Consider a Solow economy that begins with a capital stock equal to $300 billion, and suppose its steady- state level of capital is $500 billion. To its pleasant surprise, the economy receives a generous gift of foreign aid in the form of $100 billion worth of capital (electric power plants, machine tools, etc.). (a) Use the Solow diagram, other graphs, and the mathematics of the Solow model to explain what happens to the economy, both immediately and over time. By what proportion does consumption per person initially increase? What happens to consumption in the long run? (b) Suppose instead of starting below its steady state, the economy begins in steady state, with a capital stock equal to $500 billion. Answer part (a) for this case. (c) Summarize what this exercise teaches you about the possible consequences of foreign aid. In this example, does foreign aid exert a long- run effect on the welfare of poor countries? What is the benefit of foreign aid?
> Suppose Congress and the president decide to increase government purchases today, say for national defense. Explain how this affects the IS curve. How does your answer depend on the way in which the spending is financed and on the extent to which Ricardi
> Consider the following changes in the macro economy. Show how to think about them using the IS curve, and explain how and why GDP is affected in the short run. (a) The government offers a temporary investment tax credit: for each dollar of investment tha
> According to the permanent income hypothesis, how does your consumption change in each of the following scenarios? (The first question is answered for you.) To keep things simple, suppose the interest rate is 10% and you will live forever. Feel free to g
> According to the life- cycle/permanent- income hypothesis, consumption depends on the present discounted value of income. An increase in the real interest rate will make future income worth less, thereby reducing the present discounted value and reducing
> The University of Chicago Booth School of Business hosts an online panel of economic experts every two weeks or so to consider a timely economic question. A specific economic opinion is put forward, and the experts either “agree” or “disagree.” Most of t
> Many economists have recommended higher capital requirements to solve the problems associated with financial crises. (a) What is a capital requirement? (b) How could higher capital requirements potentially help the economy in terms of financial stability
> Consider the following balance sheets for two hypothetical financial institutions, bank B and bank C: (a) Fill in the missing entries in the balance sheets (denoted ???). (b) What is the leverage ratio in each bank? (c) Suppose housing prices fall shar
> Apply the supply- and- demand model to the following markets. In each case, state the key endogenous variables in the market as well as some important exogenous variables or parameters. Also, express each model as a system of mathematical equations. As a
> Choose two financial institutions and look up their balance sheets online. (For example, Yahoo! Finance provides these data in an easily accessible form at http://finance.yahoo.com/q/bs?s=GS.) What is the leverage ratio of the two companies you’ve chosen
> By now, you are relatively familiar with recent economic events in the United States. But what about Europe? Write two paragraphs about the state of the economy in the Euro area over the past several years. What has happened to inflation, real GDP growth
> Using the FRED database, create a graph of the price of crude oil since 1987 based on “Crude Oil Brent— Europe.” (a) Display this graph. (b) How much more expensive (in nominal terms) is oil today than it was in the 1990s? (A rough average for the earlie
> Pick two figures from this chapter, and update them to include the latest available data. What does this tell you about how the economy has evolved since the Great Recession?
