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8. Economic Growth II: Technology, Empirics, and Policy. Introduction. In the Solow model of Chapter 7, the production technology is held constant. income per capita is constant in the steady state. Neither point is true in the real world:

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### Economic Growth II:Technology, Empirics, and Policy

In the Solow model of Chapter 7,

• the production technology is held constant.

• income per capita is constant in the steady state.

Neither point is true in the real world:

• 1904-2004: U.S. real GDP per person grew by a factor of 7.6, or 2% per year.

• examples of technological progress abound(see next slide).

CHAPTER 8 Economic Growth II

• A new variable: E = labor efficiency

• Assume: Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g:

CHAPTER 8 Economic Growth II

• We now write the production function as:

• where LE = the number of effective workers.

• Increases in labor efficiency have the same effect on output as increases in the labor force.

CHAPTER 8 Economic Growth II

• Notation:

y = Y/LE = output per effective worker

k = K/LE = capital per effective worker

• Production function per effective worker:y = f(k)

• Saving and investment per effective worker:sy = sf(k)

CHAPTER 8 Economic Growth II

( +n +g)k = break-even investment: the amount of investment necessary to keep k constant.

Consists of:

• k to replace depreciating capital

• nk to provide capital for new workers

• gk to provide capital for the new “effective” workers created by technological progress

CHAPTER 8 Economic Growth II

(+n+g)k

sf(k)

k*

Capital per worker, k

Technological progress in the Solow model

k=s f(k)  ( +n +g)k

CHAPTER 8 Economic Growth II

Symbol

Steady-state growth rates in the Solow model with tech. progress

Capital per effective worker

k =K/(LE )

0

Output per effective worker

y =Y/(LE )

0

Output per worker

(Y/L) = yE

g

Total output

Y = yEL

n + g

CHAPTER 8 Economic Growth II

To find the Golden Rule capital stock, express c* in terms of k*:

c* = y*i*

= f(k*) ( +n +g)k*

c* is maximized when MPK = +n+g

or equivalently, MPK = n+g

In the Golden Rule steady state, the marginal product of capital net of depreciation equals the pop. growth rate plus the rate of tech progress.

CHAPTER 8 Economic Growth II

Growth empirics: Balanced growth

• Solow model’s steady state exhibits balanced growth - many variables grow at the same rate.

• Solow model predicts Y/L and K/L grow at the same rate (g), so K/Y should be constant.

• This is true in the real world.

• Solow model predicts real wage grows at same rate as Y/L, while real rental price is constant.

• This is also true in the real world.

CHAPTER 8 Economic Growth II

• Solow model predicts that, other things equal, “poor” countries (with lower Y/L and K/L) should grow faster than “rich” ones.

• If true, then the income gap between rich & poor countries would shrink over time, causing living standards to “converge.”

• In real world, many poor countries do NOT grow faster than rich ones. Does this mean the Solow model fails?

CHAPTER 8 Economic Growth II

• Solow model predicts that, other things equal, “poor” countries (with lower Y/L and K/L) should grow faster than “rich” ones.

• No, because “other things” aren’t equal.

• In samples of countries with similar savings & pop. growth rates, income gaps shrink about 2% per year.

• In larger samples, after controlling for differences in saving, pop. growth, and human capital, incomes converge by about 2% per year.

CHAPTER 8 Economic Growth II

• What the Solow model really predicts is conditional convergence - countries converge to their own steady states, which are determined by saving, population growth, and education.

• This prediction comes true in the real world.

CHAPTER 8 Economic Growth II

• Differences in income per capita among countries can be due to differences in

1. capital – physical or human – per worker

2. the efficiency of production (the height of the production function)

• Studies:

• both factors are important.

• the two factors are correlated: countries with higher physical or human capital per worker also tend to have higher production efficiency.

CHAPTER 8 Economic Growth II

• Possible explanations for the correlation between capital per worker and production efficiency:

• Production efficiency encourages capital accumulation.

• Capital accumulation has externalities that raise efficiency.

• A third, unknown variable causes capital accumulation and efficiency to be higher in some countries than others.

