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1Macroeconomics I (IG). Topic 2. Javier AndrMacroeconomics I (IG). Topic 2. Javier Andrééss

Macroeconomics I International Group

Course 2004-2005

Topic 2: THE DETERMINANTS OF NATIONAL INCOME.

THE LONG RUN


• What determines the amount of goods and services produced in an economy in a period of time?

• How are incomes generated in the production process distributed among the owners of productive factors?

• Consumption, saving and investment decisions.

• What can the public authorities do to increase output?

Learning objectives

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Topic Outline


• In this Topic we take a long-run perspective. In doing so we may answer these questions by looking at the demand and the supply sides of the economy independently from each other.

• This is not what we shall usually find in macroeconomics, which is about how aggregate markets interact. As we know from microeconomics it takes both the demand and the supply side of one particular market to determine the equilibrium prices and quantity traded.

• NOTE: With flexible prices the aggregate supply curve is vertical; output is determined by the supply side alone, and equilibrium prices for that level of output are determined by the demand side. This makes it possible to conduct an independent analysis of aggregate supply and demand.

Learning objectives

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Aggregate markets in the long run

Aggregate (long-run) demand and supply

Supply and demand in a single market


• Since marginal costs rise with ouput, the supply curve of a firm is upward sloping. Recall that the supply curve reflects how the firm’s production reacts to changes on its relative price: P(j)/P

• If each single firm increases output as prices rise, why does the aggregate curve reflect that aggregate output does not change when the aggregate price rises?

From microeconomics to macroeconomics

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• Notice that when the aggregate price rises, we are assuming thatall individual prices rise in a similar proportion. Thus relative prices do not change and individual firms do not find it optimalto change production.

• When the relative price rises, a firm finds that its revenue rises faster than its costs. Thus it is optimal to increase output. If all prices rise in a similar proportion the firm knows that its costs will rise as much as its revenues, thus there is no incentive tochange production.

• This is why in an economy with flexible prices, a change in aggregate demand leads to a change in all prices with no reaction of aggregate output: the aggregate supply curve is vertical under flexible prices.

From microeconomics to macroeconomics


• Under flexible prices (the long run) real variables are determined on the supply side of the economy (nominal variables are determined by the amount of money in the economy).

The ‘classical dichotomy’


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The ‘classical dichotomy’Real variables are determined independently of the amount of money in

circulationThis is what we learned in microeconomics. If all prices change in the same proportion, so does nominal income, and individual households and firm’s decisions are left unaffected.

Nominal variables (P, W, R) are determined by the amount of moneyThe CPI is the inverse of the price of money. Thus as the amount of money in circulation

grows, its price falls and the CPI rises

Real wages, the rental cost of capital, employment, capital and output are determined by the conditions of the supply side

The real interest rate r is determined by the (real) decisions of saving and investment

This the decision of how much to spend today and how much to leave for tomorrow (saving)


Inflation and growth in the OECD

TUR

ICE

J APSWI

NZE

FRA FINDEN

GER NETBEL

AUL

LUX

GRE

SP AITA

NORIRE

P OR

CAN AUT

UK

SWEUSA

0

5

10

15

20

25

30

35

40

1 2 3 4 5 6

Per capita income rate of growth

Infla

tion

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How we organize the study of the long run

• In this Topic we study:– The determination of real variables: output,

employment, factors income, etc. We focus here on the supply side of the economy.

– The determination of the real interest rate: the market for ‘loanable’ funds (the saving-investment decision).

• We leave aside until Topic 3 the study of the interaction between the amount of money and prices in the money market.


The aggregate supply• The aggregate supply is the relationship between the price level

and the amount of goods and services that the firms in an economy are willing to produce in a given period.

• To establish this relationship we consider the following elements:– Output depends on the amount of inputs (factors of

production) available as well as technology. We summarize this relationship in the PRODUCTION FUNCTION

– Technology depends on the general knowledge accumulated by the society. Its evolution (rate of change) is called TECHNOLOGICAL PROGRESS

– The amount of inputs used in production depends on their availability as well as on the decisions of the firm: (SUPPLY AND DEMAND) FACTORS MARKETS

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• The production function relates output with inputs. It shows how much output (Y ) the economy can produce using K units of capital and L units of labor. It is a technological relationship not an economic one, and can be represented as:

( , , )Y F A K L=

The aggregate supply: The production function

• K, L: represent the amount of capital and labor used.Why we do not include intermediate inputs in the production function?A: reflects the ‘state of the art’ of technological knowledge. Is technological knowledge a productive factor? Why is it different from K and L?


