Intermediate MacroeconomicsLecture 3 - Markets, Prices, Supply and Demand

Zsofia L. Barany

Sciences Po

2011 September 21

Summary of economic growth

I long-run models

I focus: potential output and its expansionI extensive model of growth, sources of growth:

I labour force ↑ - exogenousI technology ↑ - exogenousI capital ↑ - endogenous

supply side factors

I change in absolute level of Y ,K

I growth rate of per capita values of Y /L,K/L, equals thegrowth rate of technology, which is exogenous

I endogenous growth models - model the source oftechnological progress

New topic: Economic Fluctuations

I economies undergo significant short-run variations inaggregate output and employment

I at some times Y , L ↑, while U ↓I at others Y , L ↓, while U ↑

example: US recession of early 1980s1981 Q3 - 1982 Q3: Y fell by 2.9%, L fell by 1.3 percentagepoints, U increases from 7.4% to 9.9%1982Q3 - 1984 Q3: Y increased by 12.8%, L increased by 2percentage points, u back to 7.4%

I understanding the causes of these fluctuations is a centralgoal of macroeconomics

I first have to understand what the data tells us → FACTS

Business cycle facts I.

Fluctuations do not exhibit any simple regular or cyclical patterns

0

2000

4000

6000

8000

10000

12000

14000

1947 1953 1959 1965 1971 1977 1983 1989 1995 2001 2007

US GDP in billions of 2005$

Business cycle facts II.

Year and quarter # of quarters until Change in real GDP,of peak in real GDP trough in real GDP peak to trough

1948:Q4 2 -1.7%1953:Q2 3 -2.7%1957:Q3 2 -3.7%1960:Q1 3 -1.6%1970:Q3 1 -1.1%1973:Q4 5 -3.4%1980:Q1 2 -2.2%1981:Q3 4 -2.9%1990:Q2 3 -1.5%2001:Q1 3 -0.3%2007:Q4 6 -4%

Business cycle facts III.

Fluctuations are distributed unevenly across components of output:

Average share in fallAverage share in GDP in recessions

Component of GDP in GDP relative to normal growth

ConsumptionDurables 8.4% 15.6%Non-durables 25% 11.2%Services 29.5% 9.1%InvestmentResidential 4.7% 20.9%Fixed non-residential 10.7% 11.7%Inventories 0.7% 40.6%Net exports -0.4% -12.3%Government purchases 20.6% 3.3%

Business cycle modelling

I in the 70s fluctuations were interpreted as a combination ofdeterministic cyclesattempt to discern Kitchin (3-year), Juglar (10-year), Kuznets(20-year), and Kondratiev (50-year) cycles

I this has been abandoned as unproductiveexception: large seasonal fluctuations look similar to businesscycles in many ways

I modern macro: the economy is perturbed by disturbances ofvarious types and sizes at random intervals→ these disturbances then propagate through the economyfluctuations are the result of some stochastic process

I however, there is no consensus on what these shocks are andwhat the propagation mechanisms are

Modelling economic fluctuations

I describe a stochastic world, where shocks hit the economyI the models are based on

I competitive marketsI optimising agents

⇒ the economy is in EQUILIBRIUM

I micro-founded models

I fluctuations do not mean dis-equilibrium, this is the reactionof the economy to an outside shock

I short-term analysis

Markets

I market-process is modeled using the familiar supply anddemand approach

I in four markets:

1. the goods market2. the labour market3. the capital market4. the bond market

I analyse the factors that determine the supply and demand

I identify the market clearing conditions

I assume that households perform all of the functions in theeconomy

Money as a medium of exchange

I the exchanges on each of these markets use a single form ofmedium of exchange

I a medium of exchange is an object held, not for its own sake,but to facilitate trade, for example of goods and services

I here we call it money

I assume that money is just a piece of paper, a paper currencyissued by a government

I money is denominated in an arbitrary unit, such as a ”dollar”or ”euro”

I dollar amounts are in nominal termsI paper money earns no interest

I the sum of the individual holdings of money equals theaggregate quantity of money in the economy

I the aggregate quantity of money is assumed to be constant,for now

I the total money held by all households must equal thisconstant

Market 1: The goods market I.

