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MACROECONOMICS: PROBLEMS AND SOLUTIONS for B-level course Joakim Persson, fall 2009. The problems below are primarily intended for the B-level course in macroeconomics.
NOTE: Some questions on economic growth are harder and are only intended for the economics growth students.
Extra credit question: Below the B-level students find one problem for extra credit. The economic growth students find 2 problems that give extra credit if handed in. Topics: Based on chapters in the textbook by Mankiw 1.Introduction
- National income accounting
- Aggregate supply: Factor markets
- The labor market Appendix 8. Growth accounting (“Tillväxtbokföring”)
- Economic growth theory. Skim chapter 8.
- Money and inflation, excluding appendix. Skim chapter 19
- The Keynesian model for a closed economy in the long run = The classical model for a closed economy
- The Keynesian model for a small open economy in the long run = The classical model for a small open economy
- Introduction to the Keynesian model in the short and long run (for a closed economy) 10.-11. The Keynesian model for a closed economy with a horizontal SRAS-curve
- The Keynesian model for a small open economy with a horizontal SRAS-curve. Focus on floating exchange rates. Fixed exchange rates not included in the course.
- The Keynesian model in the short and long run with a positively-sloped SRAS-curve
- Stabilization policies. Skim appendix.
- Government debt
- EMU
- Consumption
- Investment Not included in course. Endogenous labor supply. Not relevant for B-macroeconomics, but relevant for Economics growth students.
- More questions on economic growth intended for economics growth students.
1. INTRODUCTION
Problem 1.3: Use the market model of supply and demand to explain how a fall in the price of frozen yogurt would affect the price of ice cream and the quantity of ice cream sold. In your explanation, identify the exogenous and endogenous variables.
Problem 1.4: Regarding the assumption of sticky prices in macroeconomics in the short run: How often does the price you pay for a haircut change?
2 NATIONAL INCOME ACCOUNTING
In Swedish: Nationalräkenskaper Problem 2.1: Fill in all numbers where there now are question marks (?) in the table. Private consumption (C) Privat konsumtion (C)?
Government purchases= government consumption and governemnt investment(G)
Offentlig konsumtion och offentliga investeringar (G)
Private investment (I) Privata investeringar, Inklusive lagerinvesteringar (I)
Trade balance (NX) Handelsbalansen (NX) 400 Labor income inclusive of income taxes and social security contributions
Arbetskraftskostnader inklusive sociala avgifter
Capital income Kapitalinkomster 400 Depreciation of capital Kapitalförslitning 100 Indirect taxes (VAT etc.) Indirekta skatter, t ex moms 200 Net factor incomes from abroad (NFI)
Faktorinkomster från utlandet, netto (NFI)
Net transfers from abroad (NFTr) Transfereringar från utlandet, netto (NFTr) 0 Government taxes (including indirect taxes)
Skatter, inklusive moms 350
Current Account Balance Bytesbalansen? Gross Domestic Product(GDP) Bruttonationalprodukten till Marknadspris (BNP)
Gross National Product(GNP) Bruttonationalinkomst till Marknadspris (BNI)
National saving Nationellt finansiellt sparande? Public saving Offentligt finansiellt sparande? Private saving Privat finansiellt sparande? NOTE: For a country and for the private and public sector: SAVING equals income minus consumption.
Problem 2.2: A farmer grows a bushel of wheat and sells it to a miller for 1 dollar. The miller turns the wheat into flour and then sells the flour to a baker for 3 dollars. The baker uses the flour to make bread and sells the bread to an engineer for 6 dollars. The engineer eats the bread. What is the value added by each person?
Problem 2.3: Suppose a woman marries her butler. After they are married, her husband continues to wait on her as before, and she continues to support him as before (but as a husband rather than as an employee): How does marriage affect GDP? How should it affect GDP?
3. THE SUPPLY SIDE OF THE ECONOMY: AGGREGATE PRODUCTION AND
FACTOR MARKETS
Problem 3.1: Use the neoclassical theory of distribution to predict the impact on the real wage and the real rental price of capital of each of the following events: A. A wave of immigration increases the labor force. B. An earthquake destroys some of the capital stock. C. A technological advance improves the production function.