The production function

( , , )zY F A zK zL=

( ,0, ) ( , ,0) 0F A L F A K= =

( , , ) 0

( , , ) 0

F A K LL

F A K LK

∂>

∂∂

>∂

2

2

2

2

( , , ) 0

( , , ) 0

F A K LL

F A K LK

∂<

∂∂

<∂

• Constant returns to scale

• Both factors of production are necessary

• Marginal products are positive and decreasing:

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The production function for a given level of capital

1) Y rises with L. L rises with Kand A.

2) The ratio (∆Y/∆L) is positive

3) The ratio (∆Y/∆L) is decreasing in L

The production function


The long run• As we discussed in the previous Topic, the long run

has two dimensions: – A notional one: all prices and wages are fully flexible and all

markets clear.– A time dimension: as time goes by the capital stock,

population growth and technological knowledge improves. • We shall concentrate on the first dimension, and thus

we shall assume that:– A is constant (normalized to A=1)– Capital supply is given– Labor supply is given

• Thus, the key decision is how much of the available capital and labor to use.

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The labor market: labor demand

• The MPL is decreasing in L

• The firm demands L* that satisfies MPL (L*)=(W/P)– L(-): MPL (L(-))>(W/P)– L*: MPL (L*)=(W/P)– L(+): MPL(L(+))<(W/P)

• Increases in K and A shift the marginal product of labor rightwards so that the firm is willing to demand more labor: L(+)


• If the labor demand falls from L1 to L2, the use of labor input does not fall if the real wage adjusts downwards from (W/P)1to (W/P)2.

• If the real wage adjusts: there is NO UNEMPLOYMENT

• Autonomous changes in the price level do not affect the real wage if the nominal wage adjusts in the same proportion.

1

1

10 15 552 3 1

10 14 425 7 2

WPWP

= = = =

= = = =

The labor market: equilibrium

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The capital market: capital demand

• The MPK is decreasing in K

• The firm demands K* that satisfies MPK (K*)=(R/P)– K(-): MPK (K(-))>(R/P)– K*: MPK (K*)=(R/P)– K(+): MPK(K(+))<(R/P)

• Increases in L and A shift the marginal product of capital rightwards so that the firm is willing to demand more capital: K(+)


• If capital demand falls from K1 to K2, the use of labor input does not fall if the rental cost adjusts downwards from (R/P)1 to (R/P)2.

• If the rental cost adjusts there is full CAPITAL UTILIZATION.

• Autonomous changes in the price level do not affect the real rental cost if the nominal rental cost adjusts in the same proportion.

The capital market: equilibrium

1

1

20 30 10102 3 1

18 36 663 6 1

RPRP

= = = =

= = = =

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Under flexible prices and wages a rise in P does not change the use of labor

• If P rises for some reason (because nominal aggregate demand rises for instance), this tends to reduce the real wage (W/P) thus increasing labor demand.

• At this new real wage, labor demand is higher than labor supply.

• This induces a rise in the nominal wage until the labor market clears at the same real wage as before (but with higher P and W).

• Thus the use of labor is not altered.

The aggregate supply curve is vertical


Under flexible prices and wages a rise in P does not change the use of capital

• If P rises for some reason (because nominal aggregate demand rises for instance), this tends to reduce the real rental cost (R/P) thus increasing capital demand.

• At this new real rental cost, the capital demand is higher than capital supply.

• This induces a rise in the nominal rental cost (R) until the capital market clears at the same real rental cost as before (but with higher P and R).

• Thus the use of capital is not altered.


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• If P rises, the amount of output that firms are willing to produce does not change.

• Their marginal revenue and marginal cost rise by the same amount in nominal terms.

• They find it optimal to produce the same amount of output as they did before the price rise.

• Aggregate output does not change if all prices (P, W, R) are fully flexible and adjust.




( )

( )

,

,

( , )

d d WP

sd

d d RP

sd

s

L L K

L L L

K K L

K K K

Y F K L Y

== = = = =

= =

Changes in P have no real effect on L, K, Y, W/P, R/P:formal analysis

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From production to income: Income distribution• The total value generated in the production process minus the

payment to productive factors are the aggregate profits:

PY profits WL RK− = +

( ) ( )L LPY profits P MP L P MP K− = +

,L KW RMP MPP P

= =

• But we know that factors are paid according to their marginal product:

• Thus:


Income distribution

• But recall that CRS functions have the following property

( , ) L KY F K L MP L MP K= = +

• Thus, combining all previous results we have that:

0L KW Rprofits Y L K Y MP L MP KP P

= − − = − − =

• Check this property for the following function:(1 )( , )Y F K L K Lα α−= =

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• Thus,

W RY L KP P

= +

Income distribution

• Under constant returns to scale the payment to productive factors exhausts total output. There are not extraordinary profits (over and above the remuneration for the service of capital).