CHAPTER 8 Economic Growth II

Policy issues: efficiencyEvaluating the rate of saving

To estimate (MPK ), use three facts about the U.S. economy:

1. k = 2.5 yThe capital stock is about 2.5 times one year’s GDP.

2.  k = 0.1 yAbout 10% of GDP is used to replace depreciating capital.

3. MPKk = 0.3 yCapital income is about 30% of GDP.

CHAPTER 8 Economic Growth II

Policy issues: efficiencyEvaluating the rate of saving

1. k = 2.5 y

2.  k = 0.1 y

3. MPKk = 0.3 y

To determine  , divide 2 by 1:

CHAPTER 8 Economic Growth II

Policy issues: efficiencyEvaluating the rate of saving

1. k = 2.5 y

2.  k = 0.1 y

3. MPKk = 0.3 y

To determine MPK, divide 3 by 1:

Hence, MPK = 0.12  0.04 = 0.08

CHAPTER 8 Economic Growth II

Policy issues: efficiencyEvaluating the rate of saving

• From the last slide: MPK = 0.08

• U.S. real GDP grows an average of 3% per year, so n+g = 0.03

• Thus, MPK = 0.08 > 0.03 = n+g

• Conclusion:

The U.S. is below the Golden Rule steady state: Increasing the U.S. saving rate would increase consumption per capita in the long run.

CHAPTER 8 Economic Growth II

Policy issues: efficiencyHow to increase the saving rate

• Reduce the government budget deficit(or increase the budget surplus).

• Increase incentives for private saving:

• reduce capital gains tax, corporate income tax, estate tax as they discourage saving.

• replace federal income tax with a consumption tax.

• expand tax incentives for IRAs (individual retirement accounts) and other retirement savings accounts.

CHAPTER 8 Economic Growth II

Policy issues: efficiencyAllocating the economy’s investment

• In the Solow model, there’s one type of capital.

• In the real world, there are many types,which we can divide into three categories:

• private capital stock

• public infrastructure

• human capital: the knowledge and skills that workers acquire through education.

• How should we allocate investment among these types?

CHAPTER 8 Economic Growth II

Policy issues: efficiencyAllocating the economy’s investment

Two viewpoints:

1. Equalize tax treatment of all types of capital in all industries, then let the market allocate investment to the type with the highest marginal product.

2. Industrial policy: Govt should actively encourage investment in capital of certain types or in certain industries, because they may have positive externalities that private investors don’t consider.

CHAPTER 8 Economic Growth II

Policy issues: efficiencyEstablishing the right institutions

• Creating the right institutions is important for ensuring that resources are allocated to their best use. Examples:

• Legal institutions, to protect property rights.

• Capital markets, to help financial capital flow to the best investment projects.

• A corruption-free government, to promote competition, enforce contracts, etc.

CHAPTER 8 Economic Growth II

Growth in output per person efficiency

(percent per year)

2.9

1.8

France

4.3

1.6

Germany

5.7

2.0

Italy

4.9

2.3

Japan

8.2

2.6

U.K.

2.4

1.8

U.S.

2.2

1.5

CASE STUDY: The productivity slowdown

1948-72

1972-95

CHAPTER 8 Economic Growth II

Growth in output per person efficiency

(percent per year)

2.9

1.8

2.4

France

4.3

1.6

1.7

Germany

5.7

2.0

1.2

Italy

4.9

2.3

1.5

Japan

8.2

2.6

1.2

U.K.

2.4

1.8

2.5

U.S.

2.2

1.5

2.2

CASE STUDY: I.T. and the “New Economy”

1948-72

1972-95

1995-2004

CHAPTER 8 Economic Growth II

CASE STUDY: efficiencyI.T. and the “New Economy”

Apparently, the computer revolution did not affect aggregate productivity until the mid-1990s.

Two reasons:

1. Computer industry’s share of GDP much bigger in late 1990s than earlier.

2. Takes time for firms to determine how to utilize new technology most effectively.

The big, open question:

• How long will I.T. remain an engine of growth?

