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The classical model of economics

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Economics 122aFall 2013

Agenda for next two classes:

1. The classical macro model 2. How economists measure

output/income

Some announcements• Course is limited to those on course list on web page plus

juniors (appeals are under consideration and should be decided early next week).

• There will probably be an optional section on logs and math review next Friday (Sept 8).

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4

The great chasm of macroeconomics

Classical macro:- perfect markets

-rational individuals

- flexible wages and prices

- full employment

Keynesian macro:- imperfect competition

-bounded rationality

- sticky wages and prices

- unemployment

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>0DR: ∂2Y/∂K2<0; ∂2Y/∂L2<0

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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>0DR: ∂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.

u* = Jones “long-run or natural rate of unemployment” = non-accelerating inflation rate of unemployment

(NAIRU) = unemployment rate at which inflation neither rises

or falls = lowest sustainable rate of unemployment = around 5-6 percent today

Real GDP over the cycle

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12,000

12,500

13,000

13,500

14,000

14,500

15,000

2004 2005 2006 2007 2008 2009 2010 2011 2012

Real GDP (Actual)Real Potential GDP

Rea

l GD

P (b

illion

s of

200

5 $)

Large GDP “gap”

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Anyone heard of the Cobb-Douglas production function?

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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 + RK

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Distribution with the 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 slides on historical data on factor shares.

Incomes in the National Income Accounts

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Source: U.S. Bureau of Economic Analysis (www.bea.gov)

1929 1948 1965 1992 2012

Compensation of employees 54.6% 59.0% 61.5% 66.8% 61.6%

Wages and salaries 53.6% 55.3% 55.1% 53.9% 49.6%

Proprietors' income with IVA/CCA 14.9% 16.0% 9.6% 7.3% 8.8%

Rental income of persons with CCA 6.5% 3.1% 2.9% 1.2% 3.9%

Corporate profits with IVA and CCA 11.5% 12.8% 13.5% 8.6% 14.4%

Net interest and misc 4.9% 1.1% 3.0% 7.0% 3.1%

Taxes on production and imports 7.2% 8.0% 9.2% 8.8% 8.0%

TOTAL 99.5% 100.0% 99.8% 99.6% 99.8%

19481929

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0%

10%

20%

30%

40%

50%

60%

70%

80%

1929 1939 1949 1959 1969 1979 1989 1999 2009

Compensation of employees

Wages and salaries

Near-constancy of labor’s share of national income

0%

10%

20%

30%

40%

50%

60%

70%

80%

1929 1939 1949 1959 1969 1979 1989 1999 2009

Share of compensation

Share of wages

?

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Applications of static neoclassical model

Impact of immigration (today)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 (later in course):

• 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.

So this is the simplest classical model

K = givenL = givenY = F(K,L)Factors paid their marginal products

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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 LY 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 LResults: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…”

Immigration and increasing wage inequality?

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“Just what is this ‘Y’?”

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