Intermediate Macroeconomics: IAS 107: Spring 2011: U.C. Berkeley

Problem Set 8 Answers

(1) Quantity Theory of Money: Suppose that the rate of labor force growth is 1% per year, the efficiency of labor is growing at 2% per year, and the economy is on its steady state growth path. Suppose also that the trend is that the velocity of money is growing at 1% per year.

a. How fast should the Federal Reserve seek to make the growth rate of the money stock if it its inflation target is price stability--a 0% per year rate of growth of the CPI? 2%/year b. How fast should the Federal Reserve seek to make the growth rate of the money stock if it its inflation target is a 2% per year rate of growth of the CPI? 4%/year c. How fast should the Federal Reserve seek to make the growth rate of the money stock if it its inflation target is a 5% per year rate of growth of the CPI? 7%/year

(2) Economic Growth: With the ebbing of the computer revolution and the growing worry that an increasing share of economic activity in the future will be concentrated in high labor-cost low productivity-growth sectors, many economists fear that the rate of growth of the efficiency of labor in the United States will average 1.2 percent per year in the the future rather than the 2.0 percent per year that has been the average since 1900. Assume that the rate of labor force growth remains constant at 0.8 percent per year, that the depreciation rate were to remain constant at 3 percent per year, that the year-2010 efficiency of labor in the United States was $25,000 per year, that the diminishing-returns-to-capital parameter α in the production function is 1/2, and that the American savings rate (plus foreign capital invested in America) has averaged 20 percent per year.

a. What was the level of output per worker in 2010 if the United States was then on its steady-state balanced-growth path? 20/5.8*25000 = $86,200 b. If these fears that productivity growth will fall to 1% per year are justified, what is your forecast of the efficiency of labor in the United States in 2050? 25000*1.012^40 = $40,300 c. If these fears that productivity growth will fall to 1% per year are justified, what is your forecast of the level of GDP per worker in the United States in 2050 if the savings rate remains at 20 percent? 4*40300 = 161200 d. If these fears that productivity growth will fall to 1% per year are justified, what is your forecast of the level of GDP per worker in the United States in 2050 if tax cuts and large deficits lead the savings rate to average 15 percent? 120900 e. If these fears that productivity growth will fall to 1% per year are justified, what is your forecast of the level of GDP per worker in the United States in 2050 if wise fiscal policies and government-subsidized savings plans lead the savings rate to average 25 percent? 201500.

(3) National Income Accounting: a. What was the level of real GDP in 2005 dollars in 1970? $4,269.9 trillion b. What was the rate of inflation in the United States in 2000? 2.2%/year c. Explain whether or not, how, and why the following items are included in the calculation of GDP: (i) rent you pay on an apartment, (ii) purchase of a used textbook, (iii) purchase of a new tank by the Department of Defense, (iv) watching an advertisement on youtube. Yes: consumption of housing services. No: used good. Yes: government purchases. No: intermediate good.

(4) Depression Economics: In the simple income-expenditure model with real GDP Y equal to the sum of consumption spending by households C, investment spending by businesses I, government purchases G, and with net exports NX; with consumption spending C given by the equation: C = co + cyY(1-t); and with imports IM given by the equation: IM = imyY...

a. Suppose I = $1.7 trillion, G = $2 trillion, GX = $1.3 trillion, co = $3 trillion, cy = 0.85, the tax rate t=0, and imy = .10. What is GDP Y? Multiplier of 4; $32 trillion b. Suppose I = $1.7 trillion, G = $3.5 trillion, GX = $0.8 trillion, co = $3 trillion, cy = 0.65, the tax rate t=0, and imy = .15. What is GDP Y? Multiplier of 2; $18 trillion c. Suppose I = $2.3 trillion, G = $4 trillion, GX = $1.7 trillion, co = $3 trillion, cy = 0.6, the tax rate t=0.67, and imy = .2. What is GDP Y? Multiplier of 1; $11 trillion d. Suppose I = $1.5 trillion, G = $2.5 trillion, GX = $1.0 trillion, co = $3 trillion, cy = 0.67, the tax rate t=0, and imy = .0. What is GDP Y? Multiplier of 3; $24 trillion