CHAPTER 8 Economic Growth II

Endogenous growth theory efficiency

• Solow model:

• sustained growth in living standards is due to tech progress.

• the rate of tech progress is exogenous.

• Endogenous growth theory:

• a set of models in which the growth rate of productivity and living standards is endogenous.

CHAPTER 8 Economic Growth II

A basic model efficiency

• Production function: Y = AKwhere A is the amount of output for each unit of capital (A is exogenous & constant)

• Key difference between this model & Solow: MPK is constant here, diminishes in Solow

• Investment: sY

• Depreciation: K

• Equation of motion for total capital: K = sY  K

CHAPTER 8 Economic Growth II

A basic model efficiency

K = sY  K

• Divide through by K and use Y = AK to get:

• If sA > , then income will grow forever, and investment is the “engine of growth.”

• Here, the permanent growth rate depends on s. In Solow model, it does not.

CHAPTER 8 Economic Growth II

• Depends on definition of “capital.”

• If “capital” is narrowly defined (only plant & equipment), then yes.

• Advocates of endogenous growth theory argue that knowledge is a type of capital.

• If so, then constant returns to capital is more plausible, and this model may be a good description of economic growth.

CHAPTER 8 Economic Growth II

A two-sector model efficiency

• Two sectors:

• manufacturing firms produce goods.

• research universities produce knowledge that increases labor efficiency in manufacturing.

• u = fraction of labor in research (u is exogenous)

• Mfg prod func: Y = F [K, (1-u)EL]

• Res prod func: E = g(u)E

• Cap accumulation: K = sY  K

CHAPTER 8 Economic Growth II

A two-sector model efficiency

• In the steady state, mfg output per worker and the standard of living grow at rate E/E = g(u).

• Key variables:

s: affects the level of income, but not its growth rate (same as in Solow model)

u: affects level and growth rate of income

• Question: Would an increase in u be unambiguously good for the economy?

CHAPTER 8 Economic Growth II

Facts about R&D efficiency

1. Much research is done by firms seeking profits.

2. Firms profit from research:

• Patents create a stream of monopoly profits.

• Extra profit from being first on the market with a new product.

3. Innovation produces externalities that reduce the cost of subsequent innovation.

Much of the new endogenous growth theory attempts to incorporate these facts into models to better understand technological progress.

CHAPTER 8 Economic Growth II

Chapter Summary efficiency

1. Key results fromSolow model with tech progress

• steady state growth rate of income per person depends solely on the exogenous rate of tech progress

• the U.S. has much less capital than the Golden Rule steady state

2. Ways to increase the saving rate

• increase public saving (reduce budget deficit)

• tax incentives for private saving

CHAPTER 8 Economic Growth II

slide 33

Chapter Summary efficiency

3. Productivity slowdown & “new economy”

• Early 1970s: productivity growth fell in the U.S. and other countries.

• Mid 1990s: productivity growth increased, probably because of advances in I.T.

4. Empirical studies

• Solow model explains balanced growth, conditional convergence

• Cross-country variation in living standards isdue to differences in cap. accumulation and in production efficiency

CHAPTER 8 Economic Growth II

slide 34

Chapter Summary efficiency

5. Endogenous growth theory: Models that

• examine the determinants of the rate of tech. progress, which Solow takes as given.

• explain decisions that determine the creation of knowledge through R&D.

CHAPTER 8 Economic Growth II

slide 35

9 efficiency

### Introduction to Economic Fluctuations

In this chapter, you will learn… efficiency

• how the short run differs from the long run

• an introduction to aggregate demand

• an introduction to aggregate supply in the short run and long run

• how the model of aggregate demand and aggregate supply can be used to analyze the short-run and long-run effects of “shocks.”

CHAPTER 8 Economic Growth II

• GDP growth averages 3–3.5 percent per year over the long run with large fluctuations in the short run.

• Consumption and investment fluctuate with GDP, but consumption tends to be less volatile and investment more volatile than GDP.

• Unemployment rises during recessions and falls during expansions.

• Okun’s Law: the negative relationship between GDP and unemployment.