Problem 3.2: If a 10-percent increase in both capital and labor causes output to increase by less than 10 percent, the production function is said to exhibit decreasing returns to scale. If it causes output to increase by more than 10 percent, the production function is said to exhibit increasing returns to scale. Why might a production function exhibit increasing or decreasing returns to scale?
Problem 3.3: Suppose that an economy’s production function is Cobb-Douglas with parameter alpha=0.3. One way to solve B.-D., assume numerical values, e.g.: Assume A=1, K=1, L0=1 and L1=1.1.
3.3A. What fractions of income do capital and labor receive? 3.3B. Suppose that immigration raises the labor force by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage? One way to solve B., assume A=1, K=1, L0=1 and L1=1.1. 3.3C. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage? 3.3D. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage?
Problem 3.4.: Empirically the trend in the real wage closely tracks the trend in labor productivity. Explain why?
Problem 3.5. A. Over the past century, the productivity of farmers has risen substantially because of technological progress. According to the neoclassical theory, what should have happened to their real wage? B. In what units is the real wage in part (a) measured? C. Over the same period, the productivity of barbers has remained constant. What should have happened to their real wage? D. In what units is the real wage in part (c) measured? E. Suppose workers can move freely between farmers and being barbers. What does this mobility imply for the wages of farmers and barbers? F. What do your previous answers imply for the price of haircuts relative to the price of food? G. Who benefits from technological progress in farming – farmers or barbers?
Problem 3.6.: (Harder) Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function is:
Y = K^ 1/ 3^ ⋅ L 1/ 3^ ⋅ H 1/ 3 Problem 3.6A. Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? Problem 3.6B. Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital? Problem 3.7C. What is the income share paid to labor? What is the income share paid to human capital? In the national income accounts of this economy, what share of total income
do you think workers would appear to receive? (Hint: Consider where the return to human capital shows up.) Problem 3.7D. An unskilled workers earns the marginal product of labor, whereas a skilled worker earns the marginal product of labor plus the marginal product of human capital. Using your answers to (a) and (b), find the ratio of the skilled wage to the unskilled wage. How does an increase in the amount of human capital affect this ratio? Explain. Problem 3.7E. Some people advocate government funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholarships help only those who are able to go to college. Do your answers to the preceding questions shed light on this debate?
6. THE LABOR MARKET
Problem 6.1: Suppose that students look for part-time jobs. On average it takes 2 weeks to find a part-time job, and the part-time job lasts on average 12 weeks. A. Calculate the rate of job finding per week and the rate of job separation per week B: What is the natural rate of unemployment for this population of students.
Problem 6.3: The residents of a certain dormitory have collected the following data: People who live in the dorm can be classified as either involved in a relationship or uninvolved. Among the involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 5 percent will enter into a relationship every month. What is the steady-state (“equilibrium”) fraction of residents who are uninvolved?
Problem 6.4: Suppose that Congress passes legislation making it more difficult for firms to fire workers. If this legislation reduces the rate of job separation without affecting the rate of job finding, how would the natural rate of unemployment change? Do you think that it is plausible that the legislation would not affect the rate of job finding? Why or why not?
Problem 6.5: Consider an economy with the following Cobb-Douglas production function: Y = K^ 1/ 3^ ⋅ L 2 / 3. The economy has 1000 units of capital and a labor force of 1000 workers. A. Derive the equation describing the labor demand in this economy as a function of the real wage and the capital stock. B. If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what is employment, output, and the total amount earned by workers? C. Assume that a minimum wage of 1 dollar is imposed by Congress. What happens to employment, output, and the total amount earned by workers. D. Did the minimum wage help the working class in this example?
Problem 6.6: Suppose that a country experiences a reduction in productivity (A); A.What happens to the labor demand curve? B.What is the effect on employment, unemployment and the real wage if we assume perfect competition? Assume that the labor supply curve is vertical. C.How would this change in productivity affect employment if unions prevent the real wage from falling?
