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N. Gregory Mankiw N. Gregory Mankiw

PowerPoint

PowerPoint^®^®Slides by Ron CronovichSlides by Ron Cronovich Modified by the instructor

Modified by the instructor

MACROECONOMICS MACROECONOMICS

2011/12/13

Topic 3

National Income:

Where It Comes From and Where It Goes

(Chapter 3)

Instructor: Tuan Khai Vu

ICU, Winter Term 2011

Principles of Macroeconomics

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Learning objectives

In this chapter, we will learn :

what determines the economy’s total output/income

how the prices of the factors of production are determined

how total income is distributed

what determines the demand for goods and services

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Production process of a firm

production process capital

labor

intermediates

output

inputs

Since intermediates (materials, parts etc), as we learnt in Ch.2,

do not contribute to the creation of value added below we will focus on capital and labor.

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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:

Y = F( K,L)

shows how much output (Y ) the economy can produce from K units of capital and L units of labor

reflects the economy’s level of technology

exhibits constant returns to scale

(We assume this property because it fits the data well.)

This concept is applied primarily to a firm, but it can be extended to the economy as a whole.

Think of a typical firm that behaves like the economy as a whole.

Technology is defined as the way inputs are transformed into output

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Returns to scale: A review

Initially Y₁ = F (K₁, L₁ )

Scale all inputs by the same factor z: K₂= zK₁and L₂= zL₁

(e.g., if z = 1.2, then all inputs are increased by 20%)

What happens to output, Y₂ = F (K₂, L₂)?

If constant returns to scale, Y₂ = zY₁

If increasing returns to scale, Y₂ > zY₁

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R e tu rn s t o s c a le : E x a m p le 1

constant returns to scale for any z> 0

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R e tu rn s t o s c a le : E x a m p le 2

decreasing returns to scale for any z> 1

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R e tu rn s t o s c a le : E x a m p le 3

increasing returns to scale for any z> 1

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Outline of model

A closed economy, market-clearing model

Supply side

factor markets (supply, demand, price)

determination of output/income

Demand side

determinants of C, I, and G

Equilibrium

goods market

loanable funds market

Now we will learn a

neoclassical model describing the economy in the long run.

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Assumptions

1. All prices are flexible and all markets clear. 2. Technology is fixed.

3. The economy’s supplies of capital and labor are fixed at

These are what we mean by the long run.

Put differently, the assumptions describe an economy in which the time span is long enough for prices to adjust to equate demand and supply,

but not long enough for capital and labor to change significantly.

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Determining GDP

Output is determined by the fixed factor supplies and the fixed state of technology:

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The distribution of national income

determined by factor prices,

the prices per unit firms pay for the factors of production

wage = price of L

^ren^{tal rate} = price of K

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Notation

W = nominal wage

R = nominal rental rate

P = price of output

W /P = real wage

R /P = real rental rate

W = nominal wage

R = nominal rental rate

P = price of output

W /P = real wage

R /P = real rental rate

“real” here means measured by units of output, not money

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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?

You should ask first: who demands these factors ?

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Marginal product of labor ( MPL)

Definition of MPL:

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)

Properties of MPL _Æ the next 2 slides.

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Y output

MPL and the production function

L labor

1

MPL 1

MPL

1 ^MPL As more labor is added, MPL^↓

Slope of the production function equals MPL

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Diminishing marginal returns

As a factor input is increased, its marginal product falls (other things equal). For the case of labor: holding K fixed, L^↑ ^⇒ MPL^↓.

^Intuition:

Suppose L^↑ while holding K fixed

⇒ fewer machines per worker

⇒ lower worker productivity

⇒ _MPL↓

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Demand for labor

Assume markets are competitive:

each firm takes W, R, and P as given.

Basic idea: If a firm is to maximize its profit, it will hire labor such that

marginal cost = marginal benefit.

marginal cost = real wage (cost of hiring one more unit of labor)

marginal benefit = MPL (benefit of hiring one more worker = the additional output that the new worker produces)

⇒Profit maximizing condition: MPL = W/P

A important view here is that economists think of firms as profit maximizing agents.

