Lectures in Macroeconomics

1 Bachelor 2nd year Course of J. Hellier 20 hours;

Lectures in Macroeconomics (short term macro-equilibria and disequilibria)

2

Synopsis The purpose of this course is to introduce the students to macroeconomic analyses in the short term and to its implications on stabilising policies. A usual distinction is made between (i) the ‘classical approach’ in which all markets are perfectly competitive and the adjustment is quickly brought about through prices, and (ii) the ‘Keynesian approach’ in which prices are downward rigid and adjustment is realised through quantity on the demand side, generating thereby equilibria with unemployment. The impacts of monetary and fiscal policies are analysed within both approaches. The analysis is firstly made by assuming a closed economy, which reveals the major macro-mechanisms. It is subsequently extended to the case of open economies. The general introduction defines macroeconomics and its two conceptions, directly global or by aggregation of micro-functions.The conditions for aggregation are discussed. The course is subsequently divided into three parts. Part 1 presents the agents and the markets, i.e., the foundations of macromodelling. Part 2 exposes the traditional classical approach (perfect price adjustment and perfect competition) and its major outcomes. The third Part presents the traditional Keynesian approach which is characterised by downward price rigidity and by demand-constrained production.

3

Slide 1 Content, Introduction, Agents and Markets

4

Content Introduction (3hs): Central issue: How does a market economy works ? / What is Macroeconomics: 2 conceptions. / The global approach and its limits. / The approach by aggregation of micro-functions and its shortcomings: Nataf theorem and representative agent. / Mathematical bases.

1

Agents, markets and economic policies (5 hs)

1.1. Agents a) Households / b) Firms / c) Public agent / d) Abroad 1.2. Agents’ accounts a) Agents accounting / b) Markets / c) Walras law 1.3. Adjustment, agents’ behaviours and general equilibrium a) Adjustments in a market economy/ b) Agents behaviours 1.4. Economic policies and exchange rate regimes a) Monetary policy/ b) Fiscal policy / c) Policy mix/ d) Exchange rate regimes

2

Perfect price adjustment: the ‘classical’ approach (7 hs)

Introduction : General philosophy of the ‘classical’ approach 2.1. Macro-equilibrium in a closed economy a) General architecture / b) The labour market and the real wage / c) General ‘real’ equilibrium / d) The money and the nominal equilibrium. 2.2. Macroeconomic policies in the ‘classical’ approach a) Monetary policy and inflation / b) Fiscal policy and crowding out effect. 2.3. Open economy a) Monetary approach to the payments / b) Exchange rate regimes and independence of national economic policies / c) Stabilising speculation Conclusion: Limits and extensions of the classical approach

3 Adjustment through quantities: the basic Keynesian approach (7hs) Introduction : the Keynesian pattern 3.1. The IS-LM model with fixed prices a) The market for goods & services and the IS relation / b) The market for money and the LM relation/ c) Equilibria and unemployment 3.2. Macroeconomic policies a) Policy multipliers / b) Full employment policies. 3.3. The Mundell-Fleming approach a) General architecture / b) Exchange rate regimes and capital mobility / c) Economic policy Conclusion: Limits and extensions of the Keynesian approach.

5

1. Aggregation and the representative agent (from micro to macro) n agents depicted by i. Micro-functions: yi  fi ( xi ) , i  1...n Macro-functions: Y  F ( X ) with Y   yi and X   xi . i

i





 Find a function Y = F(X) such that F   xi    fi ( xi ) , xi , i  1...n .

 i  i In most cases, it is impossible, e.g., yi  axi ; yi  ai xi ; yi  axit ; yi  log xi etc. Cases in which it is possible:

1. Affine functions with the same slope for all agents (Nataf theorem) : yi  axi  bi   yi  a xi   bi  Y  aX  B, B   bi i

i

i

i

2. The distribution of X across agents is unchanged: xi  ai X Y   yi   fi  ai X   F ( X )   fi  ai X  i

i

i

Function F(X) can be very complex…

3. Representative agent: all agents i are identical  xi  x  X / n et fi  f , i  1...n . hence: Y   yi   fi ( xi )  n  f ( X / n)  F ( X )  n  f ( X / n) . i

i

In addition, when function f() is homogenous of degree 1: Y  f ( X ) . Limit: The representative agent is not the average agent  This assumption is convenient to simplify the analysis and to have micro-foundations, but it impedes to analyse the economic issues and dysfunctions linked to agents’ heterogeneity.

4. Heterogenous agents Heterogeneity is introduced, e.g., differences in skills and productivity across individuals, differences in technology between firms etc. This typically makes the analysis more complex because it creates different types of agents who act differently.

