economics 122a fall 2009 agenda for this week: 1. the classical macro model 2. measuring output

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Economics 122aFall 2009

Agenda for this week:

1. The Classical macro model2. Measuring output

Some announcements• First problem set will be posted the week of Sept 21 and

due the next week.

• Course is limited to those on course list on web page.

• I will post readings on logarithms on the course web page. There will probably be an optional section on logs and math review in the next couple of weeks.

• We may have occasional optional extra sessions on Fridays, 11:35-12:50 for technical review.

• Sections will begin next week. You should sign up on the Registrar’s section list.

Wednesday 4:50-4:50 and 5:00-5:50

Wednesday 7:00-7:50 and 8:00-8:50

Thursday 4:50-4:50 and 5:00-5:50

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Repeat: The two themes of macro

There are two major recurrent themes running through macro:

i) Business cyclesii) Economic growth

Virtually every macroeconomic issue revolves around these issues, or a confusion concerning them.

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The Other Central Concern of Macroeconomics:Economic growth

Economic growth concerns the trend in output over the long run.

Questions:1. What determines “potential output” (Mankiw: “natural

output”)?2. What determines to growth of output over time?3. What determines the differences in productivity among

nations?In macroeconomics, we use the neoclassical growth model to

understand economic growth.

GDP trends in 3 big regions

5

100

1,000

10,000

1960 1970 1980 1990 2000 2007

GD

P (2

007

inte

rnati

onal

pri

ces,

bill

ions

of $

)

China US SubSaharanAfrica

Per capita growth trends in 3 big regions

6

200

2,000

20,000

1980 1985 1990 1995 2000 2007

GD

P pe

r cap

ita (

2007

inte

rnati

onal

US

dolla

rs)

China USSubSaharanAfrica

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Basics of Static Classical Model: Production Theory

Classical production model. The basic model is simplest

representation of the classical approach. When dynamized, it

becomes the neoclassical growth model.

Factor markets: capital and labor inputs (K and L)

One sector for output (Y).

Aggregate production function (for real GDP, Y)

What is a production function? Recipe for combining

inputs into outputs for given technology.

(1) Y = F( K, L)

Standard assumptions: positive marginal product (PMP),

diminishing returns (DR), constant returns to scale (CRTS):

CRTS: mY = F( mK, mL)

PMP: ∂Y/∂K>0; ∂Y/∂L>0

DR: ∂2Y/∂K2<0; ∂2Y/∂L2<0

Production function for omelette

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Courtesy of Elizabeth David, An Omelette and a Glass of Wine

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Basics of Static Classical Model: Production Theory

Classical production model. The basic model is simplest

representation of the classical approach. When dynamized,

it becomes the neoclassical growth model.

Factor markets: capital and labor inputs (K and L)

One sector for output (Y).

Aggregate production function (for real GDP, Y)

(1) Y = F( K, L)

Standard assumptions: positive marginal product (PMP),

diminishing returns (DR), constant returns to scale (CRTS):

CRTS: mY = F( mK, mL)

PMP: ∂Y/∂K>0; ∂Y/∂L>0

DR: ∂2Y/∂K2<0; ∂2Y/∂L2<0

Potential Output

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Potential output. With exogenous labor force (LF), inherited capital (K) , unemployment at the NAIRU (u*), this gives potential output (Yp):(2) Yp = F[K, (1-u*)LF]

Potential output critical for unemployment theory and growth theory and for medium and long-run forecasts.

NAIRU (Mankiw “natural rate of unemployment”) = non-accelerating inflation rate of unemployment = unemployment rate at which inflation neither rises

or falls = lowest sustainable rate of unemployment.

Actual and Potential GDP

11

11,000

11,500

12,000

12,500

13,000

13,500

14,000

01 02 03 04 05 06 07 08 09 10

Actual Real GDPPotential Real GDP

Output gap (potential minus actual GDP)

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-200

0

200

400

600

800

1,000

01 02 03 04 05 06 07 08 09 10

Gap (at annual rate)[Billions of 2005 dollars]

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Example: Cobb-Douglas production function

Very important production function: Cobb-Douglas (log linear)F( K, L) = AKαL1-α

Properties:MPL = ∂[AKαL1-α]/∂L=(1-α)AKαL1-α /L = (1-α)Y/L = (1-α) x APL(and similarly for MPK)

F( K, L) = 1.5L1-.5

L YMPL (discrete)

MPL (continuous/ derivative)

0.00 0.00 na1.00

1.00 1.00 0.500.41

2.00 1.41 0.350.32

3.00 1.73 0.290.27

4.00 2.00 0.25

0.00.20.40.60.81.01.21.41.61.82.0

0 0.5 1 1.5

Y, M

PL

Labor inputs (L)

Y

MPL

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Factor Markets

Factor markets: capital and labor inputs (K and L):- Capital inherited from past investments- Labor inputs exogenous (from biology, health, customs,

pharma)Real wage rate: = W/P = MPL = ∂Y/∂L = ∂[F( K, L)]/∂L (see Fig.