7. ECONOMIC GROWTH THEORY: THE SOLOW MODEL
Problem 7.00: Show in the Solow-diagram and explain in words: A. The effect of an increased saving rate on the steady-state levels of production per worker (Y/L), capital per worker (K/L), and the real wage (W/P). B. The effect of a lower population growth rate on the steady-state levels of production per worker (Y/L), capital per worker (K/L), and the real wage (W/P). C. The effect of a better technology on the steady-state levels of production per worker (Y/L), capital per worker (K/L), and the real wage (W/P).
Problem 7.01A. In the long-run equilibrium, assume that the long-run population growth rate is 2 percent (that is, n=0.02), and the long-run growth rate of A is 0 percent (that is, g=0), calculate the long-run equilibrium growth rate of Y, (Y/L), K, (K/L), and the real wage (W/P). Problem 7.01B. In the long-run equilibrium, assume that the long-run population growth rate is 2 percent (that is, n=0.02), and the long-run growth rate of A is 2 percent (that is, g=0.02), calculate the long-run equilibrium growth rate of Y, (Y/L), K, (K/L), and the real wage (W/P).
Voluntary exercise to be handed for extra credit: 2 points on the exam. Deadline: XXXXX. Instruction: Please do the following exercise on economic growth in EXCEL. Your memo should be written In WORD; that is, tables should be written in WORD and figures From Excel should be pasted into a word document. Please do Attach your excel- sheet where all your calculation are performed. Send your memo + your EXCEL-sheet to joakim.persson@kau.se. To perform exercise read my handouts (and Mankiw). The names of the authors of the memo should be written in the memo.
Excel1. Transition to equilibrium 1a. Fill out the table below. You need probably to make 2 tables to make room for all the numbers. 1b. Plot y, K/L, the real wage, and the real return to capital against time in diagrams. Plot ln y against time in a diagram. 1c. Plot the growth rate of y against y in one diagram. Assume starting value: k(year=0)=2.00.
Assume also: A=1, s=0.25, δ = 0.1, α =0.5, and n=0.02. N(year=0)=
Year K y = k^ α c^ i δ ⋅ k ∆ ⋅ k ∆ ⋅ y k
k
y
∆ ⋅ y Real
wage
r Y K N
Note= r is real return to capital. r=MPK-depreciation rate. Briefly comment your results.
2A. Assume the parameter values above, and that the economy is in its steady state in period
- Assume that in period 1 the parameter A increases to 2. Make a new table showing the transition to the new steady state. 2b. Plot ln y against time. 2c. Plot the growth rate of y against y in one diagram. Briefly comment your results.
- What happens if s increases? Assume that the economy in period 0 is in its equilibrium (described by the parameter values in exercise 1), and that s increases to 0.35.
- Assume that the economy in period 0 is in its equilibrium (described by the parameter values in exercise 1), and that n increases to 0.04. Make a new table showing the transition to the new steady state. Compare the old equilibrium with the new equilibrium with respect to Y/L, K/L, the real wage, the real return to capital (r), K, and Y.
Quantitative questions ch. 7 of Mankiw, which are relevant for B-macroeconomics, and economic growth course:
Problem 7.1: Country A and B has the production function:
Y = F K L ( , ) = K^ 1/ 2^ ⋅ L 1/ 2 A. Does this production function have constant returns to scale? B. What is the per-worker production function, Y/L=f(K/L) C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year, and country B saves 20 percent of output each year. Find the steady state level of capital per worker, the steady-state level of income per worker and consumption per worker. D. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is gross investment minus depreciation, calculate capital stock per worker, income per worker, and consumption per worker over time. How many years will it be before consumption per worker in Country B is higher than the level of consumption per worker in country A.
Problem 7.2: In the discussion of German and Japanese postwar growth, the text describes what happens when part of the capital stock is destroyed in a war. By contrast, suppose that a war does not affect the capital stock, but that casualties reduce the labor force. A. What is the immediate impact on total output and on output per person? B. Assuming that the saving rate is unchanged and that the economy was in a steady state before the war, what happens subsequently to output per worker in the postwar economy? Is the growth rate of output per worker after the war smaller or greater than normal?