6

2. Notations A value with a subscript + is a supply ; a value with a subscript – is a demand. * indicates foreign values (P is the price of domestic product and P* that of foreign product). A small letter with an overdot is a rate of variation of a capital. If Y is the real income, y = is the rate of variation (growth rate) of Y. t depicts time (or period) t.  indicates a variation in discrete time and d●/dt a variation in continuous time We denote :

Y (Y  ,Y  ) , the real product (and the real income). C, I

Real total consumption and real total investment

G

Real public expenditures

T

Taxes ( T j is the tax paid by agent j)

 ( w , c )

Tax rate (on income, on consumption)

L ( L , L )

Labour,

K

Capital (stock of)

S

Savings



Profits

M (M , M  ) B

Money

Financial assets = Bonds ( B  variation in bonds)

B & B Supply and demand of NEW bonds over a period of time.

IM, X,

Real imports and exports

BE

Trade (goods & services) balance (surplus or deficit) ( BE  P  X  E  P *IM )

W

nominal wage

P,

General price index (product)

Pi , r

Price of i Interest rate

E

Exchange rate (amount of domestic currency for one unit of foreign currency)

7

ECAP, SCAP BC

Entry and exit of capital (with foreign countries) Capital account with foreign countries balance (BC=ECAP–SCAP)

RES

monetary reserves (reserves of foreign currency)

Subscript M depicts households, F firms and G the public authorities (government).

Nominal and real values A real value is a quantity in volume or purchasing power. A nominal value is the price of this quantity. Examples: 1) Y is the real product and P  Y the nominal product. PY, PC, PI et PG are nominal product, nominal consumption, nominal investment, and nominal public expenditures (assuming that all those aggregates have the same price). 2) The real wage :  = W / P est le salaire réel (en pouvoir d’achat). 3) r is the nominal interest rate and  such that   =

P 1+ r the (1 + r) = P' 1+ p

real interest rate, 1  p  P '/ P, p being the inflation rate.



r  p when r and p are sufficiently close to 0 (ebetween -0,1 and 0.1).

Explanation: invest S at the nominal interest rate r at the present period. the period after, I receive (1+r)S. At the present period, the purchasing power of S is S/P. and at the period after, the purchasing power of (1+r)S is (1+r)S/P’. The real interest rate is then:



(1  r )S / P ' S / P P 1 r  (1  r )  1   1 with P '  P(1  p) S/P P' 1 p

8

3. Mathematical bases

1. Derivatives Partial and total derivatives

y  f ( x1, x2 , , xn ) Partial derivatives (direct effect): f  0  f increases with xi xi

f x ( x) 

f xi

f  0  f decreases with xi xi

Total derivative (sum of the direct and indirect effects) : Total differential: df   i

n df f dx j  dxi j 1 x j dxi

f dx xi i

Usual derivatives Functions ax  b xn log x exp x f ( x )  g ( x)

Derivatives a nx n 1 1/ x exp x f x ( x)  g ( x)  g x ( x)  f ( x)

f  g ( x) 

f g ( g )  g x ( x)

log  f ( x)

f x ( x) / f ( x)

exp  f ( x)

f x ( x)  exp  f ( x)

f ( x) g ( x)

f '( x)  g ( x)  g '( x)  f ( x)

 g ( x) 

2

9

Growth rates Production at time t with growth rate 

growth rates Discrete time

y (t ) 

Y (t )  Y (t  1) Y (t  1)

continuous time

y (t ) 

Y dY / dt  Y Y (t )

We denote y = the rate of growth of Y : y 

Yt  Y0  (1   )t Yt  Y0  e t

 logY Y / t  t Y

Rate of variation of a product (see: log-linear functions) :

Y  A  X11  X 22 

 X n1n  y  i  xi i

rate of variation of a sum : Y  A   ai . X i  y   qi  xi , i

i

avec q j 

ajX j A   ai X i i

Rate of variation of an exponential

Y  Ae xt  y  dY / dt  x Y Ae xt is a continuous dynamics with the constant growth rate x.

2. Homogeneity f ( x1, x2 , , xn ) is homogenous of d°k  f ( x1,  x2 , ,  xn )   k f ( x1, x2 , , xn ) .

Two important applications: Homogeneity of degree zero: Prices and nominal income in demand functions Homogeneity of degree 1: Constant return to scale in production functions.

10

3. Optima f ( x) is continuous and derivable in ithe interval I 

.

Maximum: f '( x)  0 et f "( x)  0 (concave function) Minimum: f '( x)  0 et f "( x)  0 (convex function). f ( x)  has a maximum (minimum) in xˆ in Theorem: Function f ( x) : x  the interval I  . Let function g ( z ) be continuous, monotonous and increasing in z in the interval f ( I )  . Then, function g  f ( x)  has a maximum (minimum) in xˆ .