• Households are the owners of the factors of production (K, L) and perceive income (Y).

• They use their income: – To pay taxes (T). After tax income (Y-T) is called

disposable income and may be used:– To purchase goods and services today: Consumption

(C).– To accumulate for the future: Saving (S).

From income to spending: the uses of income

Y C S T= + +

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• Aggregate output produced by firms becomes aggregate income earned by households.

• Income in turn becomes spending which constitutes aggregate demand.

• In equilibrium aggregate supply and aggregate demand are equal. Thus we shall close the circle: income equals spending, which equals output, which equals income ....

• But there is something missing in this chain. Households only spend a fraction of their income: consumption. Neither taxes nor saving involve the purchase of goods and services.

• Thus, where does the rest of spending come from, so that all output produced (Y) is demanded?

From income to spending: aggregate demand


• Consumption (C): Purchases of goods (durable and non-durable) and services by households.

• Investment (I): Purchases of equipment and buildings by firms.

• Public spending (G): Purchases of goods and services by the public sector (this does not include transfers).

From income to spending: aggregate demand

The components of aggregate demand: total spending

Y C I G= + +

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Consumption depends mainly on disposable income

Aggregate demand: consumption

( )C C Y T= −

The marginal propensity to consume (MPC) reflects by how much consumption increases with each new euro earned:

CPMCY

∆=∆


Private investment depends mainly on the real interest rate: r

Aggregate demand: investment

1) The real interest rate approximates the user cost of capital and represents the opportunity cost of those funds spent on investment goods.

2) Investment also increases if the prospects of future profits improve.

( )I I r=

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1e

t t

t

P Pr iP

+ −≈ −

• Let us assume that I borrow 100€ in 2004 to be repaid in 2005. The nominal interest rate (i) is 5%. The 2004 CPI is 40 and is expected to be 41 in 2005.

• The true cost of the loan is given by the ratio:

How much do I have to pay in 2005/How much have I borrowed in 2004

• The real interest rate (r) is approximated as the difference between the nominal rate (i) and expected inflation (πe).



• Gross nominal interest rate

1 0 0 (1 0 .0 5) 11 0 0

i+ = +

• Gross real interest rate

1 0 0 (1 0 . 0 5 )1 . 0 54 1 1 . 0 2 51 0 0 1 . 0 2 5

4 0

+ = ≈


• Net real interest rate er i π= −

2 0 0 4

2 0 0 3

(1 ) 1 1 ( )1

ee

i i iPP

ππ

+ + = ≈ + − +

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• Public spending: purchases of goods and services (consumption goods or equipment) made by the public sector.

• Public transfers are not public spending. They are considered as‘negative taxes’. As far as aggregate demand or total spending is concerned, public spending and transfers are very different: – An increase in public spending increases total spending– An increase in public transfers may or may not increase public spending,

depending on the use that the recipients of such transfers make of them.

• For most of this course we shall assume that public spending is exogenously given and any changes are considered as policy decisions. The implications of alternative ways of public spending financing (taxes, public debt) shall be analyzed in Macro II.

Aggregate demand: public spending


• Aggregate demand may be expressed as:

Aggregate demand and supply equilibrium

( ) ( )DY C Y T I r G= − + +

( ) ( )Y C Y T I r G= − + +

• Aggregate demand equals aggregate supply in equilibrium. We shall assume that the goods and services market clears. Thus,

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Note

• Notice that, because of the equilibrium condition, Y represents not only output and income but also spending. Thus we shall refer toany of these indistinctively. We shall also use Y to refer to aggregate demand and aggregate supply. This is not a lack of imagination. We do it on purpose to remind ourselves that we areanalyzing the joint determination of variables, which interact in different markets.

• Although they are equal in equilibrium, they are not conceptually the same. Output (Y) is what the firms in the economy produce, income (Y, also) is what the owners of the factors of production (labor and capital) are paid for the use of these, and spending (Y, again) is the total amount spent, by households, firms and the government, in purchases of goods and services.



