Ch3: National Income:Where it Comes From

and Where it Goes

Mankiw: Macro Ch 3Mankiw: Econ Ch24, Ch26Varian: Ch10, Ch19, Ch29

Williamson: Ch 7

Learning Objectives 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 how equilibrium in the goods market is

achieved

Outline of modelA closed economy, market-clearing model

Three markets Labor market: MPL=W/P Goods market:YS=Yd

(Financial market) Loanable funds market: S=I

Aggregate Supply side AS=YS=Production function

Aggregate Demand side AD=Yd=C+ I + G

Aggregate Supply Side:The production function describe relationship between inputs and output. Real Output (Y ，這章定義為大寫 ) Inputs: factors of production 生產要素 Y = F(K, L)

K = capital: tools, machines, and structures

L = labor: physical and mental efforts of workers

F(●) reflects the economy’s level of technology Assumes constant returns to scale

Returns to scale: 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

Examples

2 2

2

( , ) :

( , ) :

( , ) :

( , ) :

( , ) :

F K L K L CRS

F K L K L IRS

F K L KL CRS

F K L K L DRS

KF K L CRS

L

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

Notation

W = nominal wage Re = nominal rental rate P = price of output W /P = real wage

(measured in units of output) Re /P= real rental rate

W = nominal wage Re = nominal rental rate P = price of output W /P = real wage

(measured in units of output) Re /P= real rental rate

= change in a variable X = “the change in X ”

Marginal Product of Labor:

L

Y YMP

L L

K

Y YMP

K K

Marginal Product of Capital:

Diminishing marginal returns: diminishing MPL Suppose L while holding K fixed fewer machines per worker lower worker productivity

Youtput

Fig 3.3: MPL( K fixed ) Diminishing marginal returns

Llabor

F K L( , )

1

MPL

1

MPL

1MPL

As more labor is added, MPL

Slope of the production function equals MPL

Eg, Which of these production functions have

diminishing marginal returns to labor?

a) 2 15F K L K L ( , )

F K L KL( , )b)

c) 2 15F K L K L ( , )

Determination of factor pricesVarian: 19.7-19.9 and Appendix Factor prices are determined by supply and

demand in factor markets. Assume: Supply of each factor is fixed. Assume markets are competitive:

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

( , ) Re

K : Re

:K

L

Max PF K L K WL

FOC wrt P MP

FOC wrt L P MP W

Demand for labor

benefit = MPL cost = real wage

A firm hires each unit of labor if the cost does not exceed the benefit.

,

( Y) :

L L

L

WP MP W MP

PW

Profit Mazimization FOC wrt P MCMP

:

L

L

WMP

PW

MP demand for laborP

Fig 3.4:MPL = Demand for labor

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

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

Labor Market:the equilibrium real wage

Units of output

Units of labor, L

MPL, Labor demand

equilibrium real wage

Labor supply

L

Determining the rental rateMPK = Re/P :diminishing returns to capital:

MPK as K Firms maximize profits by choosing K

such that P ． MPK = Re . MPK curve is firm’s demand curve

for renting capital. (for one-time decision)

Neoclassical Theory of Distribution

total labor income =

If production function has CRS,

total capital income =

WL

P LMP L

ReK

P KMP

L KY MP L MP

laborincome

capitalincome

nationalincome

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

Labor’s share

of total income

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

(Hence, capital’s share is, too.)

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

(Hence, capital’s share is, too.)

Taiwan data: labor share (%)薪資報酬佔所得比例

0

20

40

60

80

100

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

年度

%

薪資報酬佔所得比例

Cobb-Douglas Production Function

A: the level of technology. (A is exogenous)

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

K

L

YMP AK L

KY

MP AK LL

1 1

(1 ) (1 )

1Y AK L

C-D Production Function C-D production function has

constant factor shares:

capital income = MPK x K = Y

labor income = MPL x L = (1 – )Y

= capital’s share of total income1- = labor’s share of total income

C-D Production FunctionProof that

--- Exhaustion of the product--- imply zero profits for competitive

firms in the LR.--- Since π=0 for all periods,

can ignore intertemporal analysis: profit maximization over-time

L KY MP L MP

Aggregate Demand Side:Demand for goods & services

Components of aggregate demand:AD = C+I+G+NX = C+I+G

C = consumer demand for goods & services

I = demand for investment goods

G = government demand for goods & services

(closed economy: no NX )

Consumption, C Disposable income

total income minus total taxes:

Yd=Y – T. Consumption function: C = C(Yd)

assume Yd C Marginal propensity to consume (MPC)

d

CMPC

Y

Fig 3.6: Consumption function

C

Y – T

C (Y –T )

1

MPCThe slope of the consumption function is the MPC.