Application: Function f(x) can be transformed by function g  f ( x)  by keeping the same optima. This is convenient when g  f ( x)  is easier to analyse than f(x). Example of the CES utility function: u  ax1  (1  a) x2  is easier to analyse than u   ax1  (1  a) x2  

1/ 

Constrained maximisation max f ( x, y ) x, y

s.t. :

y  g ( x)

f 2 f f 2 f with: f x   0 ; f xx  2  0 ; f y   0 ; f yy  2  0  f concave y y x x g gx  0 x

f(x)

Transformation: h( x)  f  x, g ( x) max h( x)  hx  f x  f g ( x )  g x  0  xˆ  yˆ  g ( xˆ ) . x

11

4. Functions’ profiles (curves) 1 Recall: x   x

y=ax+b, a > 0

x=b b

y=b b y=ax+b, a < 0

b

b

concave

b

convex

c

concave

convex

12

4. Agents

Agents

behaviours - Labour supply - consume and save (demand for goods && services)

Households

- Saving and demand for financial assets - Cash holdings (demand for money) - Produce goods & services

Firms

- Demand for labour - Invest  - Supply of financial assets - Receives Taxes.

Government

- Public expenditures. - Supply of public bonds (financial assets) - Money creation (money supply = central bank). - Exports G&S (the country’s imports) - Imports G&S (exportations du pays)

Outside (foreign area)

- Receives capital from abroad (country’s capital outflows) - Exports capital (country’s inflow of capital). - Possesses and provides currency reserves

13

1. Households Operating account

P C TM

Entry

Resources W  L r  BF  r  BG

S Financial and capital account Entry

BF



Resources S

BG  M 

2. Firms Operating account Entry WL rBF

Resources PY 

TF



Financial and capital account Entry PI

Resources  BF 

14

3. Public accounts (government) Operating account Entry

Resources

PG rBG

TM

SG (surplus)

SG  0 (deficit)

TF

Financial and capital account Entry

Resources

SG  0 (deficit)

SG (surplus)

BG  (-)

BG  (+)

M  (-)

M  (+)

4. Foreign accounts The exchange rate E = amount of domestic currency for 1 unit of foreign currency. Hence when the domestic currency appreciates, E decreases; An increase in E indicates a depreciation of the domestic currency. We describe the accounts of the country vis à vis its outside. Trade Entry E  P * IM

Resources

P X

BE (domestic surplus)

-BE > 0 (domestic deficit)

Financial and capital account Entry -BE > 0 (deficit)

Resources BE (surplus

Sortie CAP

Entrée CAP

RES () ou RES *()

RES *() ou RES ()

Remark !!!!!! : The accounts are always balanced by construction (any resource has an utilisation).

15

5. Market equilibria (Closed economy)

The market for goods and services Supply

Demand Y  C  I G

Y

The labour market Supply L

Demand L

The market for financial assets (bonds) Supply

Demand

B   BF   BG 

B   BF   BG 

The market for Money Supply

Demand

M 

M 

16

5. Walras law In an economy with n markets, if (n-1) markets are at equilibrium, the n-th is ipso facto at equilibrium. Here we have 4 markets: Labour, Goods & services, Financial assets, Money. By construction (we assume SG  0 , BG   0 et M   0 ) :

Entry = Resources Hence: PC+ TM + S + BF  + BG  + M  + WL + rBF + TF +  + PI + PG + rBG + SG

= WL + rBF + rBG + S + PY  +  + BF  + TM + TF + SG + BG  + M 

PC  TM  S  BF   BG   M   WL  rBF  TF    PI  PG  rBG  SG   WL  rBF  rBG  S  PY     BF   TM  TF  SG  BG   M 

By erasing the doublets: PC  PI  PG + WL + BF   BG  + M  PY  B

= PY  + WL + BF   BG  + M 

B

 If 3 markets are in equilibrium, the fourth is in equilibrium as well

17

6. Adjustments in a market economy

 Adjustment through prices  Adjustment through quantities  Adjustment through structures

Adjustment through prices Equilibrium =  Qˆ , Pˆ  such that Qˆ  Q ( Pˆ )  Q ( Pˆ )

Q

P

The ‘classical’ equilibrium is characterised by a perfect adjustment through prices.

18

Adjustment by quantities PP

Equilibrium =  Q, P  such that Q  min Q ( P), Q ( P) Q

P

The basic Keynesian equilibrium is characterised by an adjustment through quantities with supply being constrained by demand

Adjustment by structures PP

Equilibrium =  Q, P  such that Q  Q ( P)  Q ( P) Q

P

It is typically considered as a long term adjustment.

19

7. Agents’ behaviours The consumer’s Optimum Maximising the utility function subject to the income constraint, with prices and wages being exogenously given. c = Consumption ;   l  l  leisure ; l  disposable time ; l   labour supply The simplest case:

max u  u(c,   l  l  ) , s.t. : Pc  Wl  c,

Pc  Wl  at the maximum  We insert Pc  Wl   c  (W / P)  l  inside u :

max u  u  (W / P)  l  , l  l    l

u     0  l  l (W / P), l

l   0  c = c(W/P). (W / P)

The two-period case (intertemporal with savings for retirement): 

max u  u(c, c ',   l  l ) , c, 

P  c  s  W  l   P ' c '  s.t. :   Wl  P  c  1 r P ' c '  (1  r )s 

The firm’s optimum Maximise its present profit subject to the technological constraint (production function), with prices (of goods and factors) being given as well as capital + maximise the following period profit so as to determine investment (capital in the next period, future prices (of goods and factors) being perfectly known. The simplest case (one period of time) In the short term: k  k . Hence rk  rk is given: max   Py  Wl   rk ,  y ,l

such that: y  F (k , l ) .

