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Economics 122a
Fall 2013
Agenda for next two classes:
1. The classical macro model
2. How economists measure output/income
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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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The great chasm of macroeconomics
Classical macro:
- perfect markets
-rational individuals
- flexible wages and
prices
- full employment
This is our
topic for today:
classical
approach
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Keynesian macro:
- imperfect
competition
-bounded
rationality
- sticky wages and
prices
- unemployment
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
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DR: ∂2Y/∂K2<0; ∂2Y/∂L2<0
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
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Production function for popovers
Courtesy of Florence Kling Harding , Twentieth Century Cookbook, 1921
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Potential Output
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
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Real GDP over the cycle
15,000
Real GDP (billions of 2005 $)
14,500
Real GDP (Actual)
Real Potential GDP
14,000
13,500
Large
GDP “gap”
13,000
12,500
12,000
2004
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2005
2006
2007
2008
2009
2010
2011
2012
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)
L
MPL
(discrete)
Y
0.00
0.00
MPL
(continuous/
derivative)
na
1.00
1.00
1.00
0.50
0.41
2.00
1.41
0.35
0.32
3.00
1.73
0.29
0.27
4.00
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2.00
0.25
Y, MPL
F( K, L) = 1.5L1-.5
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Y
MPL
0
0.5
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Labor inputs (L)
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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)]/∂K
National income = labor income + capital income = WL + RK
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Distribution with the Cobb-Douglas production function
National income
Y = 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.
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Incomes in the National Income Accounts
1929
1948
1965
1992
2012
54.6%
59.0%
61.5%
66.8%
61.6%
53.6%
55.3%
55.1%
53.9%
49.6%
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%
99.5%
100.0%
99.8%
99.6%
99.8%
Compensation of employees
Wages and salaries
Proprietors' income with IVA/CCA
TOTAL
Source: U.S. Bureau of Economic Analysis (www.bea.gov)
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Near-constancy of labor’s share of national income
80%
80%
70%
70%
60%
60%
?
50%
50%
40%
40%
30%
30%
Compensation of employees
Share of compensation
Wages and salaries
Share of wages
20%
20%
10%
10%
0%
0%
1929
1929
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1939
1939
1949
1949
1959
1969
1979
1959
1969
1979
1989
1989
1999
1999
2009
2009
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.
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So this is the simplest classical model
K = given
L = given
Y = 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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W/P
Real wages and MPL:
graphics
(W/P)*
MPL
L*
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L
W/P
L*
Output = sum of the
slices of MPL from 0 to L*
MPL
L
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L*
Calculus of marginal and total product
Total product = sum of marginal products up to input level.
L*
Y  F ( K , L *) 

0
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L*
M P L ( L )d L 
 [  F ( K , L ) /  L ]d L
0
Neoclassical distribution of
output/income
W/P
*More generally,
all non-labor
income
Capital
income*
Can reverse axes
and get analogous
results for capital.
(W/P)*
Total wages
MPL
L*
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L
W/P
(W/P)1
Effect of immigration
E1
E2
(W/P)2
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.
MPL
L*
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L
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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Immigration and increasing wage inequality?
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“Just what is this ‘Y’?”
“Just how do we measure GDP and real GDP?”
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