}{( ) ( )Y C Y T I r G r= − + + ⇒

• As much as we had to study the labor and capital market to understand how production is carried out and incomes earned, we must also study the goods market.

• In a decentralized economy demand and supply decisions are made by different agents independently of each other. Equilibrium in factor markets is achieved because factor prices are flexible and move to eliminate any excess demand or supply.

• Equilibrium in the goods market. Notice that output is given by the supply side, taxes and public spending are exogenous. Thus the only remaining (endogenous) variable that may adjust to bring the goods market equilibrium about is the real interest rate (r).

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( )

( ) ( )

( ) ( )

Y C I r G

Y C Y T S Y T T

S Y T T G I r

= + +

= − + − +

− + − =

How do we explain that the real interest rate adjustment ensures the goods market equilibrium? The market for ‘loanable’ funds


( )S T G I r r+ − = ⇒

Saving (private, S, plus public, T-G) equals investment (I)


• The goods market equilibrium can also be viewed as the total saving-investment equilibrium. Movements in the interest rate ensure that part of the income that households withdraw from spending (S+T) is transferred to other agents with no income, who spend it in goods and services (G+I).

• Aggregate supply and demand equilibrium is the same as the saving-investment equilibrium. Total savings constitutes the supply of ‘loanablefunds’, whereas investment is also the demand for ‘loanable funds’. Supply does not depend on the interest rate (although it might, as we shall see later) but demand always does. The real interest rate moves to clear this market, thus ensuring aggregate demand and supply equilibrium of goods and services as well.

• NOTE. This argument should make it clear that the interest rate is not the price of money (as it is commonly named) but the price of loans. Most people get confused since loans are usually made in money. You may borrow 100 tons of wheat today and promise to return 105 tons of wheat tomorrow. No money would be involved in the transaction but the interest rate would still be 5%.


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(( ), ) ( )S Y T r T G I r− + − =

So far we have assumed that consumption only depends on income. However the real interest rate may also affect the consumption/saving decision. In such a case, the equilibrium can be represented as:



The determinants of the real interest rate

Oferta y demanda agregadaImprovement

in expectations:Both I and r rise

Reduction in public saving(G rise or T cut):r rises and I falls

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Deficit and real interest rates in EMU

-0.04

-0.02

0

0.02

0.04

0.06

0.08

70 74 78 82 86 90 94 98

T

Tipo

de

inte

rés

real

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

Supe

rávi

t /PI

B

T ipo de interés real Superávit /PIB

Rea

l int

eres

t rat

e

Surp

lus/

GD

P

Real interest rate Surplus/GDP


0.02

0.03

0.04

0.05

0.06

0.07

0.08

tipo

de in

teré

s re

al

-0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01

superávit(+)/déficit(-) (sobre PIB)

70

71

7273

74

75

76

77

78

79

80

8182

83

84

85

86

8788

89

90

9192

9394

95

96

97

Rea

l int

eres

t rat

e

Deficit (-) Surplus (+)/GDP

Deficit and real interest rates in Spain

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( )

( ) }{

,

, , , , ,

( , )

d d WP

sd

d d WR RP P P

sd

s

L L K

L L L

K K L K Y L

K K K

Y F K L Y

== = = ⇒= =

= =

}{( )d

d s

Y C I r Gr

Y Y Y

= + + ⇒= =

}{

( , ) , ( , )

s dM M i Y P W R

P P

= ⇒Nominal variables (P, W, R)

are determined by the amount of money circulating

The real interest rate r is determined by the decisions

of saving and investment


Real variables are determined independently of the amount of

money in circulation

W/P, R/P, L, K Y are determined by the conditions

of the supply side


• The level of output (aggregate supply) is determined by the amount of capital and labor and by the level of technological knowledge available in the economy. Aggregate supply is independent of the price level.

• Factors of production are paid according to their marginal product. Labor income plus capital income exhaust the value of output.

• Part of the income is used to pay taxes. The remaining amount of income (disposable income) is used for consumption or is saved.

• Total spending (aggregate demand) is made by households (consumption) firms (investment) and the public sector (government spending).

What have we learned?

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What have we learned?• The goods and services market clears: aggregate demand equals

aggregate supply.

• The mechanism that ensures that aggregate demand equals aggregate supply is the adjustment in the real interest rate. Adjustments in the interest rate ensure that total savings (private saving plus the public surplus) equal investment.

• The real interest rate depends on saving and investment decisions. A fall in either private or public saving raises the real interest rate and reduces investment.

• An improvement in firms’ expectations raises the real interest rate and investment.

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