20

Inserting the production function in the profit: max   P  F (k , l  )  Wl   rk  l

  0  l   l  (W / P),  l

l  0 (W / P)

The two-period case (intertemporal with investment): Lifetime of capital = 1 period of time Add:

max  '  P ' y ' W 'l '  (1  r ) Pk ' , y ', k '

s.t. : y '  F (l ' , k ') ; k '  i  b / P

Discounting Discounted value: The sum s perceived in the next period is equivalent to

s today: 1 r

If I want to spend today the amount of money corresponding to s perceived in the next period, I must borrow the sum  such that s perceived in the next period allow me to reimburse this loan.

 is the discounted value of s perceived in the next period of time: it is what I can spend today with the s I shall receive tomorrow. If I borrow  I shall pay back (1  r) . Hence:

(1 r)  s    s . 1 r Same reasoning for the t-th period from now :  

s (1  r )t

21

Slide 2

Macroeconomic Policies & Exchange rate regimes

22

Macroeconomic policies

1. Monetary policy

Money is created by banks under the control of the central bank.

Monetary policy = determines the money supply M .

Monetary policy is implemented by the Central bank rale which intervenes in the ‘money market' (market on which banks lend monetary liquidity): 1. Open market policy: rediscount of the banks’ financial assets by the central bank. 2. Reserve requirements. 3. Credit control.

Monetary policy is modelled by assuming that the central bank discretionarily determines domestic money supply:

Closed economy:

Open economy:

M   M  dM   dM M   M  E  RES  RES*  dM   dM  E  dRES  dRES

Remark: Normally, d  E  RES   E  dRES  RES  dE , but we assume that, in this case, the central bank freezes the variations in money due to variations in E.

23

2. Budget policy & crowding out

Budget policy = Public expenditure + Tax revenue.

a) Public expenditure and taxes Public expenditures = purchase and production by public authorities of goods and services which are freely provided to private agents + direct money tranfers from rthe state to private agents.

Financing of public expenditures = Taxes + Seigniorage + Public debt (issue of Treasury bonds).

Taxes = Labour income tax + Consumption tax (VAT) + capital income tax + Tax on wealth (on capital) + tax on wages + corporate tax (on firms’ benefits). Proportional tax / lump sum tax.

b) Budget policy and crowding out Crowding out = situation in which public expenditures (and their financing) reduce private expenditures. Partial crowding out = the related loss in private expenditure is lower than the increase in public expenditure; Total crowding = the related loss in private expenditure is equal to the increase in public expenditure; Over-crowding = the related loss in private expenditure is higher than the increase in public expenditure.

24

Remark: Crowding out can derive from the public expenditure itself or from its financing (taxes), or from both. It can be direct or indirect (public spendi,ng acts upon variables which in turn reduce private spending).

c) Budget policy in macro-models 3 types of variables : 1) Public expenditures (G), 2) Taxes (T,  , w , c ), 3) Public edficit (  SG ) public debt ( DG ) and the net provision of public bonds ( BG  SG if there is no seigniorage).

3. Policy mix Policy mix = couple (monetary policy, budget policy).

M  ,(G,T ) or  M  , G  When monetary and budget policies are not equally efficient and when those efficiencies change with their utilisation, and when these utilisations are costly, the policy maker selects the most efficient policy.

25

Exchange rate regimes Fixed exchange rate 1. Pure fixed exchange rates: Exchange rates are fully fixed. In reality, it never exists (except temporarily) because it is then better to set a common currency. 2. Adjustable fixed exchange rates : exchange rates can fluctuate inside a limited interval and there can be devaluation / revaluation depending on the decisions of public authorities.

Flexible exchange rates 1. Pure flexible exchange rate regime : The exchange rate is determined on the exchange market by adjustment of supply and demand for currencies, without intervention of central banks ( no change in the CB currency reserves). 2. Imperfect flexible exchange rate regime: Central banks intervene.

An in-between regime : Target zone There is a rather large fluctuation interval which defines the limits of fluctuation around the reference exchange rate, and a narrower interval which is the interval of no-intervention. As long as the exchange rate stands inside the no-intervention interval, central banks do not intervene and the exchange rate regime is purely flexible. When the exchange rate attains the limits of no-intervention, the central banks implement coordinated interventions to maintain the exchange rate inside the limits of fluctuation.

