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The classical model of macroeconomics

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Economics 122aFall 2010

Agenda for this week:

1. The classical macro model (Chap 3)

2. How economists measure output/income (Chap 2)

Some announcements• First problem set will be posted next week and due

Wednesday Sept 22.

• 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 will meet FRIDAY this week here, not Wednesday.

• Sections will begin next week

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

Thursday 4:50-4:50 and 5:00-5:50Thursday 7:00-7:50 and 8:00-8:50

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Alternative Schools of Macroeconomics

Frictions in market institutions?

Market clearing and perfect competition

Market frictions: sticky prices and wages; imperfect competition

Frictions in indiv-idual

Rational consumers and profit maximizers

Neoclassical (Solow, Arrow-Debreu); new classical macro; real business cycles

Neo-Keynesian (menu costs and contract theory); structuralism

decisionmaking?

Bounded rationality, behavioral economics

Original Keynes; monetarist?

Mainstream Keynesian

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Alternative Schools of Macroeconomics

Frictions in market institutions?

Market clearing and perfect competition

Market frictions: sticky prices and wages; imperfect competition

Frictions in indiv-idual

Ultra-rational

Classical model; Neoclassical growth; new classical macro; real business cycles

decisionmaking? Bounded

rationality

This is our topic for today:

classical approach

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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 popovers

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Courtesy of Florence Kling Harding , Twentieth Century Cookbook, 1921

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.

GDP loss in recession[potential minus actual output, billions of 2005 $]

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-80

-40

0

40

80

120

160

200

240

280

2005 2006 2007 2008 2009 2010

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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 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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Next class on Friday: Chapter 2

“Just what is this ‘Y’?”

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