Econ Class 5
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Transcript of Econ Class 5
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slide 0Mariko J. Klasing
ECON 2102 I: Intermediate
Macroeconomics
Lecture 5: Supply of goods and
services (Ch. 3.1 & 3.2)
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slide 1Mariko J. Klasing
Outline of general model
A closed economy, market-clearing model
Supply side
factor markets (supply, demand, price)
determination of output/incomeDemand side
determinants of C, I, and G
Equilibrium goods market
loanable funds market
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slide 2Mariko J. Klasing
In this lecture, you will learn
what determines the economys total
output/income ( = supply side of the economy)
how the prices of the factors of production are
determined
how total income is distributed
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slide 3Mariko J. Klasing
Factors of production
K = capital:
tools, machines, and structures used in
production
L = labor:
the physical and mental efforts of
workers
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slide 4Mariko J. Klasing
The production function
denoted Y= F(K,L)
shows how much output (Y) the economy can
produce from
Kunits of capital and L units of labor
reflects the economys level of technology
exhibits constant returns to scale
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slide 5Mariko J. Klasing
Returns to scale: A review
Initially Y1 = F(K1 ,L1 )
Scale all inputs by the same factor z:
K2 = zK1 and L2 = zL1
(e.g., if z= 1.25, then all inputs are increased by 25%)
What happens to output, Y2= F(K2,L2)?
If constant returns to scale, Y2= zY1
If increasing returns to scale, Y2> zY1
If decreasing returns to scale, Y2< zY1
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slide 7Mariko J. Klasing
Example 2
( , )F K L K L
( , )F zK zL zK zL
z K z L
( , )z F K L decreasingreturns to scalefor anyz> 1
z K L
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slide 8Mariko J. Klasing
Example 3
( , )F K L K L 2 2
( , ) ( ) ( )F zK zL zK zL 2 2
( , )z F K L 2increasing returns
to scale for anyz> 1
z K L 2 2 2
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slide 9Mariko J. Klasing
Now you try
Determine whether constant, decreasing, or increasing
returns to scale for each of these production functions:
(a)
(b)
LKY(K,L) /2
0.50.3LKY(K,L)
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slide 10Mariko J. Klasing
Assumptions of the model
1. Technology is fixed.
2. The economys supplies of capital and labor
are fixed at
andK K L L
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slide 11Mariko J. Klasing
Cobb-Douglas production
function
a particular production function we will be using a lot in
this course features constant returns to scale
10,),(1
LKLKF
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slide 12Mariko J. Klasing
Determining GDP
Output is determined by the fixed factor supplies
and the fixed state of technology:
, ( )Y F K L
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slide 13Mariko J. Klasing
The distribution of national
income
determined by factor prices,
the prices per unit that firms pay for the
factors of production
wage = price of L
rental rate = price of K
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slide 15Mariko J. Klasing
How factor prices are determined
Factor prices are determined by supply and
demand in factor markets.
Recall: Supply of each factor is fixed.
What about demand?
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slide 16Mariko J. Klasing
Demand for labor and capital
Assume markets are competitive:
each firm takes W, R, and Pas given.
Basic idea:
A firm hires another unit of labor
and capital if the cost does not exceed the
benefit.
cost = real wage / real rental rate of capital benefit = marginal product of labor / marginal
product of capital
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slide 17Mariko J. Klasing
Formally: Profit maximization of
firms
Firms want to maximize profits, taking W, Rand Pasgiven:
Marginal product of labor (MPL) = Real wage
Intuition?
),(
0),(
:1)FOC
),(max,
P
W
L
LKF
WL
LKFP
RKWLLKFPLK
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slide 18Mariko J. Klasing
Marginal product of capital (MPK) = Real rental rate
Intuition?
),(
0),(
:2)FOC
P
R
K
LKF
RK
LKFP
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slide 19Mariko J. Klasing
Marginal product of labor (MPL)
definition:
The extra output the firm can produce
using an additional unit of labor
(holding other inputs fixed):
MPL = F(K,L+1) F(K,L)
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slide 20Mariko J. Klasing
Exercise 1
a. Determine MPL at eachvalue of L.
b. Graph the production
function.c. Graph the MPL curve with
MPL on the vertical axis
and
L on the horizontal axis.
L Y MPL0 0 n.a.
1 10 ?
2 19 ?
3 27 84 34 ?
5 40 ?
6 45 ?
7 49 ?8 52 ?
9 54 ?
10 55 ?