E 

E E 

26

Choice of an exchange rate regime Should the market define alone the exchange rate values (purely flexible regime) ? Should we enforce a fixed exchange rate regime even if it induces exchange rate adjustments (devaluations and revaluations) when lasting imbalances arise ? Should we let speculation free in the exchange rate market and, if not, what exchange rate regime to select ?

27

Slide 3 Equilibrium in perfect competition (perfect price flexibility) : The classical approach in closed economy

28

1. General framework It is micro-founded (representative agent). Prices clean all the markets (except when this is impeded by public intervention) and this adjustment operates rapidly  the analysis is brought about at equilibrium.. Perfect competition : atomicity; neoclassical utility and production functions; homogeneity of goods and factors; no transaction costs  Law of one price. We are in the short term  the amount of capital K is given. In its simplest form, money is a veal.

Maximising representative agent in perfect competition

Supply and demand MICRO-functions

Aggregation

Supply and demand MACRO-functions

Supply = Demand in all markets except 1

MACRO-equilibrium

Households: maximise their utility subject to the income constraint  Labour Supply, Demand for consumption and invested savings (Demand for Financial assets). Firms: maximise their profits under technological constraint (production function)  Labour Demand, Supply of financial assets (Bonds to finance investment), Supply of goods & services (production).

29

Utility and production functions are ‘neoclassical’: Continuous, monotonic increasing (first derivatives > 0), twice derivable in  , second derivatives < 0 (decreasing marginal utility and decreasing marginal productivity). The production function is homogenous of d° 1. Money is a veal  The real equilibrium is determined without money. It defines quantities and relative prices.

2. A one-period simple model of ‘classical’ equilibrium For not to build an intertemporal model (too complex in L2), we ignore investment, savings and financial investments and we construct a very simple one-period model. We consequently assume that there is a capital which does not depreciate (infinite life time) and which is utilised by owners-entrepreneurs and transmitted from one generation to the next (inheritance). Households : m wage-earning households who supply labour and n entrepreneur households, each possessing the amount k of capital and managing their firm. The former are paid for their labour and the latter receive the return from their capital. Firms : At each period, the n firms produce a good with labour and the capital owned by the entrepreneur.. Capital has an infinite lifetime (no depreciation).

There are 3 markets (G&S, Labour, Money). Money is a veal  2 markets. Walras Law  It is enough to determine equilibrium in 1market. We eliminate the market for goods & services

 We select the LABOUR MARKET.

30

1. Equilibrium in the Labour market a) Households All households (wage earners and entrepreneurs) have the same utility function

u  c  a(1 l  ) ,

0  1

C.E.S. function:  

1 1

The m wage-earner households

max u  c  a(1  l  ) , 

s.c.: Wl   Pc  Pk

c ,l

At the optimum, the constraint becomes : Wl   Pc  c  (W / P)l   l  with   W / P the real wage Inserting c  l  into u : 

max u  l    a(1  l  )  l

u   1  a (1  l  ) 1  0    l l 



 1

  l  

 l 



1

 a(1  l  ) 1   (1  l  )1  a l   1

a1/(1 )  /(1 )  1

since  

1 1

1 lˆ   1 a  1

 1/(1 ) (1  l  )  a1/(1 )l 

31

l   (1   )  2   1  1



(  1) 





1

1

2

0

At the MACRO-level :

L 

m

1  1

L 0 

,

 Labour supply is an increasing function of the real wage

Labour supply curve

b) Firms n identical firms, each of them having the capital k . Firms’ behaviour: Profit maximisation for a given technology and a given amount of capital:  Labour demand

max   Py  Wl   R ,  y,l

with R given

With the Cobb-Douglas technology:  Labour demand

y  A  l  k 1

32

Labour demand

 

max   PA l  l

 l 

 

  PA l

 1

 Wl   R

k

  1 1

1 1

 W  0  l   AP / W  

k

k

As   W / P  real wage : 1 l   ( A)1



1 1  ( A) 

l   1

2   k  1

 0;

2 

 l   2

k



1 1

1 1  (2   )( A) 

(1   )2

k



3 2 1

0

At the MACRO-level: 



1 n( A)1



1  ( A)1

L  nl 

L

k



1 1

K



1  ( A)1

1 1 ,

K



1 1

L  2 L with  0 and 0   2

Labour demand curve

33

c) Equilibrium Diagrammatic determination of the labour market equilibrium:

L

Equilibrium can be determined analytically:  1 1 1   1   1 1   1   1  K  m  ( A)  K  0   L  L   ( A) 1 1   L  ( A)1 K 1 

L 

m

1

1 1   ( A) 

1

K

1 1   m 

1 1   ( A) 

K  0 can be written by multiplying both

sides by  1 :  1 1 m 

1 1   ( A) 

 1

K

1 1    ( A) 

