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Conceptual 1. Using the aggregate supply–aggregate demand model, explain how output and prices are determined. Will output vary or stay fixed in the long run? Suppose the aggregate demand curve were to remain fixed: what can we infer about the behavior of prices over time?

Technical 1. Suppose that actual output is \$120 billion and potential (full-employment) output is \$156 billion. What is an output gap in this hypothetical economy? Based on your estimate of the output gap, would you expect the unemployment level to be higher or lower than usual?

Empirical 1. In this exercise, we will calculate by how much U.S. per capita real income has increased between the year you were born and today. Go to http://fred.stlouisfed.org. To find real GDP data, click on “Categories” under “National Accounts,” select “National Income & Product Accounts,” then “GDP/GNP”. Then search “GDPCA.” For population data, go back to the FRED II home page and click on “Categories” under “Population, Employment, & Labor Markets,” select “Population,” then search “Employment & Population.” Under “Categories,” select “Population,” “POP.” Use the information provided at these two places to fill in columns 1 and 2 in the table below. Note that you may need to transform the series into annual averages; to do this, take the average of the monthly data in the desired years. You can calculate real GDP per capita by dividing real GDP by population. After filling in columns 1 and 2, you can find out how much per capita income is higher today compared to the year you were born (Hint: Simply divide the value in column 1 by the value in column 2). Variable Today’s Year 1 Your Birth Year 2 Real GDP Population Real GDP per capita = real GDP/population

KEY TERMS government purchases gross domestic product (GDP) gross investment gross national income (GNI) gross national product (GNP) gross private domestic investment human capital inflation intermediate goods investment national income accounting identity net domestic product (NDP) net exports net investment nominal GDP nominal interest rate personal consumption expenditure deflator (PCE) producer price index (PPI) production function real GDP real interest rate saving trade deficit trade surplus transfer payments unemployment rate value added PROBLEMS

Conceptual 1. What would happen to the measure of GDP if the government hired unemployed workers, who had been receiving amount \$TR in unemployment benefits, as government employees and now paid them the same amount to do nothing? Explain.

2. In the national income accounts, what is the difference between

a. A firm’s buying an auto for an executive and the firm’s paying the executive additional income to buy the automobile herself?

b. Your hiring your spouse (who takes care of the house) rather than having him or her do the work without pay?

c. Your deciding to buy an American car rather than a German car? dor90638_ch02_022-053.indd 50 22/07/17 12:27 PM chapter 2•National Income Accounting 51

3. What is the difference between GDP and GNP? Is one a better measure of income/output than the other? Why?

4. What is NDP? Is it a better or worse measure of output than GDP? Explain.

5. Increases in real GDP are often interpreted as increases in welfare. What are some problems with this interpretation? Which do you think is the biggest problem with it, and why?

6. The CPI and PPI are both measures of the price level. How are they different, and when might you prefer one of these measures over the other?

7. What is the GDP deflator, and how does it differ from the consumer and producer price indexes? Under what circumstances might it be a more useful measure of price than the CPI and PPI?

8. If you woke up in the morning and found that nominal GDP had doubled overnight, what statistic would you need to check before you began to celebrate? Why?

9. Suppose you make a loan of \$100 that will be repaid to you in 1 year. If the loan is denominated in terms of a nominal interest rate, are you happy or sad if inflation is higher than expected during the year? What if the loan had instead been denominated in terms of a real return?

Technical

1. In the text, we calculated the change in real GDP in the hypothetical economy of Table 2-3, using the prices of 2005. Calculate the change in real GDP between 2005 and 2012 using the same data but the prices of 2012. Your answer should demonstrate that the prices that are used to calculate real GDP do affect the calculated growth rate, but typically not by very much.

2. Show from national income accounting that a. An increase in taxes (while transfers remain constant) must imply a change in net exports, government purchases, or the saving-investment balance. b. An increase in disposable personal income must imply an increase in consumption or an increase in saving. c. An increase in both consumption and saving must imply an increase in disposable income. [For both parts b and c assume there are no interest payments by households or transfer payments to foreigners.]

3. The following is information from the national income accounts for a hypothetical country: GDP \$6,000 Gross investment 800 Net investment 200 Consumption 4,000 Government purchases of goods and services 1,100 Government budget surplus 30 What is a. NDP? d. Disposable personal income? b. Net exports? e. Personal saving? c. Government taxes minus transfers? dor90638_ch02_022-053.indd 51 22/07/17 12:27 PM 52 Macroeconomics

4. Assume that GDP is \$6,000, personal disposable income is \$5,100, and the government budget deficit is \$200. Consumption is \$3,800, and the trade deficit is \$100. a. How large is saving (S)? b. How large is investment (I)? c. How large is government spending (G)?