Problem 7.3: Consider an economy described by the production function:
Y = F K L ( , ) = K^ 0.3^ ⋅ L 0. A. What is the per-worker production function? B. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate. C. Assume that the depreciation rate is 10 percent per year. Make a table showing steady- state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, and 30 percent and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker? D. Use calculus to find the marginal product of capital. Add to your table the marginal product of capital net of depreciation for each of the saving rates.
4. MONEY AND INFLATION
Problem 4.1: What are the 3 functions of money? Which of the functions do the following items satisfy? A. A credit card. B. A painting by Rembrant. C. A subway token. Problem 4.2: In the country of Wiknam, the velocity of money is constant. Real GDP grows by 5 percent per year, the money stock grows by 14 percent per year, and the nominal interest rate is 11 percent? What is the real interest rate? Problem 4.5. During the World War II, both Germany and England had plans for a paper weapon: they each printed the other’s currency, with the intention of dropping large quantities by airplane. Why might this have been an effective weapon. Problem 4.6: What happens to a debt when there is high inflation? Make a distinction between expected and unexpected inflation.
4. MONEY AND INFLATION Answer: Problem 4.1:A. A credit card is a medium of exchange. B. A painting is a store of value. C. A subway token, within the subway system, satisfies all 3 functions of money, which are store of value, unit of account, and medium of exchange.
Answer:Problem 4.2: Use the quantity equation to calculate the inflation rate. Using this rate of inflation and the Fischer equation yields a real interest rate of 2 percent.
Answer: Problem 4.5. Paper weapon might create inflation, and even hyperinflation.
Answer: Problem 4.6: If the debt is in nominal terms (which is the usual case; that is, in dollars), inflation reduces the real value of. Inflation has to be unexpected. If high inflation is expected, banks demand a higher (fixed) nominal interest rate. So if you are debtor and have a fixed nominal interest rate and the actual inflation rate is higher than the expected one, you are happy. This is because your actual real interest rate on your loan becomes lower than the expected real interest rate. If you have a floating interest rate, a higher actual inflation rate should not matter as the nominal interest rate tends to adjust
Problem 4.7: Some economic historians have noted that during the period of the gold standard (which was a period during which money and gold are in a fixed ratio), gold discoveries were most likely to occur after a long deflation.
Answer:Problem 4.7: A deflation is a fall in the general price level, which is the same as a rise in the value of money. Under a gold standard, a rise in the value of money is a rise in the value of gold because money and gold are in a fixed ratio. Therefore, after a deflation, an ounce of gold buys more goods and services. This creates an incentive to look for new gold deposits and, thus, more gold is found after a deflation.
3. THE CLASSICAL MODEL FOR THE CLOSED ECONOMY= THE KEYNESIAN
MODEL FOR A CLOSED ECONOMY IN THE LONG RUN
Problem 3.7: The government raises taxes by 100 billions USD. If the marginal propensity to consume is 0.6, what happens to public,private, and national saving and to investment? Do they rise or fall? By what amounts?
Problem 3.8: Suppose that an increase in consumer confidence raises consumers’ expectations about their future income and thus increases the amount they want to consume today. This might be interpreted as an upward shift in the consumption function. How does this shift affect investment and the interest rate.
Problem 3.9 Consider an economy described by the following equations: Y=C+I+G, Y=5000, G=1000, T=1000, C=250+0.75(Y-T), I=1000-50r. A. In this economy, compute private saving, public saving, and national saving. B. Find the equilibrium interest rate. C. Now suppose that G rises to 1250. Compute private saving, public saving, and national saving. D. Find the new equilibrium interest rate. E. Now suppose T decreases to 750 (and G=1000). Compute private, public and national saving, and find the new equilibrium interest rate.
Problem 3.10: Suppose that the government increases taxes and government purchases by equal amounts. What happens to the interest rate and investment in response to this balanced budget change? Does your answer depend on the marginal propensity to consume?