K 0

The value  at the equilibrium, ˆ , is the positive root of this equation (its does exist and it is unique, as shown by the above figure). Labour at equilibrium Lˆ can be determined by inserting ˆ either in labour demand or in labour supply. E.g. in labour demand: 1

1

 Lˆ  ( A)1 Kˆ 1

34

2. The ‘real’ equilibrium We have determined the real wage ˆ and the labour utilisation Lˆ at the equilibrium. We can then calculate the equilibrium on the Market for goods & services. Inserting Lˆ in the production function (homogenous of degree 1):

Yˆ  ALˆ K 1 It can be checked that the sum of demands is equal to the sum of supplies on the market for goods & services : Profit maximisation  the wage bill accounts for the proportion  of the income created by firms (

 l 

 

  PA l 

 1 1

k

 

 W  0  Wl    PA l 

 1 1

k

  Py )

 incomes from capital represent 1   : R  (1   ) Py . As all households, wage earners as well as entrepreneurs, consume the whole of their incomes , the sum of the demand for goods and services is equal to the supply of G&S : nWL  R   PY  (1   ) PY  PY . demande

Offre

We have determined:

Lˆ ,

The amount of Labour at equilibrium

Yˆ ,

Production at equilibrium

ˆ  W / P ,

The real wage at equilibrium

 The real equilibrium has been determined without money. We must now determine the price level P to calculate nominal values: W    P, W  Lˆ, P  Yˆ

35

3. The market for Money and the nominal equilibrium 1. Determination of the price level Money demand : M     P Y (equivalent to M V  P Y )

 = Cash holding behaviour of households M     P Y   M  M  M   Pˆ  ˆ Y  Y  Yˆ  

2. The nominal wage: Pˆ  M /  Yˆ     ˆ   Wˆ  ˆ M /  Yˆ   W / P  

 We have determined the real equilibrium (without money), and then the nominal equilibrium (by introducing money).

Key point: The real equilibrium is determined without money

 real-nominal Dichotomy Money does not appear in demand functions How is price variation realised?

 No micro-foundation to price setting !

36

Summary

1) We have determined al the real variables at the macro-equilibrium without money through market clearing (supply = demand) in all markets:

Lˆ ,

Labour

Yˆ ,

Production

ˆ  W / P ,

The real wage

2) We have introduced money, which has determined nominal variables: P,

The general price level

W  P 

The nominal wage

W L

The cost of labour

P Y

Nominal production

The model developed here is over-simple as regards the real economy since there is no savings, no financial assets and no investment.

To integrate those markets and the related behaviours, one must at least consider a two-period (intertemporal) approach: households invest their savings to consume in the next period (e.g. retirement) and firms invest to produce in the next period. A model of this type is exposed in the ‘cours de Macroéconomie, L2 Mathéco’.

37

Slide 4 Macro-policies in the ‘classical’ approach

38

1. Monetary policy and Inflation

Monetary policy  M . We know that: 1. The real equilibrium ( Yˆ , Lˆ , and ˆ  W / P ) is determined without money ; 2. The monetary policy determines the price level and the related nominal values:

P

M .   Yˆ

 Any monetary policy which modifies the money supply M has typically no impact on the real values and equilibrium. It has an impact on: 1) the general price level, 2) the nominal wage, 3) the nominal values (production and wage bill). However the ‘classics’ recommend a monetary policy without inflation for two major reasons: 1) Real cash balances 2) To have no failures in price and wage expectations when the model is inter-temporal (explanation...)

39

2. Budget policy and crowding-out effect

Budget policy = Taxes + public expenditures. (we suppose that the budget is balanced)

Crowding out = situation in which public expenditure reduces private expenditure.

Partial crowding out / total crowding out / overcrowding

Taxes = Tax on labour income + Tax on consumption (VAT) + Tax on capital income + Tax on capital

We utilise the simple model developed before (no saving, no financial market) to study the impact of budget policy on labour supply and production. We introduce: Taxes = Tax on labour income + Tax on consumption.

Public expenditures = transfers to private agents (househlods) in the form of goods & services freely provided.

It is shown that: Budget policy reduces labour supply  decrease in production and demand

 Over-crowding.

40

Household behaviour without budget policy (recall): max u  c  a(1  l  ) , 0    1,

s.c. : W  l   P  c

We insert the income constraint in the utility function and denoting   W / P 

 

u  l 

 a(1  l  )

Maximisation (1st order condition):

 

u 1    1   l  a (1  l  ) 1  0  l    l 1  (a /  )1/(1 )

1  micro-labour supply : l    1 , a  1 with   1/ (1   )  1 , the elasticity of substitution consumption/leisure.

At the MACRO-level (m households):

m L   1 a  1 L ma    (  1) 0 2   1   a  1





Labour supply increases with the real wage.

41

Budget policy is introduced:  Goods & services freely provided by the government:

cG given to each household  CG  m  cG , financed by taxes on labour income and consumption:

T  W  (WL)   C  ( PC)



P  CG  P  m  cG

 Public goods are perfectly substitutable to private consumption goods.  Budget policy modifies the situation of households but not that of firms.