CHAPTER 8 Economic Growth II

Real GDP efficiencygrowth rate

Consumption growth rate

Average growth rate

Growth rates of real GDP, consumption

10

Percent change from 4 quarters earlier

8

6

4

2

0

-2

-4

1970

1975

1980

1985

1990

1995

2000

2005

CHAPTER 8 Economic Growth II

Real GDP efficiencygrowth rate

Investment growth rate

Consumption growth rate

Growth rates of real GDP, consumption, investment

Percent change from 4 quarters earlier

40

30

20

10

0

-10

-20

-30

1970

1975

1980

1985

1990

1995

2000

2005

CHAPTER 8 Economic Growth II

1970 efficiency

1975

1980

1985

1990

1995

2000

2005

Unemployment

Percent of labor force

12

10

8

6

4

2

0

CHAPTER 8 Economic Growth II

1966 efficiency

1951

1984

2003

1987

1975

2001

1982

1991

-3

-2

-1

0

1

2

3

4

Okun’s Law

10

Percentage change in real GDP

8

6

4

2

0

-2

-4

Change in unemployment rate

CHAPTER 8 Economic Growth II

Index of Leading Economic Indicators efficiency

• Published monthly by the Conference Board.

• Aims to forecast changes in economic activity 6-9 months into the future.

• Used in planning by businesses and govt, despite not being a perfect predictor.

CHAPTER 8 Economic Growth II

Components of the LEI index efficiency

• Average workweek in manufacturing

• Initial weekly claims for unemployment insurance

• New orders for consumer goods and materials

• New orders, nondefense capital goods

• Vendor performance

• New building permits issued

• Index of stock prices

• M2

• Yield spread (10-year minus 3-month) on Treasuries

• Index of consumer expectations

CHAPTER 8 Economic Growth II

Index of Leading Economic Indicators efficiency

160

140

120

100

1996 = 100

80

60

40

20

0

Source: Conference Board

1970

1975

1980

1985

1990

1995

2000

2005

CHAPTER 8 Economic Growth II

Time horizons in macroeconomics efficiency

• Long run: Prices are flexible, respond to changes in supply or demand.

• Short run:Many prices are “sticky” at some predetermined level.

The economy behaves much differently when prices are sticky.

CHAPTER 8 Economic Growth II

Recap of classical macro theory efficiency(Chaps. 3-8)

• Output is determined by the supply side:

• supplies of capital, labor

• technology.

• Changes in demand for goods & services (C, I, G ) only affect prices, not quantities.

• Assumes complete price flexibility.

• Applies to the long run.

CHAPTER 8 Economic Growth II

When prices are sticky… efficiency

…output and employment also depend on demand, which is affected by

• fiscal policy (G and T )

• monetary policy (M )

• other factors, like exogenous changes in C or I.

CHAPTER 8 Economic Growth II

The Quantity Equation as efficiencyAggregate Demand

• From Chapter 4, recall the quantity equation

M V = P Y

• For given values of M and V, this equation implies an inverse relationship between P and Y:

CHAPTER 8 Economic Growth II

P efficiency

Y

The downward-sloping AD curve

An increase in the price level causes a fall in real money balances (M/P),

(v is constant)

CHAPTER 8 Economic Growth II

P efficiency

Y

Shifting the AD curve

An increase in the money supply shifts the AD curve to the right.

(since MV=PY, and increase in M, increase PY)

Every value of P has associated higher Y.

CHAPTER 8 Economic Growth II

Aggregate supply in the long run efficiency

• Recall from Chapter 3: In the long run, output is determined by factor supplies and technology

is the full-employment or natural level of output, the level of output at which the economy’s resources are fully employed.

“Full employment” means that unemployment equals its natural rate (not zero).

CHAPTER 8 Economic Growth II

LRAS efficiency

P

Y

The long-run aggregate supply curve

does not depend on P, so LRAS is vertical.

CHAPTER 8 Economic Growth II

LRAS efficiency

P

P2

In the long run, this raises the price level…

Y

…but leaves output the same. (money neutrality)

Long-run effects of an increase in M

An increase in M shifts AD to the right.