Alternative ( 具個體化更完整的設定 ):Household’s intertemporal analysis: utility maximization over-time With micro-foundation:

refer to Ch16 and Varian: Ch10r ＝ the real rate of return for saving (the payment to compensate the deferment of C) = the real cost of borrowing

C = C(lifetime wealth, real interest rate)

= C (current income, future income, real interest rate)

Investment, IInvestment function: I = I (r ),

r :real interest rate, the nominal interest rate corrected for inflation.

Real interest rate近似 = Nominal interest rate – Inflation rate

Real and Nominal Interest Rates You lend out $100 for one year. P=$1/candy Nominal interest rate was 10%. During the year inflation was 6%. Present $100/$1= 100 units of candies $100*(1+10%)/[$1*(1+6%)]=103.7 units of candies Real return= 3.7 units, real rate of return= 3.7% Real interest rate （ real rate of return ）近似 = Nominal interest rate – Inflation rate= 10% - 6% = 4% ( r=R-π)

Investment function Real interest rate is

the cost of borrowing the opportunity cost of using one’s own

funds to finance investment spending. (for over-time decision)

So, r I

Fig 3.7: The investment function

r

I

I

(r )

Firm’s intertemporal analysis: profit maximization over-time With micro-foundation:

refer to Ch17 and Williamson Ch7

--- over-time decision rule: I=I(r)Cost of investment= r+δBenefit of investment = MPK

Earlier: one-time period decision rule:

1 1

, 1

t t t

K t

I K Y

MP r

ReKMP

P

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:

and G G T T

Goods market equilibrium Aggregate demand:

Aggregate supply:

Equilibrium:

The real interest rate adjusts to equate demand with supply.

( ) ( )dY C Y T I r G

( , )sY F K L

= ( ) ( )Y C Y T I r G

Saving and Investment in the National Income Accounts (1) GDP= Y=total expenditure Y = C + I + G + NXY = C + I + G + NX A closed economyclosed economy: no international trade Y = C + I + G → Y – C – G =IY = C + I + G → Y – C – G =I(2) GDP = Y = national income Y= C + G + S→ National Saving ： S= Y – C - G→ (3) For the economy as a whole, S = I

The Meaning of Saving and Investment National Saving 國民儲蓄 S = Y –C – G

the total income that remains after paying for consumption and government purchases.

Private Saving 私部門儲蓄 Sp ≡ Y – T – C the amount of income that households have left after p

aying their taxes and paying for their consumption. Public Saving 公部門儲蓄 Sg ≡ T –G the amount of tax revenue that the government has lef

t after paying for its spending.

Gov’t budget constraint (Gov’t BC): Surplus and Deficit （預算盈餘與赤字）

Sg≡ T –G >0 if T > G (budget surplus )Sg≡ T –G <0 if G > T (budget deficit)Budget Deficit ≡ D ≡ G-T = - Sg

Gov’t Bond （公債）： Bg Gov’t issue new bonds to finance Budget Deficit △B

g = D ≡ G-T ，亦即 Gov’t BC: G= T + △Bg

Flow vs. Stock The accumulation of past budget deficits =Public Debt （ Gov’t Bond ）

Flow 流量： I, education, S, D vs. Stock 存量： K, H, wealth, Bg

Market for Loanable Funds Financial markets

coordinate economy’s saving and investment

in the market for loanable funds. market for loanable funds. (( 可貸資金市場，可貸資金市場， LF)LF)

Supply and Demand for Loanable Funds

The supply of loanable funds (SLF ）＝ S (net)

The demand for loanable funds （ DLF ）＝ I

The price (of loan) in the LF market is

real interest rate. r=R-π

r ＝ the real rate of return for saving

= the real cost of borrowing

Supply and Demand for Loanable Funds SLF =S ： (+)vely-slpoed ， Qs

LF↑ =S ↑ as r ↑其實不一定是正斜率 Varian:Ch10

As r ↑ ， S ↑ ： if Substitution effect >Income effect As r ↑ ， S ↓ ： if SE <IE

Here we assume SE >IE, so r ↑→ S ↑( 課本忽略 r 對 C 與對 S 的影響，故設 SLF 為垂直線 )

DLF=I ： (-) vely-slpoed ， QdLF↓= I↓ as r ↑

r as the opportunity cost of investment.

LF Market equilibrium: the intersection of SLF and DLF determines r*.

Fig 3.12 Market for Loanable Funds

Loanable Funds(in billions of dollars)

0

InterestRate Supply

Demand

5%

$1,200

Copyright©2004 South-Western

Alternative setup (FYI)In equilibrium: Sp + Sg = I

You can set up the model asin equilibrium: Sp= I-Sg = I+ △BgSLF=Sp

DLF=I+△Bg=I+(G-T) The following comparative static analysis (△SLF ，△ DLF) would be different, but the result still be the same.