This condition shows how the firm chooses labor _Æ it’s exactly the labor demand function.

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MPL and the demand for labor

Each firm hires labor up to the point where MPL = W/P.

Units of output

Units of labor, L MPL, Labor demand

Real wage

Quantity of labor demanded

The firm chooses labor along the MPL line.

Since L^↑⇒ MPL^↓, the line is downward sloping.

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The equilibrium real w age

The real wage adjusts to equate labor demand with supply.

Units of output

Units of labor, L MPL, Labor demand

equilibrium real wage

Labor supply

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Marginal product of capital ( MPK)

Definition of MPK:

The extra output the firm can produce using an additional unit of capital

(holding other inputs fixed):

MPK = F (K +1, L) – F (K, L)

Just similar to that of MPL in sl.17.

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Determining the rental rate

We have just seen that MPL = W/P.

The same logic shows that MPK = R/P:

diminishing returns to capital: MPK^↓ as K^↑

The MPK curve is the firm’s demand curve for renting capital.

Firms maximize profits by choosing K such that MPK = R/P.

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The equilibrium real rental rate

The real rental rate adjusts to equate demand for capital with supply.

Units of output

Units of capital, K MPK, demand for capital

equilibrium R/P

Supply of capital

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The Neoclassical Theory of Distribution

states that each factor input is paid its marginal product

a good starting point for thinking about income distribution

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How income is distributed to L and K

total labor income =

If production function has constant returns to scale, then

total capital income =

labor income

capital income national

income

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The ratio of labor income to total income

in the U.S.,

^{1960- 2007}

Labor’s share of total income

Fact: Labor’s share of income is approximately constant over time.

(Thus, capital’s share is, too.) Fact: Labor’s share of income is approximately constant over time.

(Thus, capital’s share is, too.)

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The Cobb- Douglas Production Function

The Cobb-Douglas production function has constant factor shares:

α = capital’s share of total income: capital income = MPK x K = ^αY labor income = MPL x L = (1 –^α)Y

The Cobb-Douglas production function is: where A represents the level of technology.

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The Cobb- Douglas Production Function

Each factor’s marginal product is proportional to its average product:

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Labor productivity and w ages

Theory: wages depend on labor productivity

^{U.S. data:}

period productivity growth

real wage growth

1959-2007 2.1% 2.0%

1959-1973 2.8% 2.8%

1973-1995 1.4% 1.2%

1995-2007 2.5% 2.4%

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Outline of model

A closed economy, market-clearing model Supply side

determination of output/income Demand side

determinants of C, I , and G Equilibrium

goods market

DONE

₉

DONE

₉

Next _Î

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Demand for goods & services

Components of aggregate demand:

C = consumer demand for goods & services I = demand for investment goods

G = government demand for goods & services (closed economy: no NX )

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Consumption, C

def: Disposable income is total income minus total taxes: Y – T.

Consumption function: C = C (Y – T ) Property: (Y – T )^↑ ^⇒ C^↑

def: Marginal propensity to consume (MPC) is the change in C when disposable income increases by one dollar.

This simply shows C depends on Y-T

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T h e c o n s u m p ti o n f u n c ti o n

C Y –T

C(Y –T ) 1

MPCThe slope of the consumption function is the MPC.

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I nvestment, I

The investment function is I = I (r ),

where r denotes the real interest rate,

the nominal interest rate corrected for inflation.

The real interest rate is

the cost of borrowing

the opportunity cost of using one’s own funds to finance investment spending So, r^↑ ^⇒ I ^↓

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The investment function

r

I I (r )

Spending on

investment goods

depends negatively on the real interest rate.

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Government spending, G

G = govt spending on goods and services.

G excludes transfer payments (e.g., social security benefits,

unemployment insurance benefits).

