Macro Session 3

7/27/2019 Macro Session 3

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How does the entire economy work?

Understanding by using

Basic Classical Model


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Firms Households

Government

Financial

Markets

Market for goodsand Services

Market for Factors

of ProductionFactor Payment

Income (Y)

Taxes (T)

Private

Savings (S)

Consumption (C)

expenditure

Firms Revenue

Government Purchase (G)

Investment (I)

Simple Circular flow of income model (Closed economy)

Public

Savings (S)

Goods/

Services

Loans


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Again: How does an economy work?

Sources and Uses of Nations GDP

What determines the level of production (andthus the level of national income)?

How the markets for factors of production

distribute the income? How much of the income is consumed and

how much is saved?

How are demand for goods and services (C, Iand G) and supply are brought intoequilibrium?


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An economys output or Supply of goods and services (GDP)

depends on:

(1) Quantity of inputs : Factors of Production (Capital andLabor)

(2) Ability to turn inputs into output : Production Function

Needs clear understandings on:

Factor Market and

Goods (and Services) Market


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Classical theory: Assumption 1

and K K L L

Relating to Factors of Production

Capital: set of tools that workers use

Labor: time people spend on working

The economys supplies of capital and labor are

fixed.

Factors of production are fully utilized i.e. no

resources are wasted.


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Classical Theory: Assumption 2

Reflects the economys level of technology.

Denoted by Y= F(K,L)

Shows how much output (Y) the economy canproduce from Kunits of capital and L units of labor.

Three Properties: Increasing, constant and Decreasing(Diminishing) returns to scale.

Classical Assumption: PF exhibits constant returns toscale

(Meaning: If we increase all inputs by 25%, output will alsoincrease by 25%.)

Relating to Production function:


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The Supply of Goods and Services

Y = F (K,L)

, ( )Y F K L

Y = F (K, L)

Y = YSince Technology (production function) and K and L

are assumed to be fixed, the output (Y) is also

assumed to be fixed in an economy.


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How is National Income distributed to the

Factors of Production?

Depends on: how much economy uses K or L.

How much economy employs K or L depends on their

prices or factor prices.

The prices per unit that economy pays for employing

FOP: factor prices:

wage (w) is the price ofL

Rental/Interest rate (r) is the price ofK.


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How factor prices are determined

Factor prices are determined by supply and demand in

factor markets.

The intersection of demand and supply of the factors

determine the factor prices and quantity of factors

utilized. Which one plays major role?

Recall: Supply of each factor is fixed.

Therefore, it is the demand for the factors that

ultimately determine the factor prices

and

K K L L


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Factor

price

(Wage or

rental

rate)

Quantity of factor

Factor demand

Factor supply

Equilibriumfactor price

This vertical supply curve

is a result of the

supply being fixed.

Determination of Factor Prices

Factor prices are determined by supply and demand in factor

markets.

Because the factor supply curve is vertical and fixed, it is the

demand curve for the factors of productions which determines the

factor prices.


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Factors determining profit

Profit = Revenue Cost

= PY (wL + rK)

= PY wL rK

= PF(K,L) wL rK

So, Profit depends on product price P, factor

prices w and r ,and the factor quantities L and

K.


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Big Question:

What determines the

demand for factors of

production?

Answer: Depends upon Marginal Product of

Labor (MPL) and Marginal Product of Capital

(MPK).


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slide 14

MPL and the demand for labor

Each firm hires laborup to the point where

P MPL (VMPL) = W

MPL= W/P

Units ofoutput

Units of labor, L

MPL, Labordemand

Real

wage

Quantity of labordemanded


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The equilibrium real rental rate

The real rental rate

adjusts to equate

demand for capital with

supply.

Units ofoutput

Units of capital, K

MPK, demandfor capital

equilibriumr/P

Supply ofcapital

K


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How Total Income (Y) is distributed?

total labor income =

If production function has constant returns to

scale, then

total capital income =

WLP

MPL L

RK

PMPK K

Y MPL L MPK K

laborincome

capitalincome

nationalincome


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The Cobb-Douglas Production Fu

Paul Douglas

Paul Douglas observed that the division of

national income between capital and labor has been

roughly constant over time.

In other words, the total income of workers and the total

income of capital owners grew at almost exactly the

same rate.

He then wondered what conditions might lead to constant

factor shares. Cobb, a mathematician, said that the

production function would need to have the property that:

Capital Income = MPK K = Y

Labor Income = MPL L = (1- ) Y


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Capital Income = MPK K = Y

Labor Income = MPL L = (1-

) Y

is a constant and measures capital and

labors share of income.

Cobb showed that the function with this property is:

F (K, L) = A K

L1-

A is a parameter that measures the productivity

of the available technology. (Total Factor Productivity)

Cobb-Douglas

Production

Funct

ion

CobbDouglas Production Function


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CobbDouglas Production Function:

Y = F (K, L) = A K

L1-

Differentiating, we get the Marginal product of labor:

MPL = (1- ) A K

L

Multiply and Divide right hand side by L. Then,

MPL = (1- ) [A K

L

] L / L = (1- ) [A K

L1-

] / L

MPL = (1- ) Y / L

Similarly, The Marginal product of capital is:

MPK = A K-1

L1

or, MPK = Y/K

Average Labor

Productivity

Average Capital

Productivity

CobbDouglas Production Function


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Properties of the CobbDouglas Production Functio

Equation (i) tells us that marginal product of the labour is

proportional to output per worker (average productivity ofworker).

Similarly, equation (ii) states that marginal product of the capital

is proportional to the output per unit of capital (average

productivity of capital).In conclusion,

Marginal productivity of a factor is proportional to its average

productivity.

(1) Consider the CobbDouglas production function with:

MPL = (1- )Y/L .(i)

MPK= Y/ K (ii)


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Properties of the CobbDouglas Production Function

2) The CobbDouglas production function has constant returns to

scale. That is, if capital and labor are increased by the sameproportion, then output increases by the same proportion as

well.

Proof:

Consider the Cobb-Douglas Production function:F (K, L) = A K

L1-

F(zK,zL) =A(zK)

(zL)1-

F(zK,zL) =Az

K

z1-

L1-

F(zK,zL) =Az

z

1-

K

L

1-

F(zK,zL) =Az+1-

K

L1-

F(zK,zL) =AzK

L1-

=zAK

L1-

=zF(K,L) =zY

Therefore, Cobb-Douglas production function has constant

returns to scale.


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Empirical Evidence of the CobbDouglas Production

Function

Growth in Labor productivity and Real Wages in US

Period Labor Productivity Real Wages

Growth rate Growth rate

1959-1973 2.9% 2.8%

1973-1995 1.4% 1.2%

1995-2003 3.0% 3.0%

1959-2003 2.1% 2.0%Source: US Economic Report of the President, 2005.


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Thank You

Macro Session 3

Documents

Transcript of Macro Session 3