(5) Phillips Curve: In the Phillips Curve framework in which π = E(π) + β(u* - u)—the inflation rate π equals the previously-expected inflation rate E(π) plus the Phillips Curve slope parameter β times the difference between the economy's natural rate of unemployment u* and the current rate of unemployment u...

a. If E(π) = 2% per year, u* = 6%, and u = 10%, what is the inflation rate π going to be if the Phillips Curve slope parameter β = 1/2? 0% b. If E(π) = 3% per year, u* = 4%, and u = 6%, what is the inflation rate π going to be if the Phillips Curve slope parameter β = 1/2? 2% c. If E(π) = 6% per year, u* = 7%, and u = 3%, what is the inflation rate π going to be if the Phillips Curve slope parameter β = 1/3? 7.33% d. If E(π) = 1% per year, u* = 7%, and u = 9%, what is the inflation rate π going to be if the Phillips Curve slope parameter β = 2/3? -.333% e. If E(π) = 4% per year, u* = 8%, and u = 5%, what is the inflation rate π going to be if the Phillips Curve slope parameter β = 1? 7%

(6) Monetary Policy: Suppose we have an economy with a natural rate of unemployment of 6%, current expected inflation of 4%, and a Phillips Curve slope parameter of 1/2. Suppose that the Federal Reserve has a target u0 for the unemployment rate and a target πt for the inflation rate.

a. If the target for the inflation rate is 4% and the target for the unemployment rate is 6%, what will inflation and unemployment be? 4% b. If the target for the inflation rate is 2% and the target for the unemployment rate is 6%, what will inflation and unemployment be if for each extra percentage point of inflation the Federal Reserve raises unemployment by an extra two percentage points? 3% c. If the target for the inflation rate is 2% and the target for the unemployment rate is 6%, what will inflation and unemployment be if for each extra percentage point of inflation the Federal Reserve raises unemployment by an extra half a percentage point? 3.6% d. If the target for the inflation rate is 2% and the target for the unemployment rate is 6%, what will inflation and unemployment be if for each extra percentage point of inflation the Federal Reserve raises unemployment by an extra percentage point? 3.33%

(7) Monetary Policy: Suppose we have an economy with a natural rate of unemployment of 6%, current expected inflation of 10%, and a Phillips Curve slope parameter of 1/2. Suppose that the Federal Reserve has a target u0 for the unemployment rate and a target πt for the inflation rate, and suppose that for each percentage point inflation is above its target level the Federal Reserve raises unemployment by an extra percentage point above its target level.

a. Suppose that from this year forward the Federal Reserve sets its target for the inflation rate at 3% and its target for the unemployment rate at 5%, what will inflation and unemployment be this year? 7.67% + .5(6-5)/1.5 = 8% b. Suppose expected inflation is adaptive in that each year's expected inflation is the previous year's actual inflation. What will inflation and unemployment be next year? 6.67% c. Suppose expected inflation is adaptive in that each year's expected inflation is the previous year's actual inflation. What will inflation and unemployment be two years from now? 5.78% d. Suppose expected inflation is adaptive in that each year's expected inflation is the previous year's actual inflation. What will inflation and unemployment be five years from now? 4.53% e. Suppose expected inflation is adaptive in that each year's expected inflation is the previous year's actual inflation. What will inflation and unemployment be ten years from now? 4.07%

(8) Monetary Policy: Suppose we have an economy with a natural rate of unemployment of 6%, and a Phillips Curve slope parameter of 1/2. Suppose that the Federal Reserve has a target u0 for the unemployment rate and a target πt for the inflation rate, and suppose that for each percentage point inflation is above its target level the Federal Reserve raises unemployment by an extra two percentage points above its target level.

a. If the Federal Reserve's target for the inflation rate is 2% and its target for the unemployment rate is 4%, what will the long run rate of inflation be? (6-4)/2+2 = 3% b. If the Federal Reserve's target for the inflation rate is 2% and its target for the unemployment rate is 6%, what will the long run rate of inflation be? (6-6)/2+2 = 2% c. If the Federal Reserve's target for the inflation rate is 4% and its target for the unemployment rate is 4%, what will the long run rate of inflation be? (6-4)/2+4=5% d. If the Federal Reserve's target for the inflation rate is 4% and its target for the unemployment rate is 8%, what will the long run rate of inflation be? (6-8)/2 + 4 = 3%