Assume government spending and total taxes are exogenous:

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Outline of model

A closed economy, market-clearing model Supply side

determination of output/income Demand side

determinants of C, I , and G Equilibrium

goods market

DONE

₉

DONE

₉

Next _Î DONE

₉

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The market for goods & services

Aggregate demand:

Aggregate supply:

Equilibrium:

The real interest rate adjusts to equate demand with supply.

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The loanable funds market

A simple supply-demand model of the financial system.

One asset: “loanable funds”

demand for funds: investment

supply of funds: saving

“price” of funds: real interest rate

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Demand for funds: I nvestment

The demand for loanable funds…

comes from investment:

Firms borrow to finance spending on plant & equipment, new office buildings, etc.

Consumers borrow to buy new houses.

depends negatively on r,

the “price” of loanable funds (cost of borrowing).

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Loanable funds demand curve

r

I I (r )

The investment curve is also the demand curve for loanable funds. The investment curve is also the demand curve for loanable funds.

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Supply of funds: Saving

The supply of loanable funds comes from saving:

Households use their saving to make bank deposits, purchase bonds and other assets. These funds become available to firms to

borrow to finance investment spending.

The government may also contribute to saving if it does not spend (G) all the tax revenue (T) it receives.

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Types of saving

private saving = (Y – T ) – C public saving = T – G national saving: S

S = private saving + public saving

= (Y –T ) – C + T – G

= Y – C – G

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Notation: ^Δ = change in a variable

For any variable X, ^ΔX = “the change in X ”

Δ is the Greek (uppercase) letter Delta Examples:

^If^Δ^{L = 1 and}^ΔK = 0, then ^ΔY = MPL. More generally, if ^ΔK = 0, then

^Δ^(Y⁻^{T ) =}^Δ^Y⁻ ^Δ^{T , so}

Δ_C _{= MPC}× ₍Δ_Y− Δ_{T )}

= MPC ^×^ΔY ⁻ MPC ^×^ΔT

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Budget surpluses and deficits

If T > G, budget surplus = (T – G)

= public saving.

If T < G, budget deficit = (G – T) and public saving is negative.

If T = G, “balanced budget,” public saving = 0.

The U.S. government finances its deficit by issuing Treasury bonds – i.e., borrowing.

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U.S. Federal Government Surplus/Deficit, 1940-2007 Note: Data are estimates for 2010-2015.

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U.S. Federal Government Debt,

Fiscal Years 1940- 2010

Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt.

(In 2009, it was about 10 cents) Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt.

(In 2009, it was about 10 cents)

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Loanable funds supply curve

r

S, I National saving

does not depend on r,

so the supply curve is vertical. National saving does not depend on r,

so the supply curve is vertical.

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Loanable funds market equilibrium

r

S, I I (r ) Equilibrium real

interest rate

Equilibrium level of investment

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The special role of r

r adjusts to equilibrate the goods market and the loanable funds market simultaneously:

If L.F. market in equilibrium, then Y – C – G = I

Add (C +G) to both sides to get

Y = C + I + G (goods market eq’m) Thus,

r adjusts to equilibrate the goods market and the loanable funds market simultaneously:

If L.F. market in equilibrium, then Y – C – G = I

Add (C +G) to both sides to get

Y = C + I + G (goods market eq’m) Thus,

Eq’m in L.F. market

Eq’m in goods market

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Digression: Mastering models

To master a model, be sure to know:

1. Which of its variables are endogenous and which are exogenous.

2. For each curve in the diagram, know: a. definition

b. intuition for slope

c. all the things that can shift the curve 3. Use the model to analyze the effects of

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Mastering the loanable funds model

Things that shift the saving curve

public saving

fiscal policy: changes in G or T

private saving

preferences

tax laws that affect saving

(54)

CASE STUDY:

The Reagan deficits

Reagan policies during early 1980s:

increases in defense spending: ^ΔG > 0

big tax cuts: ^ΔT < 0

Both policies reduce national saving:

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CASE STUDY:

The Reagan deficits

r

S, I I (r ) r₁

I ₁ r₂

2. …which causes the real interest rate to rise…

I ₂ 3. …which reduces

the level of investment.