5. If a country’s labor is paid a total of \$6 billion, its capital is paid a total of \$2 billion, and profits are zero, what is the level of output? (Hint: See equation (2).)

6. Consider an economy that consists only of those who bake bread and those who produce its ingredients. Suppose that this economy’s production is as follows: 1 million loaves of bread (sold at \$2 each); 1.2 million pounds of flour (sold at \$1 per pound); and 100,000 pounds each of yeast, sugar, and salt (all sold at \$1 per pound). The flour, yeast, sugar, and salt are sold only to bakers, who use them exclusively for the purpose of making bread. a. What is the value of output in this economy (i.e., nominal GDP)? b. How much value is added to the flour, yeast, sugar, and salt when the bakers turn them into bread?

7. Suppose a country’s CPI increased from 2.1 to 2.3 in the course of 1 year. Use this fact to compute the rate of inflation for that year. Why might the CPI overstate the rate of inflation?

8. Suppose you buy a \$100 government bond that is due next year. How much nominal interest will you receive if inflation is 4 percent over the year and the bond promises a real return of 3 percent?

Empirical

1. Section 2.1 in this chapter deals with the relationship between the different components included in the National Income and Product Accounts (NIPA for short). Go to www.bea.gov. Click on the heading “National,” then click on “Interactive Tables: GDP and the National Income and Product Account (NIPA) Historical Tables” and then “Begin using the data . . .” Select “Section 1-Domestic Product and Income.” Open Table 1.7.5, which should be titled “Relation of Gross Domestic Product, Gross National Product, Net National Product, National Income, and Personal Income (A) (Q).” Use the information provided there to fill in columns 1, 2, 3, and 5 in the following table, and calculate GNP and NNP based on the formulas given in the second row of the table. You may have to first adjust the “First Year” to 2010 and the “Series” to Annual under “Data Table Options.” Do the values you find correspond to the numbers reported at www.bea.gov? INCOME INCOME DEPRECIATION RECEIPTS payment GNP (Consumption) NNP GDP From Row To Row 4 = 1 + 2 − 3 of Fixed Capital NNP 6 = 4 − 5 1 2 3 5 2010 2011 2012

2. How much was U.S. real GDP growth in the year 2012? What about the growth rate of U.S. population? First, check out “Gross Domestic Product (GDP) and Components” at http://fred.stlouisfed.org. Click on “Categories,” under “National Accounts” select “National dor90638_ch02_022-053.indd 52 22/07/17 12:27 PM chapter 2•National Income Accounting 53 Income & Product Accounts,” then “GDP/GNP.” Search “GDPCA,” title “Real Gross Domestic Product.” Click on “Download Data” and change the units to “Percent Change,” then download the series. For population data, go to www.census.gov; then select “Estimates” under the “People” category. Click on “Current Estimates Data,” and then under “Nation” and “Total Population,” click on “V2012.” Select “Population Change” and click on the data set that is NOT the cumulative estimate. The data set shows the annual population change in the United States between 2011-2012. Using these two pieces of information, what can you infer about the evolution of U.S. per capita real GDP in 2012?

PROBLEMS

Conceptual

1. What information does a production function provide?

2. Can the Solow growth model help to explain the phenomenon of convergence?

3. Consider a production function that omits the stock of natural resources. When, if ever, will this omission have serious consequences?

4. If, in the context of a standard production function, Y = F(K, N ), where K represents physical capital and N represents raw labor, we were to interpret the Solow residual

(ΔA/A) as “technological progress,” we would be in error. What, besides technological progress, would this residual catch? How could you expand the model to eliminate this problem?

5. Figure 3-4 is a basic illustration of the Solow growth model. Interpret it, being careful to explain the meaning of the saving and investment requirement lines. Why does the steady state occur where they cross?

6. What factors determine the growth rate of steady-state per capita output? Are there other factors that could affect the growth rate of output in the short run?

7. Since the mid-1990s, the U.S. economy has undergone a surge in labor productivity, given by Y/N. What are some possible explanations given by equation (2) for this surge?