> A real-world problem faced by policymakers, forecasters, and businesses every day is how to judge the state of the economy. Consider the table below, showing hypothetical measures of real GDP in the coming years, starting at a level of $18.0 trillion in
> Suppose the economy exhibits a large, unexpected increase in productivity growth that lasts for a decade. Policymakers are (quite reasonably) slow to learn what has happened to potential output and incorrectly interpret the increase in output as a boom t
> Consider an economy that begins with output at its potential level and a relatively high inflation rate of 6%, reflecting some recent oil price shocks. As the head of the Federal Reserve, your job is to pick a sequence of short-run output levels that wil
> Draw a graph with a steep Phillips curve and a graph with a gently sloped Phillips curve. (a) Explain how the two economies respond differently to a boom and to a slump. (b) What are some factors that might influence the slope of the Phillips curve? (c)
> Using the FRED database, locate the Congressional Budget Office’s measure of potential GDP by searching for “GDPPOT.” Using the “Add Data Series” option, add the series “GDPA” (real annual GDP) to this graph. Adjust the sliders to show the data from arou
> Suppose the inflation rate is 5%. Suppose the marginal product of capital in a firm is 8% but that in the course of production, 6% of capital is worn out by depreciation. What is the nominal return associated with an investment in capital, and why? What
> Now we add some parameters to the labor market model: labor supply: Ls =
> Suppose the real return on investing in a machine is 5% and the inflation rate is 4%. (a) According to the Fisher equation, what should the nominal interest rate be? (b) Suppose bank A charges a nominal interest rate on loans equal to 8%. What happens? (
> What is the key endogenous variable in the quantity theory? Explain the effect on this key variable of the following changes: (a) The money supply is doubled. (b) The velocity of money increases by 10%. (c) Real GDP rises by 2%. (d) The money supply incr
> Using the FRED database, download a graph of the inflation rate for China and India. (For help with using the FRED data, see Case Study “The FRED Database” Chapter 2 on page 34.) (a) Display the two graphs. (b) What is the average inflation rate in each
> As in exercise 15, the amount of money the government raises from the inflation tax is DM. (a) Write this amount as a ratio to nominal GDP. Multiply and divide by M to get an expression for the ratio of revenue from the inflation tax to GDP. Your answer
> The amount of money the government raises from the inflation tax is DM. Use the FRED database for the last period in each year to answer the following questions: (a) How much currency was in circulation in 1981? What was the size of the monetary base in
> The complete version of the Thomas Sargent quote that began this chapter is “Persistent high inflation is always and everywhere a fiscal phenomenon.” Why did Sargent include the modifiers “persistent high”?
> Consider two possible inflation scenarios. In one, the inflation rate is 100% per year, but it has been at this level for three decades and the central bank says it will keep it there forever. In the other, the inflation rate was 3% for two decades but j
> Consider the following two questions. (a) Can the real interest rate be negative? In what circumstances? (b) Can the nominal interest rate be negative? Discuss.
> Using the FRED database, create a single graph containing the 10-year government bond yield (one measure of a nominal interest rate) and the inflation rate for Italy. You may find it helpful to use the search terms “government bond yield Italy” and “infl
> Using the data on the consumer price index reported in Table 8.1, calculate the value in 2015 of the following items (refer to the nearest year in the table to do each calculation): (a) The salary of a worker in 1900: $1,000 per year. (b) Bab
> Consider an economy that produces oranges and boomerangs. The prices and quantities of these goods in two different years are reported in the table below. Fill in the missing entries. Percentage change 2020-2021 2020 2021 Quantity of oranges Quantit
> In the text, we supposed a college education raised a person’s wage by $30,000 per year, from $40,000 to $70,000. Assume the interest rate is 3% and there is no growth in wages, then answer the following. (a) Suppose you are a high school senior deciding
> To make the calculation of the present discounted value of a worker’s human capital more realistic, suppose labor income starts at $50,000 initially, but then grows at a constant rate of 2% per year after that. Let wt be labor income in year t, so that w
> Review the discussion of the value of a typical worker’s human capital in Section 7.6 on page 191. (a) Re compute the present discounted value in the following cases: R = 0.01, R = 0.02, R = 0.04, R = 0.05. (b) What is the economic intuition for why t
> Repeat exercise 4 for an interest rate of 1%, then for an interest rate of 5%. Arrange your answers in a table so you can more easily see the difference a change in the interest rate makes. Data from exercise 4: Suppose scientists discover a new way to
> Suppose the government decides to reform the tax system to reduce the marginal income tax rate across the board. Explain the effect on wages, the employment- population ratio, and unemployment.
> Using the FRED database, download graphs of the U.S. employment- population ratio for men and women. (For help with FRED, see the case study “The FRED Database” in Chapter 2 on page 34.) (a) Display the graphs. (b) What are some possible explanations fo
> GDP per hour: Assume annual hours worked per person in the United States is equal to 800. Using the data from Table 7.2 and the “Country Snapshots” file (snapshots.pdf), compute GDP per hour for the other c
> Consider the following two proposals to reform unemployment insurance. Explain the arguments for and against each reform. (a) The insurance payment would be increased so that it replaced 100% of a worker’s regular labor income for 26 weeks. (b) Each work
> Suppose the U.S. unemployment rate in October 2009 had been 6% instead of 10.0%. How many more people would have been working (assuming the labor force remained the same)?