P1

CHAPTER 8 Economic Growth II

Aggregate supply in the short run efficiency

• Many prices are sticky in the short run.

• For now (and through Chap. 12), we assume

• all prices are stuck at a predetermined level in the short run.

• firms are willing to sell as much at that price level as their customers are willing to buy.

• Therefore, the short-run aggregate supply (SRAS) curve is horizontal:

CHAPTER 8 Economic Growth II

The efficiencySRAS curve is horizontal:

The price level is fixed at a predetermined level, and firms sell as much as buyers demand.

P

SRAS

Y

EXTREME SHORT RUN: The short-run aggregate supply curve

CHAPTER 8 Economic Growth II

P

SRAS

Y

…causes output to rise. What about Unemployment?

Y2

Short-run effects of an increase in M

…an increase in aggregate demand…

Y1

CHAPTER 8 Economic Growth II

From the short run to the long run efficiency

Over time, prices gradually become “unstuck.” When they do, will they rise or fall?

In the short-run equilibrium, if

then over time, P will…

rise

fall

remain constant

The adjustment of prices is what moves the economy to its long-run equilibrium.

CHAPTER 8 Economic Growth II

LRAS efficiency

P

P2

SRAS

Y

Y2

The SR & LR effects of M>0

A = initial equilibrium

B = new short-run eq’m after Fed increases M

C

B

A

C = long-run equilibrium

CHAPTER 8 Economic Growth II

How shocking!!! efficiency

• shocks: exogenous changes in agg. supply or demand

• Shocks temporarily push the economy away from full employment.

• Example: exogenous decrease in velocity

If the money supply is held constant, a decrease in V means people will be using their money in fewer transactions, causing a decrease in demand for goods and services.

CHAPTER 8 Economic Growth II

AD efficiency shifts left, depressing output and employment in the short run.

LRAS

P

P2

SRAS

Y

Y2

The effects of a negative demand shock

A

B

Over time, prices fall and the economy moves down its demand curve toward full-employment.

C

CHAPTER 8 Economic Growth II

Supply shocks efficiency

• A supply shock alters production costs, affects the prices that firms charge. (also called price shocks)

• Examples of adverse supply shocks:

• Bad weather reduces crop yields, pushing up food prices.

• Workers unionize, negotiate wage increases.

• New environmental regulations require firms to reduce emissions. Firms charge higher prices to help cover the costs of compliance.

• Favorable supply shocks lower costs and prices.

CHAPTER 8 Economic Growth II

CASE STUDY: efficiencyThe 1970s oil shocks

• Early 1970s: OPEC coordinates a reduction in the supply of oil.

• Oil prices rose 11% in 1973 68% in 1974 16% in 1975

• Such sharp oil price increases are supply shocks because they significantly impact production costs and prices.

CHAPTER 8 Economic Growth II

The oil price shock shifts efficiencySRAS up, causing output and employment to fall.

LRAS

P

SRAS2

SRAS1

Y

Y2

CASE STUDY: The 1970s oil shocks

B

In absence of further price shocks, prices will fall over time and economy moves back toward full employment.

A

A

CHAPTER 8 Economic Growth II

Stabilization policy efficiency

• def: policy actions aimed at reducing the severity of short-run economic fluctuations.

• Example: Using monetary policy to combat the effects of adverse supply shocks:

CHAPTER 8 Economic Growth II

LRAS efficiency

P

SRAS2

SRAS1

Y

Y2

Stabilizing output with monetary policy

The adverse supply shock moves the economy to point B.

B

A

CHAPTER 8 Economic Growth II

LRAS efficiency

P

SRAS2

Y

Y2

Stabilizing output with monetary policy

But the Fed accommodates the shock by raising agg. demand.

B

C

A

results: P is permanently higher, but Y remains at its full-employment level.

CHAPTER 8 Economic Growth II

Chapter Summary efficiency

1. Long run: prices are flexible, output and employment are always at their natural rates, and the classical theory applies.