3. …which reduces the level of

investment. 1. The increase in

the deficit reduces saving…

1. The increase in the deficit reduces saving…

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Are the data consistent w ith these results?

variable 1970s 1980s

T – G –2.2 –3.9

S 19.6 17.4

r 1.1 6.3

I 19.9 19.4

T–G, S, and I are expressed as a percent of GDP All figures are averages over the decade shown.

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Mastering the loanable funds model

^,

continued

Things that shift the investment curve:

some technological innovations

to take advantage some innovations, firms must buy new investment goods

tax laws that affect investment

e.g., investment tax credit

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An increase in investment demand

An increase in desired investment… r

S, I I ₁

I ₂ r₁

r₂

…raises the interest rate.

But the equilibrium level of investment cannot increase because the

supply of loanable

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Saving and the interest rate

Why might saving depend on r ?

How would the results of an increase in investment demand be different?

Would r rise as much?

Would the equilibrium value of I change?

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An increase in investment demand w hen

saving depends on r

r

S, I I (r)

I (r)₂ r₁

r₂ An increase in

investment demand raises r,

which induces an increase in the quantity of saving, which allows I

to increase.

I I

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FYI :

Markets, I ntermediaries, the 2008 Crisis

In the real world, firms have several options for raising funds they need for investment, including:

borrow from banks

sell bonds to savers

sell shares of stock (ownership) to savers

The financial system includes:

bond and stock markets, where savers directly provide funds to firms for investment

financial intermediaries, e.g. banks, insurance companies, mutual funds, where savers

indirectly provide funds to firms for investment

for your information

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FYI :

Markets, I ntermediaries, the 2008 Crisis

Intermediaries can help move funds to their most productive uses.

But when intermediaries are involved,

savers usually do not know what investments their funds are financing.

Intermediaries were at the heart of the financial crisis of 2008….

(63)

FYI :

Markets, I ntermediaries, the 2008 Crisis

A few details on the financial crisis:

July ’06 to Dec ’08: house prices fell 27%

Jan ’08 to Dec ’08: 2.3 million foreclosures

Many banks, financial institutions holding mortgages or mortgage-backed securities driven to near bankruptcy

Congress authorized $700 billion to help shore up financial institutions

(64)

Chapter Summary

Total output is determined by:

the economy’s quantities of capital and labor

the level of technology

Competitive firms hire each factor until its marginal product equals its price.

If the production function has constant returns to scale, then labor income plus capital income equals total income (output).

(65)

Chapter Summary

A closed economy’s output is used for:

consumption

^investment

government spending

The real interest rate adjusts to equate the demand for and supply of:

goods and services

loanable funds

(66)

Chapter Summary

A decrease in national saving causes the interest rate to rise and investment to fall.

An increase in investment demand causes the interest rate to rise, but does not affect the

equilibrium level of investment

if the supply of loanable funds is fixed.

topic3 print Recent site activity Vu, Tuan Khai's personal website

National Income:

Where It Comes From and Where It Goes

Learning objectives

Learning objectives











Production process of a firm

Factors of production

The production function:

Y = F( K,L)







Returns to scale: A review

R e tu rn s t o s c a le : E x a m p le 1

R e tu rn s t o s c a le : E x a m p le 2

R e tu rn s t o s c a le : E x a m p le 3

Outline of model

















Assumptions

Determining GDP

The distribution of national income







Notation

W = nominal wage

R = nominal rental rate

P = price of output

W /P = real wage

R /P = real rental rate

W = nominal wage

R = nominal rental rate

P = price of output

W /P = real wage

R /P = real rental rate

How factor prices are determined







Marginal product of labor ( MPL)





MPL and the production function

Diminishing marginal returns





Demand for labor









MPL and the demand for labor

The equilibrium real w age

Marginal product of capital ( MPK)



Determining the rental rate











The equilibrium real rental rate

The Neoclassical Theory of Distribution





How income is distributed to L and K

The ratio of labor income to total income

in the U.S.,

₉

₉

₉

₉

₉

Notation: ^Δ = change in a variable