> Consider the following variation: Yt = A1/2 t Lyt , ∆ At+1 = z At Lat , Lyt + Lat =
> Look back at Table 2.4. Some missing entries are labeled with question marks. Compute the values that belong in these positions. Table 2.4: TABLE 2.4 Real and Nominal GDP in a Simple Economy, 2018–2020 Percentage change 2019
> In 2015, the U.S. National Income Accounts began to “count” intellectual property products— such as R&D, computer software, books, music, and movies— explicitly as investment. More correctly, they had previously assumed these products were an intermediat
> Now suppose the parameters of the model take the following values:
> Suppose we have two economies— let’s call them Earth and Mars—that are identical, except that one begins with a stock of ideas that is twice as large as the other:
> Suppose the economy is on a balanced growth path in the Romer model, and then, in the year 2030, research productivity
> What is the growth rate of output per person in Figure 6.2? What are the growth rates of output per person before and after the changes in the parameter values in Figures 6.3 and 6.4? Figure 6.2: Figure 6.3: Figur
> (a) Use the production function in equation (5.6) and the rules for computing growth rates from page 53 of Chapter 3 to write the growth rate of per capita GDP as a function of the growth rate of the capital stock. (b) Combine this result with the last e
> Suppose an economy begins in steady state. By what proportion does per capita GDP change in the long run in response to each of the following changes? (a) The investment rate doubles. (b) The depreciation rate falls by 10%. (c) The productivity level ris
> Search the FRED database for the “investment share of GDP” and one of the first links to appear is for “gross private domestic investment.” (For help with using the FRED data, refer back to the case study “The FRED Database” in Chapter 2 on page 34.) (a)
> Consider a onetime change in government policy that immediately and permanently increases the level of the labor force in an economy (such as a more generous immigration policy). In particular, suppose it rises permanently from
> Download the file snapshots.pdf from web.stanford.edu/chadj/snapshots.html and answer the following. (At the moment, the latest year in the data file is 2014. Over time, this year will advance, so please use the latest year available in the Country Snaps
> One explanation for China’s rapid economic growth during the past several decades is its expansion of policies that encourage “technology transfer.” By this, we mean policies— such as opening up to international trade and attracting multinational corpora
> Consider a Solow model where the production function no longer exhibits diminishing returns to capital accumulation. This is not particularly realistic, for reasons discussed in Chapter 4. But it is interesting to consider this case nonetheless because o
> By manipulating the equations of the Solow model mathematically, it is possible to make more precise quantitative statements about the behavior of growth rates over time. For example, one way of quantifying the principle of transition dynamics is with th
> Suppose an economy begins in steady state and is characterized by the following parameter values:
> Suppose a country enacts a tax policy that discourages investment, and the policy reduces the investment rate immediately and permanently from
> Read the article on institutions by Mancur Olson, cited in footnote 10. (You may be able to find it on the web by typing the author’s name and a few words from the title into Google Scholar.) The last sentence of that paper says that “individual rational
> Repeat exercise 5, but this time assume the production function is given by Y =
> The table below reports per capita GDP and capital per person in the year 2014 for 10 countries. Your task is to fill in the missing columns of the table. (a) Given the values in columns 1 and 2, fill in columns 3 and 4. That is, compute per capita GDP a
> Explain whether the following goods are rivalrous or nonrivalrous: (a) Beethoven’s Fifth Symphony, (b) a portable music player, (c) Monet’s painting Water Lilies, (d) the method of public key cryptography, (e) fish in the ocean.
> In 2014, Ethiopia had a per capita income of $1,500, about $4 per day. Compute per capita income in Ethiopia for the year 2050 assuming average annual growth is (a) 1% per year. (b) 2% per year. (c) 4% per year. (d) 6% per year. (For comparison, per capi
> Suppose the production function at the core of our model is given by Y = AK 3/4L 1/4 (that is, assume the exponents on capital and labor are 3/4 and 1/4 rather than 1/3 and 2/3). (a) Create a new version of Table 4.1 for the new version of
> What determines whether a curve shifts in the Solow diagram? Make a list of the parameters of the Solow model, and state whether a change in each parameter shifts a curve (which one?) or is simply a movement along both curves.
> What is the economic meaning of the vertical gap between the investment curve and the depreciation curve in the Solow diagram?
