose that there are two groups of people in a country, the low-skilled workers and the high-skilled workers. The lowskilled workers have less human capital per person initially than do the high-skilled workers.In the
8. LO 3 Suppose a government increases investment in education to improve the quality of its e-learning systems. This investment increases a representative worker’s ability to absorb more knowledge and technology without cutting down on working hours. Does the new government policy improve
7. LO 3 Introduce government activity in the endogenous growth model as follows. In addition to working u units of time in producing goods, the representative consumer works v units of time for the government and produces gvH goods for government use in the current period, where g 7 0. The consumer
6. LO 2 In the endogenous growth model, suppose a higher real wage is paid due to improvement in production technology. Use a diagram to explain how this would afect the growth rate of human capital. What is the impact on the levels and the growth rates of consumption and output?
5. LO 1 Suppose there are two countries, A and B, and each is a Solow growth model economy. In each country, a fraction a of the population is rich, and a fraction 1-a is poor. Suppose that rich people save a fraction sr of their income, and poor people save a fraction sp of their income, no matter
4. LO 1 Suppose, in the Solow growth model, that learning by doing is captured as a cost of installing new capital. In particular, suppose that for each unit of investment, r units of goods are used up as a cost to irms.(a) Determine how r afects the steady state quantity of capital per worker, and
3. LO 1 Suppose that there are two countries with diferent levels of total factor productivity, and that these diferences exist because of barriers to technology adoption in the low-productivity country. Also suppose that these two countries do not trade with each other. Now, suppose that residents
2. LO 1 In the Solow growth model, suppose the per worker production function is given by y = zk0.4, with s = 0.4, d = 0.2, and n = 0.02.(a) Suppose that in country A, z = 1. Calculate income per worker and capital per worker in the steady state.(b) Suppose that in country B, z = 2. Calculate
1. LO 1 Could diferences across countries in population growth account for the persistence in income disparity across countries? Use the Solow growth model to address this question and discuss.
8.9 In the endogenous growth model, would two countries with different levels of human capital eventually converge in consumption and income levels? Why or why not?
8.8 How do government subsidies on education affect current and future consumption in the endogenous growth model?
8.7 Why does the endogenous growth model lead to unbounded economic growth?
8.6 Why is knowledge nonrivalrous?
8.5 What is the major difference between the explanation for total factor productivity in the Solow model and that in the endogenous growth model?
8.4 How can a country overcome low productivity?
8.3 What are three sources of differences in productivity across countries?
8.2 How is the Solow model consistent with evidence on convergence across countries?
8.1 If countries are initially identical, except with respect to levels of capital per worker, what does the Solow model predict will happen to these countries in the long run? Is this consistent with the data?
3. Refer to the Penn World Table’s database on growth accounting (http://febpwt.webhosting.rug.nl/Dmn/AggregateXs/PivotShow). The data show that real GDP in Korea is higher than that in Malaysia in 2014. Construct a table showing capital stock at constant 2011 national prices, index of human
2. Using data from the World Development Indicators database (http://databank.worldbank.org/data/reports.aspx?source=world-development-indicators), calculate capital per worker using gross capital information and total labor force for all countries for the year 2015. Then construct a scatter plot
1. Use data from the World Development Indicators database (http://databank.worldbank.org/data/reports.aspx?source=world-development-indicators) and construct a scatter plot between population growth rate and GDP per capita growth for all countries in the world for 2015. What relationship do you
13. LO 7 Consider the following data:(a) Calculate the Solow residual for each year from 2002 to 2014.(b) Calculate percentage rates of growth in output, capital, employment, and total factor productivity for the years 2002 to 2014. In each year, what contributes the most to growth in aggregate
12. LO 5 Consider a numerical example. In the Solow model, assume that n = 0, s = 0.2, d = 0.1, and F(K, N) = K0.3N0.7. Suppose that initially, in period t = 0, z = 1 and the economy is in a steady state.(a) Determine consumption, investment, savings, and aggregate output in the initial steady
11. LO 5 Alter the Solow growth model so that the production technology is given by Y = zK, where Y is output, K is capital, and z is total factor productivity.Thus, output is produced only with capital.(a) Show that it is possible for income per person to grow indeinitely.(b) Also show that an
10. LO 5 Suppose that we modify the Solow growth model by allowing long-run technological progress.That is, suppose that z = 1 for convenience, and that there is labor-augmenting technological progress, with a production function Y = F(K, bN), where b denotes the number of units of “ human
9. LO 5 Consider a numerical example in the Solow growth model. Suppose that zF(K, N) = K0.4N0.6, where d = 0.2, s = 0.4, n = 0.02, and z = 1.(a) Write the per worker production function.(b) Calculate the capital per worker, income per capita, and consumption per capita in the steady state.(c) Now,
8. LO 5 Assume an economy where a government promotes population control through family planning and birth control. In the Solow model, the efect of this policy on the standard of living as measured by consumption per worker cannot be determined. Explain.
