Question: Compute the average annual growth rate of

> 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 (

> Suppose the Fed announces today that it is lowering the fed funds rate by 50 “basis points” (that is, by half a percentage point). Using the IS- MP diagram, explain what happens to economic activity in the short run. What is the economics underlying the

> Suppose velocity is constant, the growth rate of real GDP is 3% per year, and the growth rate of money is 5% per year. Calculate the long- run rate of inflation according to the quantity theory in each of the following cases: (a) What is the rate of inf

> Suppose scientists discover a new way to extract oil from deposits that were previously thought to be unrecoverable. The extra supply of oil leads oil prices to decline by $5 per barrel. Explain the effect on wages, the employment- population ratio, and

> Suppose the parameters of the IS curve are

> Consider the following simple monetary policy rule: Rt −

> Using the FRED database, download a graph of the share of income paid to labor for the nonfarm business sector of the U.S. economy, back to 1947. (For an introduction to FRED, see the case study “The FRED Database” in Chapter 2 on page 34.) (a) Display t

> Create a new table that contains only the last three columns of the table in exercise 5. This time, instead of reporting the numbers relative to the U.S. value, report the inverse of these numbers. For example, you should have found that per capita GDP i

> When and where did sustained economic growth first begin? How much inequality in per capita income was there throughout the countries of the world a thousand years ago? How much is there today?

> Why are capital requirements an important part of any reform to improve the functioning of the financial system?

> Describe the Fed’s balance sheet in “normal” times. How did it change during the financial crisis? Why?

> What is deflation, and what problems does deflation pose for the macro economy? How does deflation interact with the zero lower bound for nominal interest rates?

> Why is the Great Recession best understood in the IS/ MP– Phillips curve framework instead of the AS/AD framework?

> What are financial frictions, and what role do such frictions play in the financial crisis? How does a financial friction enter the IS/MP diagram and the AS/AD framework?

> Why are inflation expectations so important to modern monetary policy? What are several ways that central banks try to manage inflation expectations?

> Why do inflation- output loops appear counterclockwise?

> Why does the AD curve slope downward? Why does the AS curve slope upward? How is the AS/AD graph like a standard supply- and- demand diagram? How is it different?

> Plot the following scenarios for per capita GDP on a ratio scale. Assume that per capita GDP in the year 2015 is equal to $10,000. You should not need a calculator or computer program. Use the Rule of 70 to label the value of per capita GDP on the graph

> How is a monetary policy rule helpful for understanding U.S. monetary policy?

> Why do central banks often exercise monetary policy by targeting an interest rate rather than by setting particular levels of the money supply?

> What policy change did Paul Volcker implement, and how did it affect interest rates, output, and inflation over time?

> What is the Phillips curve? What role does it play in the short- run model? Explain the role played by each term in the equation for the Phillips curve.

> What is the relevance of Milton Friedman’s phrase “long and variable lags” to this chapter?

> What is the economic justification for the sticky inflation assumption? What role does this assumption play in the short- run model?

> Figure 12.1 presents a summary of the short- run model. Explain each step in this diagram. Figure 12.1: FIGURE 12.1 The Structure of the Short-Run Model MP IS Phillips curve curve curve Change in inflation, Nominal Real Shor

> What are three insights you gained from studying the micro foundations of the IS curve?

> For the development of the rest of the short- run model in the next two chapters, we could just present the equation for the IS curve,

> What are some examples of changes in the economy that would lead to movements along the IS curve? What are some changes that would shift the IS curve?

> Suppose your retirement account has a balance today of $25,000 and you are 20 years old. If you are invested in a diversified portfolio of stocks, you might hope that the historical return of about 6% continues into the future. Consider how the balance i

> What role does the IS curve play in our short- run model? What kind of economic questions does it allow us to analyze?

> What is leverage, and why is it so important in understanding the financial crisis?

> How severe was the Great Recession? What pieces of economic data would you cite to support your answer?

> Why is Okun’s law a useful rule of thumb to keep in mind when analyzing our short- run model?

> How can you “see” the Phillips curve operating in the graph of inflation in Figure 9.5? Figure 9.5: FIGURE 9.5 Inflation in the United States, 1960-2015 Percent 14 12 10 4 2 1960 1965 1970

> Before the latest financial crisis and recession, when was the largest recession of the past 50 years, and what was the cumulative loss in output over the course of the slowdown?

> Why do we measure short- run output

> How can we understand the Great Inflation of the 1970s? Does the government budget constraint help?

> What is the government budget constraint? How does it help us understand the causes of high inflation?

> What are the costs of inflation, and how can these costs be avoided?

> Suppose xt grows at 2% per year and yt grows at 5% per year, with x0 = 2 and y0 = 1. Calculate the numerical values of zt for t = 0, t = 1, t = 2, t = 10, t = 17, and t = 35 for the following cases: (a) z = x (b) z = y (c) z = x3/4y1/4

> What is the difference between a real interest rate and a nominal interest rate? What is the intuition behind the Fisher equation?

> Why do economists think the classical dichotomy holds in the long run?

> A concise summary of the quantity theory of money is that inflation occurs because of too much money chasing too few goods. Explain.

> Give some examples of economic questions where the concept of present discounted value would be useful.

> Is the unemployment rate in Europe today higher or lower than in the United States? What about hours worked per person? What are some possible explanations for the differences?

> What is the difference between the natural rate of unemployment and cyclical unemployment? How are these related to structural and frictional unemployment?

> What are some examples of changes in the economy that would cause the labor supply curve to shift? What might shift the labor demand curve? How do these changes affect the wage rate and the employment- population ratio?

> What is the definition of the unemployment rate?

> What explains the general rise in the employment- population ratio in the United States? By how much did the ratio decline around the last recession? How many jobs does this represent?

> Why is growth accounting useful?

> Suppose k, l, and m grow at constant rates given by

> The growth rate of output in the Romer model is

> Explain how nonrivalry leads to increasing returns in the two key production functions of the Romer model.

> Suppose a friend of yours decides to write a novel. Explain how ideas and objects are involved in this process. Where do nonrivalry and increasing returns play a role? What happens if the novel is sold at marginal cost?

> What is nonrivalry, and how does it lead to increasing returns? In your answer, what role does the standard replication argument play? Is national defense rivalrous or nonrivalrous?

> What is the principle of transition dynamics? Why does the Solow model lead to this principle, and why is it useful?

> The Solow model implies that differences in total factor productivity are even more important in explaining differences in income across countries than the production model of Chapter 4 suggested. Why?

> What is the solution of the Solow model for consumption per person in the steady state, c∗ ≡ C ∗/L∗? How does each parameter in the solution affect c*, and why?