Behaviour of the representative household :

max u  (c  cG )  a(1  l  ) ,

s.t. : (1 W )W  l   (1   C )P  c

 This is equivalent to moving wage from W to (1  W )W , the price of goods from P to (1   C ) P and to freely provide a share of the households’ consumption..

We denote  

1  W W 1  W    the after-tax wage. The maximisation 1C P 1C

programme becomes max u  (c  cG )  a(1  l  ) , s.c. :  l   c

Inserting the income constraint in the utility function:

42



max u   l   cG  l





 a(1  l  )

First order condition: u l

denoting





   l   cG





 1

 a (1  l  ) 1  0  l  



1 1

1 1  a 

1  a1 c

 

G

1 1

1 the elasticity of substitution and dividing up and down by   , we 1

determine

The MACRO-supply of labour L  ml  which is:

L  m 

1  a  cG a 1  1

L We check that: 0 







 (1 ) a  1  1 cG  (  1) 1  a   cG L   ma 2  a  1  1





 a   1  0

Hence: Labour supply is an increasing function of the after-tax real wage As  

Hence:

1 W     decreases with  (   0 ) and  (   0 ). W C  W 1  C C L 0 W

and

L 0  c

 Both taxes reduce labour supply

43

In addition:

L  m 

1  a  cG L  0 cG a 1  1

 Public transfers to households reduce labour supply

 The three components of budget policy reduce labour supply

L

L L '

Lˆ 

Lˆ '

ˆ  ˆ '



 The amount of labour utilised at the equilibrium decreases  Production at equilibrium decreases ( Yˆ  ALˆ K1 )

 OVER-CROWDING Explanation : disincentive to working

44

Remark : Budget policy, savings and investment Taxes on capital income and/or on capital

 Decrease in investment  Decrease in production in the following periods  Decrease in growth

Summary

1. Taxes on labour income and consumption and public transfers to households reduce labour supply, demand and production at the equilibrium

 Overcrowding.

2. Taxes on capital and capital income lower savings, investment and thereby future production and growth.

45

Slide 5

The ‘classic’ approach in open economy: The Monetary Approach to the Payments

46

1. General framework 2 countries, Home and Foreign (the rest of the World). Open economy = free trade = law of one price at the World level Countries only differ in their monetary policy. 2 Distinctions : Exchange rate regimes and Large versus Small country. In each country, perfect competition and price flexibility enforce the full employment equilibrium production, Yˆ in the home country and Yˆ * in the foreign country. Monetary policy only impacts NOMINAL values and we study how the World adjustment (law of one price) is brought about depending on the exchange rate regime and the country size.

Exchange rate a) Law of one price (LOP)  Purchasing power parity (PPP): P  E  P*

p  e  p*



Money b) Quantity equation (money demand):

M     P Y



m  p

M *   *P *Y *



m *  p *

c) Money supply: M   M BC  E  RES



. m  q1  mBC  q2  (e  res)

M *  M BC *  E 1  RES *



. m *  q1 * m *BC q2 * (res* e)

47

d) Equilibrium on the market for money: M  M



m  m

M *  M *



m *  m *

Two cases: 1. Perfectly flexible exchange rate  Central bank do not intervene in the exchange rate market  RES and RES* are constant (to simplify, they are assumed to be nil) 2. Fixed exchange rate : E  E constant.

2. Adjustment and exchange rate regime a) Flexible exchange rate m  p ,

m *  p *

et

p  e  p* 

e  m  m *

RES et RES* constant RES  RES*  0  m  mBC et m *  m *BC

m  m  mBC et m *  m *  m *BC

 p  mBC      p*  m *BC    e  m m* BC BC 

 Each country has the inflation corresponding to its monetary policy.  International price equalisation (LOP) operates through the exchange rate (PPP).

48

 Flexible exchange rates allow full independance of monetary policies, international price equalisation being reached by exchange rate adjustments. Mecanism: Example of an increase in domestic money supply ( mBC  0 ), the foreign money supply remaining unchanged ( m *BC  0 ). Increase in M CB

 Increase in the demand for domestic and foreign goods  Increase in the price of domestic goods + demand for foreign currency  Depreciation of the domestic exchange rate  Increase in the price in domestic currency of foreign goods The increase in the prices of home and foreign goods must be the same (PPP)

b) Adjustment in fixed exchange rate regimes p  e  p * et e  0  p  p *

 Same inflation in both countries. m  m  p , m *  m *  p * et p  p *  m  m *

 Same increase in money supply in both countries. . . m  q1  mBC  q2  res , m *  q1 * m *BC q2 *  res* et



m  m *

. . q1  mBC  q2  res  q1 *m *BC q2 * res*

 Adjustment through currency reserves (international money mobility).