7. LO 5 Modify the Solow growth model by including government spending as follows. The government purchases G units of consumption goods in the current period, where G = gN and g is a positive constant. The government inances its purchases through lump-sum taxes on consumers, where T denotes total
6. LO 5 If total factor productivity decreases, determine using diagrams how this afects the golden rule quantity of capital per worker and the golden rule savings rate. Explain your results.
5. LO 5 Suppose that the economy is initially in a steady state and that some of the nation’s capital stock is destroyed because of a natural disaster or a war.(a) Determine the long-run efects of this on the quantity of capital per worker and on output per worker.(b) In the short run, does
4. LO 5 Suppose the depreciation rate in an economy decreases. In the Solow model, determine the effects of this change on the quantity of output per worker, consumption per worker, and capital per worker in the steady state. Use a diagram to illustrate your answer.
3. LO 5 In the Solow growth model, suppose that the marginal product of capital increases for each quantity of the capital input, given the labor input.(a) Show the efects of this on the aggregate production function.(b) Using a diagram, determine the efects on the quantity of capital per worker
2. LO 2 Suppose an economy’s birth rate is higher than its death rate. How does the Malthusian model predict the long-run steady state for this economy? Explain your answer using diagrams.
1. LO 2 Suppose a tsunami loods a country’s agricultural areas and decreases the quantity of land. Explain how this afects the consumption per capita, aggregate consumption, and future population in the long-run steady state in the Malthusian model. Use diagrams.
7.12 What does the Solow residual measure, and what are its empirical properties?
7.11 What is the parameter a in the production function in Equation (7-21)?
7.10 Why is a Cobb–Douglas production function useful for analyzing economic growth?
7.9 How is sustained economic growth achieved in the Solow model? Is the process similar to the one in the Malthusian model?
7.8 Explain what determines the golden rule quantity of capital per worker and the golden rule savings rate.
7.7 In the Solow growth model, what are the effects of (a) an increase in the savings rate; and(b) a decrease in the labor force on output per worker and economic growth in the long run?
7.6 What are the characteristics of a steady state in the Solow growth model?
7.5 Was Malthus right? Why or why not?
7.4 What can increase the standard of living in the Malthusian model?
7.3 According to the Malthusian model, technological improvement does not raise the standard of living in the long run. Explain.
7.2 What are the seven economic growth facts?
7.1 What is the difference between exogenous growth and endogenous growth?
3. Access the monthly data on registered unemployment and job vacancies (http://www.oecdilibrary.org/economics/data/labour/registered-unemployed-and-job-vacancies_data-00049-en). Choose any one country and construct a scatter plot between its unemployment rate and vacancy rate for the last five
2. Use the annual data on unit labor costs (https://data.oecd.org/lprdty/unit-labour-costs.htm#indicator-chart) and labor productivity (https://data.oecd.org/lprdty/multifactorproductivity.htm). Plot the trends of these variables for any one country over time. Do they move in the same direction as
1. Use the annual data on unemployment rates (https://data.oecd.org/unemp/unemploymentrate.htm) and average wages (https://data.oecd.org/earnwage/average-wages.htm#indicatorchart).Choose any one country and discuss the relationship between unemployment rates and average wages over time.
8. LO 6, 7 Suppose that all social programs simultaneously become more generous. In particular suppose that there is an increase in UI benefits, and also an increase in welfare benefits, which are represented in the two-sided search model as payments to everyone who is not in the labor force. What
7. LO 6, 7 Adapt the two-sided search model to include government activity as follows. Suppose that the government can operate irms, subject to the same constraints as private irms. In particular, the government must incur a cost k to post a vacancy. Supposing that the government operates G irms,
6. LO 6, 7 Suppose that there is technological change that reduces the cost of recruiting for irms. Using the two-sided search model, determine the efects on the unemployment rate, the vacancy rate, the labor force, the number of irms, aggregate output, and labor market tightness. Use diagrams, and
5. LO 6, 7 Suppose the government’s goal is to reduce the unemployment rate. Some legislators propose that the government should give a subsidy s to any irm that hires a worker. Some other legislators argue that it would be more efective to simply pay consumers to stay home rather than searching
4. LO 6, 7 What does the two-sided search model predict would be the efects of laborsaving devices in the home, for example dishwashers, washing machines, and vacuum cleaners? Use diagrams to show the efects on the unemployment rate, the vacancy rate, the labor force, the number of irms, aggregate
3. LO 5 Suppose your government reforms its unemployment insurance system. The duration of UI beneits received by unemployed persons shortens from nine to six months. In addition, the government reduces the taxes on labor income but not those on UI beneits. Examine the efects of this decision on
2. LO 5 Suppose that all irms raise wages of all workers but cut back on some oice jobs due to a technological change. Using the one-sided search model of unemployment, how will this afect the reservation wage and the long-term unemployment rate?
1. LO 5 Determine the efects of an increase in the separation rate, s, on the reservation wage and on the long-run unemployment rate in the onesided search model of unemployment. Explain your results.
6.21 What explains the observed Beveridge relation from 2000 to 2012?
6.20 In case of a fall in matching efficiency, is the two-sided search model’s prediction of aggregate output consistent with the observations? Explain.