IAS 107: Intermediate Macro: April 26, 2011 Review of the Entire Course Lecture

20110426 IAS 107.pdf

Problem Set 9: Due April 28, 2011

20110118 IAS 107 pset9.pdf

IAS 107: Intermediate Macro: April 21, 2011 Current State of the Global Economy Lecture

20110421 IAS 107.pdf

IAS 107: April 18, 2011: Intermediate Macro Government Budgets Lecture

20110419 IAS 107.pdf

IAS 107: April 14, 2011 Government-Budgets Health-Care Financing Lecture

20110414 ias 107.pdf

IAS 107 Spring Take Home Assignment

The level of the unemployment rate in the United States was 8.9% in the first quarter of 2011, compared to a consensus estimate of the current natural rate of unemployment of 5.5%. The level of GDP in the United States in the first quarter of 2011 was $15 trillion at the prices of 2010. There were 140 million people at work in the United States in the first quarter of 2011. Savings and investment as a share of GDP in the first quarter of 2011 were only 12.2% of GDP, compared to a normal level for the United States over the past generation of 18% of GDP.

Suppose by some implausible cinematic plot device your consciousness were to be transferred at this moment into the body of Eugene Sperling, Assistant to the President for Economic Policy, in his small cramped office on the second floor of the West Wing of the White House (no, the TV show does not give a good picture of what the offices are like: they have to get the cameras into and out of the set, after all). President Obama calls and tells you that Federal Reserve Chair Ben Bernanke has just told him that the Federal Reserve Open Market Committee is unwilling to take any additional steps to boost employment and production.

President Obama asks if you would write up a two-page memo for his political staff telling them what the ideal macroeconomic fiscal policy over the next several years for him and the congress to undertake to deal with the aftermath of the recession would be if there were no political constraints on the federal government's budget. He tells you to keep it to at most 400 words--that is all that they will read. He tells you that most of the audience for this memo took courses like Econ 1 and IAS 107 in the past, but that they have forgotten all of it. You can use equations and graphs if you wish, but they had better be understandable to somebody who knows no economics. He also asks you to forecast what will happen to the growth of the American economy over the next 25 years if we do not recover from the downturn but, like Japan after 1990, remain in a depressed state with low investment at its current share of GDP for a generation. Be sure, he tells you, to outline both the risks from adopting the policy you recommend and the risks from not adopting the policy you recommend but continuing with business as usual.

You call across to the staff in the Eisenhower Executive Office Building next door, and they tell you that the depreciation rate on capital looks to be 4%/year, the future rate of growth of the efficiency of labor looks to be 1.75%/year, the rate of labor force growth looks to be 0.75%/year, and that the diminishing-returns parameter in the production function looks to be 0.5. They also tell you that the Okun's Law coefficient is about 2, that the tax rate on income is about 1/3, that the marginal propensity to consume looks to be 3/4, and that the marginal propensity to spend on imports looks to be about 1/6.

You debate telling President Obama that you are sorry but that you are not Eugene Sperling. But you decide that you would then be hauled off to the mental hospital, that whatever else happened Eugene Sperling would never get his job back, and that after the situation is resolved he would be really unhappy and would not thank you. You decide to carry out the assignment. You decide to do the assignment yourself--you do not dare talk to anybody because it will slip that you are not really Eugene Sperling.

Email your answer to this take-home assignment as a pdf file to brad.delong@gmail.com and dzahedi@berkeley.edu by 11 AM on Tuesday April 19. Include in the title of your email your name, your SID number, and the phrase "IAS 107 take home".

Government Budget Lecture I: April 12, 2011

20110412 ias 107.pdf

Problem Set 7 Answers

20110405 pset 7 with answers.doc

Slides for April 7, 2011 "Doing Problems" Lecture

20110407 ias 107.pdf