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slide 21Mariko J. Klasing
Youtput
MPLand the production function
Llabor
F K L( , )
1
MPL
1
MPL
1MPL
As more labor is
added, MPL
Slope of the production
function equals MPL
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slide 22Mariko J. Klasing
Marginal product of capital (MPK)
definition:
The extra output the firm can produce
using an additional unit of labor
(holding other inputs fixed):
MPL = F(K+1,L ) F(K,L)
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slide 23Mariko J. Klasing
Youtput
MPKand the production function
Kcapital
1
MPK
1
MPK
1MPK
As more capital
is added, MPK
Slope of the production
function equals MPK
),( LKF
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slide 24Mariko J. Klasing
Diminishing marginal returns
We usually assume that as a factor input isincreased,
its marginal product falls (other things equal).
Intuition:Suppose L while holding Kfixed
fewer machines per worker
lower worker productivity
Or: suppose Kwhile holding L fixed
fewer people who can operate the machines
lower productivity or capital
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slide 25Mariko J. Klasing
Example: The Black Death
In 1348, the Black Death killed 60 % of the population in England huge fall in labor L
Real wages in England, 1205-1645
(index, 1865=100)
0
10
20
30
40
50
60
70
80
90
1205 1255 1305 1355 1405 1455 1505 1555 1605
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slide 26Mariko J. Klasing
Exercise (part 2)
Suppose W/P= 6.
d. If L = 3, should firm hire more
or less labor? Why?
e. If L = 7, should firm hire more
or less labor? Why?
L Y MPL
0 0 n.a.
1 10 10
2 19 9
3 27 8
4 34 75 40 6
6 45 5
7 49 4
8 52 3
9 54 2
10 55 1
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slide 27Mariko J. Klasing
MPLand the demand for labor
Each firm hires labor
up to the point where
MPL = W/P.
Units ofoutput
Units of labor, L
MPL,Labordemand
Real
wage
Quantity of labordemanded
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slide 28Mariko J. Klasing
MPKand the demand for labor
Each firm hires labor
up to the point where
MPK= R/P.
Units ofoutput
Units of capital, K
MPK,Capitaldemand
Real
rentalrate
Quantity of capitaldemanded
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slide 29Mariko J. Klasing
Brief review
Profit maximizing firms hire labor and employ capitalsuch that W/P=MPL and R/P=MPK
With a standard production function that is concave
in Kand L, the marginal product of a factor is fallingas this factor increases.
Intuition:
Suppose L while holding Kfixed
fewer machines per worker
lower worker productivity
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slide 30Mariko J. Klasing
Brief review
Or: suppose Kwhile holding L fixed fewer people who can operate the machines
lower productivity or capital
What happens to W/P(=MPL) as K and R/P(=MPK) as L
1) Each worker has more machines to use: laboris more productive, increase in MPL and real wage
2) More people available to operate eachmachine: capital is more productive, increase inMPKand the real rental rate of capital
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slide 32Mariko J. Klasing
Y
output
MPKand an increase in L
Kcapital
1
MPK
1MPK
),( 2LKF
),( 1LKF1
MPK
1
MPK
(L/K) MPK
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slide 33Mariko J. Klasing
With Cobb-Douglas
0)1)((
0)1(
)1(
10,),(
1
12
11
1
LKF
LKF
L
YLKMPL
K
YLKMPK
LKLKFY
LL
KK
Cobb-Douglas features diminishing marginal returns
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slide 34Mariko J. Klasing
How income is distributed:
total labor income =
If a production function has constant returns toscale, then
total capital income =
WL
PMPL L
RK
PMPK K
Y MPL L MPK K
laborincome
capitalincome
nationalincome
This means, that firms profits are zero!
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slide 35Mariko J. Klasing
The ratio of labor income to total
income in the U.S.
0
0.2
0.4
0.6
0.8
1
1960 1970 1980 1990 2000
Labors
shareof totalincome
Labors share of income
is approximately constant over time.
(Hence, capitals share is, too.)
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slide 36Mariko J. Klasing
Income distribution with Cobb-
Douglas Production Function
The Cobb-Douglas production function has
constant factor shares:
capital income = MPKx K =( Y/K) x K= Y
labor income = ((1 )Y/L) x L = (1 )Y Hence firms profits are zero:
0)1(
)1(
/
YYY
KK
YL
L
YY
KMPKLMPLYP
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slide 37Mariko J. Klasing
Outline of model
A closed economy, market-clearing modelSupply side
factor markets (supply, demand, price)
determination of output/income
Demand side
determinants of C, I, and G
Equilibrium goods market
loanable funds market
DONE DONENext
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