> Add another line, period 6, to Table 5.1. What are the values of K6, I6,
> What are some costs and benefits of economic growth?
> Why, and in what sense, do the three growth rates shown in Figure 3.9 add up? Figure 3.9: FIGURE 3.9 U.S. Population, GDP, and Per Capita GDP Ratio scale 3.5% Total GDP Per capita GDP 2.0% Population 1.5% 1880 19
> This question is not addressed in the chapter—and in fact is still debated among economists—but it is interesting to think about: Why do you suppose growth in living standards was virtually nonexistent for thousands of years? Why did this situation chang
> How does macroeconomics study these questions?
> Given your current knowledge, what do you think are the answers to these questions?
> By roughly how much did housing prices fall during the financial crisis? What about the stock market?
> Who pays the inflation tax?
> Write each production function given below in terms of output per person y ; Y/L and capital per person k ; K/L. Show what these “per person” versions look like in a graph with k on the horizontal axis and y on the vertical axis. (Assume
> Suppose the world population today is 7 billion, and suppose this population grows at a constant rate of 3% per year from now on. (This rate is almost certainly much faster than the future population growth rate; the high rate used here is useful for ped
> Explain how a rise in
> What is inflation? Suppose an individual’s retirement plan consists of putting $100 into a safe. What effect does inflation have on this plan?
> In the past 50 years, both the fraction of hours worked by college graduates and the relative wage of college graduates have gone up. Why?
> How are ideas different from objects? What are some examples of each?
> Which questions in macroeconomics interest you the most? Why?
> What justification can one give for a fiscal stimulus during the financial crisis?
> Throughout much of the 2010–2015 period, the fed funds rate was substantially lower than what a Taylor rule for monetary policy would seem to indicate. Why?
> What is the fundamental source of transition dynamics in our AS/AD framework? Why does the economy take several periods before returning to its steady state following a shock?
> What are some examples of shocks that shift the AD curve? What about the AS curve?
> How does a central bank influence economic activity in the short run?
> Do the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L? (Assume
> Why is the relationship between output and the real interest rate called the “IS curve”?
> Why does the IS curve slope downward?
> What is a balance sheet? What is net worth?
> A Monetary History of the United States, 1867 to 1960, by Milton Friedman and Anna Schwartz, is a classic study of monetary policy and was published in 1963. Read the interview with Anna Schwartz available at www.minneapolisfed.org/publications/ the- reg
> What are some recent shocks that have hit the macroeconomy?
> How do the long- run model and the short- run model fit together? What is the purpose of each model?
> Explain some of the costs of hyperinflations. If they are so costly to an economy, why do they occur?
> The poorest countries in the world have a per capita income of about $600 today. We can reasonably assume that it is nearly impossible to live on an income below half this level (below $300). Per capita income in the United States in 2015 was about $51,0
> Make one change to the basic combined model that we studied in this appendix: let the production function for output be Yt = AtK1/4 t L3/4 yt . That is, we’ve reduced the exponent on capital and raised it on labor to preserve constant returns to objects.
> Growth in the combined Solow- Romer model is faster than growth in the Romer model. In what sense is this true? Why is it true?
> Suppose xt =(1.04)t and yt =(1.02)t. Calculate the growth rate of zt in each of the following cases: (a) z = xy (b) z = x/y (c) z = y/x (d) z = x1/2y1/2 (e) z =(x/y)2 (f) z = x-1/3y2/3
> Consider the following (made- up) statistics for some economies. Assume the exponent on capital is 1/3 and that the labor composition is unchanged. For each economy, compute the growth rate of TFP. (a) A European economy: gY/L = 0.03, gK/L = 0.03. (b) A
> Suppose the economy has a natural rate of unemployment of 5%. (a) Suppose short- run output over the next 4 years is +1%, 0%, −1%, and −2%. According to Okun’s law, what unemployment rates would we expect to see in this economy? (b) Consider another ec
> Japanese GDP in 2012 was 468 trillion yen (U.S. GDP was $16.2 trillion). The exchange rate in 2012 was 79.8 yen per dollar. Contrary to China and India, however, Japan had higher prices than the United States: the price level in Japan (converted to dolla
> The Fisher equation relates real (R) and nominal (i) interest rates to the rate of inflation (