Problem 3.11: When the government subsidizes investment, such as with an investment tax credit, the subsidy often applies to only some types of investment. Suppose that there are two types of investment in the economy: business investment and residential investment. And suppose that the government institutes an investment tax credit only for business investment. A. How does this policy affect the demand curve for business investment? The demand curve for residential investment. B. Draw the economy’s supply and demand for loanable funds. How does this policy affect the supply and demand for loanable funds? What happens to the equilibrium interest rate? C. Compare the old and the new equilibrium. How does this policy affect the total quantity of investment? The quantity of business investment? The quantity of residential investment?
Problem 3.12: If consumption depended on the interest rate, how would that affect the conclusions reached in this chapter about the effects of fiscal policy?
your friend right or wrong? Given that total inflation over this period was 25 percent in the US and 100 percent in Mexico, has it become more or less expensive to travel in Mexico?
Problem 5.10: The nominal interest rate is 12 percent per year in Canada and 8 percent per year in the USA. Suppose that the real interest rate is the same in these two countries, and that purchasing-power parity holds. A. Use the Fischer equation (discussed in chapter 4.) what can you say about expected inflation in Canada and in the USA? B. What can you say about the expected change in the exchange rate between the Canadian dollar and the US dollar? C. A friend proposes a get-rich-quick scheme: borrow from a US bank at 8 percent, deposit the money in a Canadian bank at 12 percent, and make a 4 percent profit. What’s wrong with this scheme?
9. INTRODUCTION TO THE KEYNESIAN MODEL IN THE SHORT AND LONG
RUND FOR THE CLOSED ECONOMY
We use the regular AD-curve: AD= C(Y-T)+I(real interest rate)+G to answer the questions. In other words, we use the AD-curve from Chapter 3.
Problem 10.5. Suppose that the money demand function is: 100
d M Y r P
, where r is
the nominal interest rate=real interest rate in percent. Let Y=1000, and M=1000, and P=2. A. Graph the supply and demand for real money balances. B. What is the equilibrium interest rate? C. Assume that the price level is fixed. What happens to the equilibrium interest rate if the supply of money is raised from 1000 to 1200? D. If the central bank wishes to raise the interest rate to 7 percent, what nominal money supply (M) should it choose?
Problem 9.1 (modified): Suppose that banks start paying interest on current accounts so that holding money becomes more attractive. Recall that the money stock is the sum of currency and demand deposits, including current accounts. A. How is real money demand affected? What happens to the interest on interest-bearing government bonds? B. What happens to the velocity of money? C. If the central bank keeps the money supply constant, what will happen to output and prices in the short and in the long run? D. Should the central bank keep the central bank constant in response to this change in behavior of banks?
Problem 9.2: Suppose that the central bank reduces the nominal money supply by 5 percent. A. What happens to the aggregate demand curve? B. What happens to the level of output and the price level in the short run and in the long run? C. What happens to the real interest rate in the short run and in the long run? (Hint: Use the model of the real interest rate in chapter 3 to see what happens when output changes.)
Problem 9.3: Suppose that central bank A cares only about keeping the price level stable, and central bank B cares only about keeping output and employment at their natural levels. Explain how each central bank would respond to each of the following: A. An exogenous decrease in the velocity of money; that is, an increase in Real money demand at given levels of the interest rate and income. B. B. An exogenous increase in the price of oil.
10. THE SIMPLE KEYNESIAN MODEL FOR THE SHORT RUN FOR A
CLOSED ECONOMY
- Use the simple Keynesian Model to predict the impact of a. An increase in government purchases. b. An increase in taxes, c. An equal increase government purchases and taxes.
- In the simple Keynesian model, assume that the consumption function is given by C = 200 + 0.75 (Y – T).
Planned investment is 100, government purchases and taxes are both 100. a. Graph planned expenditure as a function of income. b. What is the equilibrium level of income? c. If government purchases increase to 125, what is the new equilibrium income? d. What level of government purchases is needed to achieve an income of 1,600?