I households sell all the goods they produce on the goodsmarket

I then they buy back from this market the goods that they wantI households buy goods

I for consumptionI for investment: to increase the stock of goods in the form of

capital used for production

I the price in this market, P, expresses the number of dollarsthat exchange for one unit of goodP is the price level

I Y = A · F (K , L), all of these goods are sold on the goodsmarket ⇒Y also represents the quantity of goods per year sold andbought on the goods market

Market 1: The goods market II.

I PY is the dollar value of the goods traded on the goodsmarket

I for a seller of goods, the price level, P, is the number ofdollars obtained for each unit of good sold

I for a buyer, P is the number of dollars paid per unit of good

I P dollars buy 1 unit of good, 1 dollar buys 1/P units of goods

I 1/P is the value of 1 dollars in terms of the goods that it buys

I M dollars exchange for

M · 1

P=

M

P

I M/P is in real terms, in units of goods, whereas a quantitylike M is in dollar or nominal terms

Market 2: The labour market

I households supply labour on the labour market

I assume that the quantity supplied, Ls , is a constant, Lfor now we assume that everyone has one unit of labour andthey all supply this one unit of labour

I in exchange for one unit of labour, they receive the dollar ornominal wage rate, wi.e. they sell their labour

I the real wage rate is w/P, this is the amount of goods theycan buy from their wage

Market 3: The rental market

I each household rents out all of the capital that it owns on arental market

I think of the capital offered on the rental market as the supplyof capital services, K s

I since we assumed that each household rents out all of itscapital ⇒ K s = K

I households rent out capital, K , for dollars at the dollar ornominal rental price, R

I a household that rents the amount of capital Kd pays thenominal amount RKd

in exchange for using the capital as an input to production

I the real rental price is R/P

Market 4: The bond market I.

I if a household wants to consume more than his income, theycan borrow from another household

I borrowing households receive a loan from another household,whereas a lending household provides a loan to anotherhousehold

I a household that gives a loan receives a piece of paper calleda bond→ the market on which households borrow or lend is the bondmarket

I the principal is the unit of the bond, i.e. the face amount

Market 4: The bond market II.

I the holder of a bond, the lender, has a claim to the amountowed by the borrower

I assume that one unit of bond commits the borrower to repay1 dollar to the holder of the bond→ 1 dollar is the principal of this bond

I a unit of bond commits the borrower to pay the holder a flowof interest payments of i dollars per year

I i is the interest rate, which is the ratio of the interestpayment, i , to the principal 1

I the interest rate, i , can vary over time

Constructing the budget constraint

I the budget constraint describes the household’s possibilities interms of fund allocation:

I flows of income are sources of fundsI purchases of goods and assets are uses of funds

I the total sources of funds must equal the total uses of funds

I this equality is called the household budget constraintI the sources of income are:

1. profits from business activities2. wage income3. rental income4. interest income

Sources of household income I.

Profits an excess of revenue over costs in their businessactivity

π = PY︸︷︷︸revenue

− wLd︸︷︷︸labour costs

− RKd︸︷︷︸capital costs

= P · A · F (K , L)− (wLd + RKd)

Wages the amount they sell their labour for

wLs = wL

w - nominal wage rateLs = L - households supply all of their labour

Sources of household income II.

Rental income the net income from renting out their capital

RK s − PδK s = RK − PδK =

(R

P− δ)PK

R - nominal rental rateK s = K - households supply all of their capitalδ - real depreciation rate(RP − δ

)- the rate of return on owning capital

Interest income income from lending money to other households

iB

i - interest rateB - nominal bond holdings

Uses of household funds I.

Consumption households consume goods

PC

P - price; C - quantity

Assets households use their savings to buy

1. money, M2. capital, K3. bonds, B

Uses of household funds II.