Comparative Statics ( 比較靜態 )

St = Yt-Ct-Gt = It

Kt+1=(1-δ)Kt+It δ: depreciation rate( 折舊率 )

St↑ → It↑ → Kt+1↑ → Yt+1↑

Government Policies that affect S and I ：1. Taxes on saving （利息所得稅）2. Tax credits on investment ( 投資抵減 )

3. Government budget deficits （預算赤字）

Policy 1: Saving Incentives

Taxes on interest income ： real rate of return = (1-t ） r t↑ reduce future payoff from current saving

→reduce the incentive to save. t↓ → increase the incentive to save:

QsLF↑ =S ↑ at any given r.

SLF curve shifts to the right.

r* ↓ ， QdLF ↑= I ↑

→ lower interest rates and greater investment.

Fig 3.9b An Increase in Supply of Loanable Funds

Loanable Funds(in billions of dollars)

0

InterestRate

Supply, S1 S2

2. . . . whichreduces theequilibriuminterest rate . . .

3. . . . and raises the equilibriumquantity of loanable funds.

Demand

1. Tax incentives forsaving increase thesupply of loanablefunds . . .

5%

$1,200

4%

$1,600

Copyright©2004 South-Western

Policy 2: Investment Incentives An investment tax credit （ 1-κ ） r

lowers the cost of borrowing

and increases the incentive to borrow. κ↑ ： Qd

LF↑ =I ↑ at any given r.

DLF curve shifts to the right.

→ higher interest rates

and greater saving/investment.

Fig 3.11 An Increase in Demand for Loanable Funds

Loanable Funds(in billions of dollars)

0

InterestRate

1. An investmenttax creditincreases thedemand for loanable funds . . .

2. . . . whichraises theequilibriuminterest rate . . .

3. . . . and raises the equilibriumquantity of loanable funds.

Supply

Demand, D1

D2

5%

$1,200

6%

$1,400

Copyright©2004 South-Western

Policy 3: Government Budget Deficits and Surpluses

I= S = (Y – T – C) + (T – G) = I= S = (Y – T – C) + (T – G) = Sp + Sg Gov’t budget deficit ： T< GT< G ， ， Sg<0

at any given r, QsLF↓ =S↓ < Sp when Sg<0

SLF curve shifts to the left.

→r*↑ ， LF*↓

higher interest rate and lower investment.

referred to as crowding out effect ( 排擠效果 ):

The deficit borrowing crowds out private investments.

Figure 3.9: The Effect of a Government Budget Deficit

Loanable Funds(in billions of dollars)

0

InterestRate

3. . . . and reduces the equilibriumquantity of loanable funds.

S2

2. . . . whichraises theequilibriuminterest rate . . .

Supply, S1

Demand

$1,200

5%

$800

6% 1. A budget deficitdecreases thesupply of loanablefunds . . .

Copyright©2004 South-Western

U.S. Federal Government Surplus/Deficit, 1940-2004

-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

1940 1950 1960 1970 1980 1990 2000

(% o

f G

DP

)

U.S. Federal Government Debt, 1940-2004

0%

20%

40%

60%

80%

100%

120%

1940 1950 1960 1970 1980 1990 2000

(% o

f G

DP

)

Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt. (Today it’s about 9 cents.)

Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt. (Today it’s about 9 cents.)

Taiwan data: 台灣政府收支淨額

Fig 26.5a台灣政府收支淨額

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

年度

百萬元 政府收入淨額

政府支出淨額

Taiwan data:台灣政府預算盈餘赤字與新增公債

Fig26.5b台灣政府收支餘絀（預算盈餘赤字）與新增公債

-500,000

-400,000

-300,000

-200,000

-100,000

0

100,000

200,000

300,000

400,000

500,000

600,000

年度

百萬元 政府收支餘絀

公債收入

Taiwan data ：公債餘額Fig 26.5c 政府公債餘額

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

年度

億元

政府公債餘額

The special role of rr adjusts to equilibrate the goods market and the loanable funds market simultaneously:

If LF market is in equilibrium, S=I → Y – C – G = I → Y = C + I + G

goods market is in equilibriumThus,

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

If LF market is in equilibrium, S=I → Y – C – G = I → Y = C + I + G

goods market is in equilibriumThus,

LF market

equilibrium

Goods market

equilibrium

Walras’ Law (Varian: Ch 29) If there are markets for k goods,

then we only need to find a set of prices where k-1 of markets are in equilibrium.

Here in our macro model, we have 3 markets, we only need 2 prices to assure general equilibrium:real wage and real interest rate

Chapter SummaryChapter 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).

CHAPTER 3 National Income slide 57

Chapter SummaryChapter 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

CHAPTER 3 National Income slide 58

Chapter SummaryChapter Summary A decrease in national saving causes the

interest rate to rise and investment to fall.

CHAPTER 3 National Income slide 59