econ class 5

8/6/2019 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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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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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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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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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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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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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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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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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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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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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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Determining GDP

Output is determined by the fixed factor supplies

and the fixed state of technology:

, ( )Y F K L


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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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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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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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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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Marginal product of capital (MPK) = Real rental rate

Intuition?

),(

0),(

:2)FOC

P

R

K

LKF

RK

LKFP


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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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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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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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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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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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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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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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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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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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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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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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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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Y

output

MPKand an increase in L

Kcapital

1

MPK

1MPK

),( 2LKF

),( 1LKF1

MPK

1

MPK

(L/K) MPK


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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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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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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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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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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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econ class 5

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