1)

Real rental rate on capital (like apartment rental as $ per month):

= R/P = MPK = ∂Y/∂K = ∂[F( K, L)]/∂KNational income = labor income + capital income = WL + RKExhaustion of product theorem: With CRTS and competitive

pricing, paying factors their marginal product leads income = output.

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Example: Cobb-Douglas production function

National incomeY = MPL x L + MPK x K = L[(1-α)Y/L] +K[αY/K ] = Y (exhaustion of product theorem)

Shares of capital and labor:share of K = RK/Y = (αY/K ) x (K/Y) = constant = α

Why do economists like Cobb-Douglas? See next slide.

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Near-constancy of labor’s share of national income

.50

.55

.60

.65

.70

.75

.80

50 55 60 65 70 75 80 85 90 95 00 05

Compensation of labor/ national income

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What are the macroeconomic effects of

immigration?

Alfred Stieglitz

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L

W/P

MPL

Real wages and MPL: graphics

L*

(W/P)*

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L

W/P

MPL

Output = sum of the slices of MPL from 0 to L*

L*

L*

Calculus of marginal and total product

Total product = sum of marginal products up to input level.

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* *

0 0

( *) ( , *) ( ) [ ( , )/ ]L L

Y L F K L MPL L dL F K L L dL

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L

W/P

MPL

Neoclassical distribution of output/income

L*

(W/P)*

Total wages

Capitalincome*

*More generally, all non-labor income

Can reverse axes and get analogous results for capital.

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L

W/P

MPL

Effect of immigration

L*

(W/P)1

(W/P)2

E1

E2

Assume immigrants are perfect substitutes for L

Results:1. Wage rate falls.2. Output and national

income rise.3. Capital income rises.4. More generally, income of

substitutes fall and complements rise.

5. Empirical studies suggest that low-skilled and Hispanic workers are hurt by Mexican immigration.

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National Academy of Sciences study (The New Americans)

“Immigration over the 1980s increased the labor supply of all workers by about 4 percent. On the basis of evidence from the literature on labor demand, this increase could have reduced the wages of all competing native-born workers by about 1 or 2 percent. Meanwhile, noncompeting native-born workers would have seen their wages increase…”

“Based on previous estimates of responses of wages to changes in supply, the supply increase due to immigration lowered the wages of high school dropouts by about 5 percent…”

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Other applications of static neoclassical model

Impact of foreign investment :• Assume that foreign firms build a factory in US. What is

effect in simple neoclassical model?• Answer: Same as immigration, but reverse the factors.

Impact of outsourcing:• What is effect of hiring foreign workers for call centers,

radiology, computer programming?• Very similar to immigration: like having workers here.

Impact of government debt:• What is the effect of a growing government debt?• Slightly more complicated, but might crowd out capital

stock. This then reduces output. Note effects on wages and rentals.

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Let’s go back and ask:

“Just what is this ‘Y’?”

“Just how do we measure GDP and real GDP?”

26 Survey of Current Business, August 2009

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Inflation as measured by the price of gross domestic purchases*

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Note: This is a new concept not in the textbooks. It reflects the prices of domestic purchases rather than domestic product.

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Major concepts in national economic accounts

1. GDP measures final output of goods and services.2. Two ways of measuring GDP lead to identical results:

• Production = income3. Savings = investment is an accounting identity.

• We will also see that it is an equilibrium condition.• Note the advanced version of this includes government and foreign

sector. 4. GDP v. GNP: differs by ownership of factors5. Constant v. current prices: correct for changing prices6. Value added: Total sales less purchases of intermediate goods

- Note that income-side GDP adds up value addeds7. Net exports = exports – imports 8. Net v. gross investment:

• Net investment = gross investment minus deprecation

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How to measure output growth?

Now take the following numerical example. • Suppose good 1 is computers and good 2 is shoes. • How would we measure total output and prices?

period 1 period 2

Ratio: period 2 to period 1

Real outputq1 1 100 100q2 1 1 1

Pricesp1 1 0.010 0.010p2 1 1.00 1.00