- Although our basic version of the simple Keynesian model assumes that taxes Are fixed amount, in many countries (including the United States) taxes depend on income. Let’s represent the tax system by writing tax revenue as T = T + t Y ⋅ Where T and t are parameters of the tax code. The parameter t is the marginal and proportional tax rate: if income rises by $1, taxes rise by t*$1. a. How does this tax system change the way consumption responds to changes in GDP? b. In the simple Keynesian model, how does this tax system alter the government- purchases multiplier?
- Consider the impact of an increase in thriftiness in the simpel Keynesian model. Suppose the consumption function is C = C + c ⋅ ( Y − T ) Where C is a parameter called autonomous consumption and c is the marginal propensity to consume. a. What happens to equilibrium income when the society becomes more thrifty, as represented by a decline C? b. What happens to equilibrium saving? c. Why do you suppose this result is called the paradox of thrift? d. Does this paradox arise in the classical model for a closed economy? Why or why not?
- Suppose that the government wants to raise investment but keep output constant. In the IS-LM model, what mix of monetary and fiscal policy will achieve this goal? In the early 1980s, the U.S government cut taxes and ran a budget deficit while the Fed pursued a tight monetary policy. What effect should this policy mix have?
- Use the IS-LM model to describe the short-run and long-run effects of the following changes on national income, the interest rate, the price level, consumption, investment, and real money balances, a. An increase in the money supply. b. An increase in government purchases. c. An increase in taxes.
- The Fed is considering two alternatives monetary policies:
- holding the money supply constant and letting the interest rate adjust, or
- adjusting the money supply to hold the interest rate constant.
In the IS-LM model, which policy will better stabilize output under the following conditions? a. All shocks to the economy arise from exogenous changes in the demands for goods and service. b. All shocks to the economy arise from exogenous changes in the demands for money.
12. THE KEYNESIAN MODEL FOR THE SHORT RUN FOR A SMALL OPEN
ECONOMY with a horizontal SRAS-curve. (The Mundell-Fleming model) Student should focus on floating exchange rates.
1.Use the Mundell-Fleming model to predict what would happen to aggregate income, the exchange rate, and the trade balance under both floating and fixed exchange rates in response to each of the following shocks: A. A fall in consumer confidence about the future induces consumers to spend less and save more. B. The introduction of a stylish line of Toyotas makes some consumers prefer foreign cars over domestic cars. C. The introduction of automatic teller machines reduces the real demand for money.
2.A small open economy with a floating exchange rate is in recession with balanced trade. If policymakers want to reach full employment while maintaining balanced trade, what combination of monetary and fiscal policy should they choose?
- The Mundell-Fleming model takes the world interest rate r * as an exogenous variable. Let’s consider what happens when this variable changes? A. What might cause the world interest rate to rise? B. In the Mundell-Fleming model with a floating exchange rate, what happens to aggregate income, the exchange rate, and the trade balance when the world interest rate rises?
- Business executives and policymakers are often concerned about the “competitiveness” of American industry (the ability of U.S. industries to sell their goods profitably in world markets). a. How would a change in the exchange rate affect competitiveness? b. Suppose you wanted to make domestic industries more competitive but did not want to alter aggregate income. According to the Mundell-Fleming model, what combination of monetary and fiscal policies should you pursue?
- Suppose that higher income implies higher imports and thus lower net exports.That is, the net exports function is: NX=NX(e,Y). Examine the effects in a small open economy of a fiscal expansion on income and trade balance under a floating exchange rate.
- Suppose that the price level relevant for money demand includes the price of imported goods and that the price of imported goods depends on the exchange rate. That is, the money
market is described by M/P=L(r,Y) where P = λ⋅ Pd + (1 − λ) ⋅ Pf / e
The parameter λ is the share of domestic goods in the price index P. Assume that the price of
domestic goods Pd and the price of foreign goods measured in foreign currency Pf are fixed. B.What is the effect of expansionary fiscal policy under floating exchange rates in this model? Explain. Contrast with the standard Mundell-Fleming model.