Technical

1. In a simple scenario with only two factors of production, suppose that capital’s share of income is .4 and labor’s share is .6 and that annual growth rates of capital and labor are 6 and 2 percent, respectively. Assume there is no technical change.

a. At what rate does output grow?

b. How long will it take for output to double?

c. Now suppose technology grows at a rate of 2 percent. Recalculate your answers to parts a and b.

2. Suppose output is growing at 3 percent per year and capital’s and labor’s shares of income are .3 and .7, respectively.

a. If both labor and capital grow at 1 percent per year, what would the growth rate of total factor productivity have to be?

b. What if both the labor and the capital stocks are fixed?

3. Suppose again that capital’s and labor’s shares of income are .3 and .7, respectively.

a. What would be the effect (on output) of increasing the capital stock by 10 percent?

b. What would be the effect of increasing the pool of labor by 10 percent?

c. If the increase in labor is due entirely to population growth, will the resulting increase in output have an effect on people’s welfare?

d. What if the increase in labor is due, instead, to an influx of women into the workplace?

4. Suppose an earthquake destroys one-quarter of the capital stock. Discuss the adjustment process of the economy, and using Figure 3-5, show what happens to growth in the short run and in the long run.

5. Suppose there is an increase in the population growth rate.

a. Show graphically how this affects the growth rate of both output per capita and total output in the short and the long run. (Hint: Use a diagram like Figure 3-5.)dor90638_ch03_054-078.indd 75 18/07/17 11:59 AM 76 Macroeconomics

b. Chart the time paths of per capita income and the per capita capital stock following this

change. (Hint: Use a diagram like Figure 3-6.)

6. Consider a production function of the form Y = AF(K, N, Z), where Z is a measure of natural resources used in production. Assume this production function has constant returns to scale and diminishing returns in each factor.

a. What will happen to output per head if capital and labor both grow but Z is fixed?

b. Reconsider part a, but add technical progress (growth in A).

c. In the 1970s there were fears that we were running out of natural resources and that this would limit growth. Discuss this view using your answers to parts a and b.

7. Consider the following production function: Y = K.5(AN).5, where both the population and the pool of labor are growing at a rate n = .07, the capital stock is depreciating at a rate d = .03, and A is normalized to 1.

a. What are capital’s and labor’s shares of income?

b. What is the form of this production function?

c. Find the steady-state values of k and y when s = .20.

d. At what rate is per capita output growing at the steady state? At what rate is total output growing? What if total factor productivity is increasing at a rate of 2 percent per year (g = .02)?

8. Suppose the level of technology is constant. Then it jumps to a new, higher constant level.

a. How does this technological jump affect output per head, holding the capital-labor ratio constant?

b. Show the new steady-state equilibrium. What has happened to per capita saving and the capital-labor ratio? What happens to output per capita?

c. Chart the time path of the adjustment to the new steady state. Does the investment ratio rise during transition? If so, is this effect temporary?

9.* For a Cobb-Douglas production function Y = AKθN(1 − θ), verify that 1 − θ is labor’s share of income. [Hint: Labor’s share of income is the piece of income that results from that labor (MPL × N) divided by total income.]

10. Consider an economy in which production is characterized by the neoclassical function Y = K.5N.5. Suppose, again, that it has a saving rate of .1, a population growth rate of .02, and an average depreciation rate of .03.

a. Write this production function in per capita form, and find the steady-state values of k and y.

b. At the steady-state value of k, is there more or less capital than at the golden-rule level?

c. Determine what saving rate would yield the golden-rule level of capital in this model.

d. In the context of this neoclassical growth model, can a country have too much saving?

Empirical

1. Go to http://fred.stlouisfed.org and download the data for the U.S. population and total employment in educational and health services over the period 2002–2012. To do so, click on “Categories,” under “Population, Employment, & Labor Markets,” select “Population” for population data (“POP”) and “Current Employment Statistics (Establishment Survey)” for educational and health services data (“USEHS”). Once you have downloaded the data into a *An asterisk denotes a more difficult problem. spreadsheet, calculate the average growth rate of U.S. population and total employment in educational services in the period 2002–2012. Everything else being constant, what could you infer about the average quality of U.S. workers? Would this have any implications on the perspectives for future growth in the United States?

2. Go to http://fred.stlouisfed.org and click on “Categories,” under “Population, Employment, & Labor Markets,” select “Current Employment Statistics (Establishment Survey),” then “Information” (“USINFO”). Using the provided graphing possibilities, take a look at the evolution of the number of employees for the information services industries during the last two decades. What event can be used to explain the increase in the employment of information technology workers during the 1990s? What about the decrease in employment during the 2000s?