Short run: prices are sticky, shocks can push output and employment away from their natural rates.

2. Aggregate demand and supply: a framework to analyze economic fluctuations

CHAPTER 8 Economic Growth II

CHAPTER 9 Introduction to Economic Fluctuations

slide 68

Chapter Summary efficiency

3. The aggregate demand curve slopes downward.

4. The long-run aggregate supply curve is vertical, because output depends on technology and factor supplies, but not prices.

5. The short-run aggregate supply curve is horizontal, because prices are sticky at predetermined levels.

CHAPTER 8 Economic Growth II

CHAPTER 9 Introduction to Economic Fluctuations

slide 69

Chapter Summary efficiency

6. Shocks to aggregate demand and supply cause fluctuations in GDP and employment in the short run.

7. The Fed can attempt to stabilize the economy with monetary policy.

CHAPTER 8 Economic Growth II

CHAPTER 9 Introduction to Economic Fluctuations

slide 70

10 efficiency

### Aggregate Demand I:Building the IS-LM Model

In this chapter, you will learn… efficiency

• the IS curve, and its relation to

• the Keynesian cross

• the loanable funds model

• the LM curve, and its relation to

• the theory of liquidity preference

• how the IS-LM model determines income and the interest rate in the short run when P is fixed

CHAPTER 8 Economic Growth II

Context efficiency

• Chapter 9 introduced the model of aggregate demand and aggregate supply.

• Long run

• prices flexible

• output determined by factors of production & technology

• unemployment equals its natural rate

• Short run

• prices fixed

• output determined by aggregate demand

• unemployment negatively related to output

CHAPTER 8 Economic Growth II

Context efficiency

• This chapter develops the IS-LM model, the basis of the aggregate demand curve.

• We focus on the short run and assume the price level is fixed (so, SRAS curve is horizontal).

• This chapter (and chapter 11) focus on the closed-economy case. Chapter 12 presents the open-economy case.

CHAPTER 8 Economic Growth II

The Keynesian Cross efficiency

• A simple closed economy model in which income is determined by expenditure. (due to J.M. Keynes)

• Notation:

I = planned investment

E = C + I + G = planned expenditure

Y = real GDP = actual expenditure

• Difference between actual & planned expenditure = unplanned inventory investment

CHAPTER 8 Economic Growth II

Elements of the Keynesian Cross efficiency

consumption function:

govt policy variables:

for now, plannedinvestment is exogenous:

planned expenditure:

equilibrium condition:

actual expenditure = planned expenditure

CHAPTER 8 Economic Growth II

E efficiency =C +I +G

MPC

1

Graphing planned expenditure

E

planned

expenditure

income, output,Y

CHAPTER 8 Economic Growth II

E efficiency =Y

Graphing the equilibrium condition

E

planned

expenditure

45º

income, output,Y

CHAPTER 8 Economic Growth II

Equilibrium efficiencyincome

The equilibrium value of income

E

planned

expenditure

E =Y

E =C +I +G

income, output,Y

CHAPTER 8 Economic Growth II

E efficiency

At Y1, there is now an unplanned drop in inventory…

E =C +I +G2

E =C +I +G1

G

Y

E1 = Y1

E2 = Y2

Y

An increase in government purchases

E =Y

…so firms increase output, and income rises toward a new equilibrium.

CHAPTER 8 Economic Growth II

Solve for efficiencyY :

Solving for Y

equilibrium condition

in changes

because I exogenous

because C= MPCY

Collect terms with Yon the left side of the equals sign:

CHAPTER 8 Economic Growth II

The government purchases multiplier efficiency

Definition: the increase in income resulting from a \$1 increase in G.

In this model, the govt purchases multiplier equals

Example: If MPC = 0.8, then

An increase in G causes income to increase 5 times as much!

CHAPTER 8 Economic Growth II

Why the multiplier is greater than 1 efficiency

• Initially, the increase in G causes an equal increase in Y:Y = G.

• But Y  C

 furtherY

 furtherC

 furtherY

• So the final impact on income is much bigger than the initial G.

CHAPTER 8 Economic Growth II