6.19 In case of a productivity increase, is the two-sided search model’s prediction of unemployment rate consistent with the observations? Explain.
6.18 In case of an increase in UI benefits, is the two-sided search model’s prediction of unemployment rate consistent with the observations you studied in this chapter?Explain.
6.17 In the two-sided search model, when a worker and firm are matched, what determines the wage paid to the worker?
6.16 What are total surplus, worker surplus, and firm surplus in the two-sided search model?
6.15 In the two-sided search model, what determines a firm’s decision to post a vacancy?
6.14 In the two-sided search model, what determines a consumer’s decision to search for work?
6.13 If a government helps unemployed workers find jobs, will the long-run unemployment rate fall or rise? Use the one-sided search model of employment to explain your answer.
6.12 In the one-sided search model of employment, how will an increase in the tax on both labor income and UI benefits affect the long-run unemployment rate?
6.11 How will an increase in the tax on income affect welfare from employment and unemployment, respectively? How will the reservation wage change?
6.10 How does an increase in the UI benefit affect the reservation wage in the one-sided search model, and why?
6.9 What determines the reservation wage in the one-sided search model?
6.8 What causes shifts in the welfare of the unemployed in the one-sided search model?
6.7 What causes shifts in the welfare of the employed in the one-sided search model?
6.6 How does the vacancy rate behave relative to the unemployment rate, and how does this matter for the Beveridge curve?
6.5 How does the employment/population ratio behave relative to the participation rate?
6.4 Which variable is more cyclical, participation rate or employment/population ratio? Why?
6.3 Define participation rate. How does participation rate move in relation to real GDP over time?
6.2 What are the long-run regularities in the behavior of the unemployment rate?
6.1 What are the short-run regularities in the behavior of the unemployment rate?
2. Plot the chosen economy’s trends of health expenditure, public expenditure, expenditure on education as a percentage of total government expenditure, and GDP growth for the same period. What is the relationship between these variables?
1. Choose any economy and plot the trends of its general government final consumption expenditure, household final consumption expenditure, and GDP growth from 1960 to the latest available year. Does the annual growth rate of government spending for this economy have a positive relationship with
12. LO 6 Change the model of public goods in the following fashion. Suppose that T units of goods acquired as taxes from the private sector produces T1/2/a units of public goods, where a 7 0.Determine the production possibilities frontier(PPF), and illustrate it in a diagram. Show in your diagram
11. LO 6 Extend the model of public goods, in the last section of this chapter, as follows. Suppose that output is produced, as in the simplified model with proportional taxation, only with labor, and that z = 1. Here, however, there is lump-sum taxation, and the PPF is given by Y = h - l - G. Now
10. LO 6 Consider the model of public goods in the last section of this chapter.(a) Suppose that preferences over private consumption C and public goods G are such that these two goods are perfect substitutes;that is, the marginal rate of substitution of public goods for private goods is a constant
9. LO 5 Suppose that a government plans to collect a tax revenue of $50 million to inance government expenditure. The government can choose the proportional tax (t1 or t2) to achieve this objective.Suppose that t2 is higher than t1.(a) Which tax rate, t1 or t2, would lead to higher welfare?(b) Is
8. LO 5 Suppose that the current tax rate is higher than t*, which is the rate that yields the highest tax revenue. Some government oicials propose to increase the tax further in order to raise more government revenue. They argue that a higher tax rate would motivate people to work harder to
7. LO 3 Suppose that, in the basic one-period model, there is no government spending and no taxes. Production by the representative irm produces pollution in proportion to the amount of output produced. Given any consumption bundle (a consumption–leisure pair), the consumer is worse of the more
6. LO 3 In the one-period model, education can be represented as time spent by the representative consumer that is neither leisure time nor time applied to producing output. What the economy gains in the future is that the representative consumer then has more time available, as measured in terms
5. LO 3 Suppose that government spending makes private irms more productive; for example, government spending on roads and bridges lowers the cost of transportation. This means that there are now two efects of government spending, the irst being the efects discussed in this chapter of an increase
4. LO 3 Suppose that the representative consumer’s preferences change, in that his or her marginal rate of substitution of leisure for consumption increases for any quantities of consumption and leisure.(a) Explain what this change in preferences means in more intuitive language.(b) What efects
3. LO 3 Suppose that total factor productivity, z, affects the productivity of government production just as it afects private production. That is, suppose that when the government collects taxes, it acquires goods that are then turned into government-produced goods according to G = zT so that z
2. LO 3 An emerging economy changes its policy, attracting more foreign direct investment, which leads to the accumulation of a more productive capital stock.(a) How does this policy afect the aggregate output, consumption, employment, and real wage? Explain your results with a diagram and
1. LO 3 Suppose that the government decides to reduce taxes. In the model used in this chapter, determine the efects this has on aggregate output, consumption, employment, and the real wage, and explain your results.
5.19 How does an improvement in government efficiency affect private and government spending?
5.18 What are the two determinants of the optimal quantity of public goods?

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