- Suppose that an economy has the Philips curve 1 0.5(^ )
π π u un
and that the natural rate of unemployment is given by an average of the past two years’ unemployment: 0.5( 1 2 ) u n u u = (^) − − − a. Why might the natural rate of unemployment depend on recent unemployment (as is assumed in the preceding equation)? b. Suppose that the Fed follows a policy to reduce permanently the inflation rate by 1 percentage point. What effect would that policy have on unemployment rate over time? c. What is the sacrifice ratio in this economy? Explain. d. What do these equations imply about the short-run and long-run tradeoffs between inflations and unemployment?
- If higher taxes cause people to want to work less and lower taxes cause people to want to work more. Consider this in the AS/AD-model: a. If this view is correct, how does a tax cut affect the natural rate of output? b. How does a tax cut affect the aggregate demand curve? The LRAS- and SRAS-curves? c. What is the short-run impact of a tax cut on output and the price level? How does your answer differ from the case without the labor-supply effect? d. What is the long-run impact of a tax cut on output and the price level? How does your answer differ from the case without the labor-supply effect?
14. STABILIZATION POLICIES
1.Suppose that the trade off between unemployment and inflations is determined by the Philips curve:
u = un^ − α π ( −π e )
Where u denotes the unemployment rate u n un the natural rate, π the rate of inflation, and
π^ e the expected rate of inflation. In addition, suppose that the Democratic party always
follows a policy of high money growth and the Republican party always follows a policy of low money growth. What “political business cycle” pattern of inflation and unemployment would you predict under the following conditions? a. Every four years, one of the parties takes control based on a random flip of a coin. [ Hint: What will expected inflation be prior to the election?] b. The two parties take turns.
- When cities pass laws limiting the rent landlords can charge on apartments, the laws usually apply to existing buildings and exempt any buildings not yet built. Advocates of rent control does not argue that this exemption ensures that rent control does not discourage the construction of new housing. Evaluate this argument in light of the time inconsistency problem.
15. GOVERNMENT DEBT
- Assume that the government sell public telecom company to the private sector. Does such actions by the government reduce the national debt as it is now measure? How would your answer change if the U.S government adopted capital budgeting? Do you think these actions represent a true reduction in the government’s indebtedness?
- Explaining and evaluating the Ricardian view of government debt.
- The social Security system levies a tax on workers and pays benefits to the elderly. Suppose that congress increases both the tax and and the benefits. For simplicity, assume that the congress announces that the increases will last for one year only. a. How do you suppose this change would affect the economy? ( Hint: Think about the marginal propensities to consume of the young and the old.) b. Does your answer depend on whether generations are altruistically linked?
- Some economists have proposed the rule that the cyclically adjusted budget deficit always be balanced. Compare this proposal to a strict balanced budget rule. Which is preferable? What problems do you see with the rule requiring a balanced cyclically adjusted budget?
17. CONSUMPTION
- Use the life-cycle model of consumption to discuss a change in the interest rate for a consumer who is a borrower in the first period. Discuss the income and substitution effects on consumption in both periods.
- Jack an Jill both obey the two-period model of consumption. Jack earns $100 in the first period and $100 in the second period. Jill earns nothing in the first period and $210 in the second period. Both of them can borrow or lend at the interest rate. r? a. You observe both Jack and Jill consuming $100 in the first period and $100 in the second period. What is the interest rate r? b. Suppose the interest rate increases. What will happen to Jack’s consumption in the first period? Is Jack better of or worse off than before the interest rate rise? c. What will happen to Jill’s consumption in the first period when the interest rate increases? Is Jill better of or worse of than before the interest rate increases?
- Explain whether borrowing constraints increase or decrease the potency of fiscal policy to influence aggregate demand in each of the following to cases: a. A temporary tax cut. b. An announced future fax cut.
- Demographers predict that the fraction of the population that is elderly will increase over the next 20 years. What does the life-cycle model predict for the influence of this demographic change on the national saving rate?
- One study found that the elderly who do not have children dissave at about the same rate as the elderly who do not have children. What might this finding imply about the reason the elderly do not dissave as much as the life-cycle model predicts?