I M - assume this is fixed

I decision between K and B - what does it depend on?

I rate of return on two assets has to be equal, otherwise hhwould only hold one type of asset

i =R

P− δ

I nominal value of assets: M + PK + B

I nominal savings are spent on buying additional units of assets

nominal savings = ∆M + P∆K + ∆B

Uses of household funds II.

I M - assume this is fixed

I decision between K and B - what does it depend on?

I rate of return on two assets has to be equal, otherwise hhwould only hold one type of asset

i =R

P− δ

I nominal value of assets: M + PK + B

I nominal savings are spent on buying additional units of assets

nominal savings = ∆M + P∆K + ∆B

The household budget constraint

The household budget constraint in nominal terms:

nominal spending = nominal income

PC + ∆M + P∆K + ∆B = π + wL + iB + (RP − δ)PKPC + P∆K + ∆B = π + wL + i(B + PK )

The household budget constraint in real terms:

cons + real savings = real income

C + ∆K + ∆BP = π

P + wP L + i(BP + K )

 

1 - only C , ∆K + ∆BP = 0

2 - only ∆K + ∆BP , C = 0

3 - a point on the budget constraint

Market clearing and wage rates

As stated in the beginning all agents behave optimally:

I firms maximize their profits, when deciding how manyemployees to have at a given wage rate, w :

∂ πP

∂L= A · FL(Kd , Ld)− w

P= 0

⇒ the real wage, w/P = MPL

I people supply all their units of labour

Ls = L

I the labour market clears:

Ld = Ls = L⇔ w

P= A · FL(Kd , L)

w/P s. t. quantity of labour demanded = quantity supplied

 

Market clearing and rental rates

I firms maximize their profits, when deciding how much capitalto rent at a given rental rate, R:

∂ πP

∂K= A · FK (Kd , Ld)− R

P= 0

⇒ the real rental rate, R/P = MPK

I in the short run the aggregate capital stock, K , is given bythe past investment flows

K s = K

I the labour market clears:

Kd = K s = K ⇔ R

P= A · FK (K , Ld)

R/P s. t. quantity of capital demanded = quantity supplied

 

The profit in equilibrium I.

π

P= A · F (K , L)− A · FL(K , L) · L− A · FK (K , L) · K

Assuming (as we did until now) that F (K , L) is homogeneous ofdegree one:

Y = A · L · F(K

L, 1

)⇒ MPK =

∂Y

∂K= A · L · FK

(K

L, 1

)1

L

similarly

Y = A · L · F(K

L, 1

)⇒

MPK =∂Y

∂L= A · F

(K

L, 1

)+ A · L · FK

(K

L, 1

)(−K

L2

)

The profit in equilibrium II.Payments to capital:

MPK · K =(A · L · FK

(KL , 1)

1L

)K

= A · FK(KL , 1)K

Payments to labour:

MPL · L =(A · F

(KL , 1)

+ A · L · FK(KL , 1) (− K

L2

))L

= A(L · F

(KL , 1)− FK

(KL , 1)K)

The profits are:

πP = A · F (K , L)− w

P L−RPK

= A · F (K , L)−MPL · L−MPK · K= A · F (K , L)− A

(L · F

(KL , 1)− FK

(KL , 1)K)− A · FK

(KL , 1)K

= A[F (K , L)− L · F

(KL , 1)

+ FK(KL , 1)K − FK

(KL , 1)K]

= A[F (K , L)− ·L · F

(KL , 1)]

= 0

Profits are zero.

Homework

1. Everyone should choose a country (OECD for data):I look at the real GDP growth over the last 60 yearsI look at the overall trend, and spot the recessionsI look at how the GDP is divided between different uses (i.e.

consumption, investment, government spending, net exports)I bring the numbers with you for the next lecture

2. Hand in Q 1.4 and 1.10 from the Romer book no later thannext Monday, the 26th of September.

I you have to solve the problems like we did in class, i.e.mathematically

I hint: always express k , and try to find the k∗ for which k = 0