49

Mecanism: Example of an increase in domestic money supply ( mBC  0 ), the foreign money supply remaining unchanged ( m *BC  0 ). . . q1  mBC  q2 *  res* q2  res Increase in M CB

 Increase in the price of domestic goods + Increase in the demand for foreign goods  Trade deficit  Exit of domestic currency (increase in the foreign country reserves) and/or exit of foreign currency (decrease in the home country reserves)  Equilibrium is reached when the foreign money supply has increased as much as (in %) the home money supply, inducing p  p * .

Distinction between large and small countries : The small country has no impact on the rest of the World equilibrium. It is in contrast impacted by changes in the rest of the World. Here: The small country’s money supply is a minute proportion of the World money supply  An increase in the country’s money supply leads to a quasizero increase in the World money supply. The large country does have an impact on the equilibrium of the rest of the World. The large country’s money supply is a non-negligible share of the World money supply  an increase in its money supply generates an increase in the World money supply. In addition, it is typically assumed that the large country’s currency is accepted as a reserve currency by other countries.

50

1. Small country: i) When the small country’s central bank increases money supply, this has no impact on the rest of the World, i.e. P* does not change  As E is constant and P = E × P* , P must remain constant.. For this, the small country’s money supply must also remain constant  All the created money must escape abroad. This can come, either from an increase in the Foreign reserves in domestic currency, or through a decrease in the Home reserve in foreign currency. If the rest of the World does not accept the small country’s currency, then the small country’s monetary policy is constrained by its reserves (it cannot create more extra-money than the amount of reserves it possesses). ii) If the rest of the World increases its money supply and the small country does not: P* augments  As E is constant and P  E  P * , P must increase as well. The small country money supply increases because of the deficit (and exit of money) of the rest of the World)  The small country suffers an inflation it has not chosen.

2. Large country: A large Home country creates money. Production prices must be the same in all countries (LOP)  The money supply must increase at the same rate in the large economy and the rest of the World.  Exit of money from the large country to the rest of the World (because of the large country’s deficit)  Increase in the money supply and prices in the rest of the World (which in turn reduces inflation in the large country).  The rest of the World suffers the inflation generated by the large country Example: the US in the sixties (financing of the Vietnam war).

51

c) Result = Superiority of the flexible exchange rate regime Exchange rate Country

Small

Large

Flexible

Fixed

- All the money created by the CB moves abroad and adjustment is brought about through moves in - Full independence of currency reserves. monetary policies - Problem when the country is - Each country has the constrained by its amount of inflation it generates reserves. - Adjustment through the - The small country suffer the exchange rate which inflation generated abroad. enforces PPP - World inflation (the money created by the large country goes abroad and inflation must be the same because of PPP)

Flexible exchange rate regime: Each country chooses tits monetary policy without constraint. Fixed exchange rate: monetary policies are not independent. Small country: if other countries do not accept its currency, its monetary policy is constrained by the amount of reserves it possesses. Large country: other countries suffer the inflation generated by its monetary policy.

52

3. Stabilising speculation Definition: Speculation consists in buying or selling an asset so as to realise a profit, i.e., a gain between the purchasing price and the selling price. un actif. Basic assumptions: 1) Speculators cannot go against 'fundamentals' which determine the equilibrium price; They can only slow down or accelerate the market adjustment process  They do not dominate the market. 2) Speculators have pieces of information before others (because they invest time to be quickly informed) and they rapidly calculate the impact of changes on the equilibrium price. Then: Speculators accelerate market adjustments  have a stabilising effect Example : If the asset price is lower than the equilibrium price determined by the fundamentals, speculators knows it before other agents and they have an interest to buy the asset so as to to sell it once it has increased. By buying the asset, speculators make its price to go up and thereby to quicker attain its equilibrium price determined by fundamentals.  Stabilising speculation.

Stabilising Speculation and exchange rate regimes Flexible exchange rate regime: The currency is under-valued: E  Eˆ  Speculators buy the currency  quicker move towards the equilibrium

X

Equilibrium value

X Market value

53

Remark: By pushing the asset (here the currency) towards its equilibrium value speculation is self-deleting: the higher speculation, the closer the currency to its equilibrium value, and the lower the profit from speculating

Adjustable fixed exchange rates: Speculation is destabilizing. Speculation does not bring the currency back to its equilibrium value

 Cumulative exit or entry of money (capital) as long as the currency has not been devaluated or revaluated.

This is because, with fixed exchange rates, speculation is no longer selfdestroying.

54

55

Slide 6 Limits and extensions of the ‘classical’ approach

56

1. Limits

The ‘classical’ approach models an economy in which price adjustments quickly leads to the equilibrium. At this unique equilibrium, expected (desired) supplies and demands are equal in all markets.

a) Perfect competition -

Atomicity / homogeneity of goods and factors / Representative agent / No market power (perfect competition) / Characteristics of the production and utility function (PF homogenous of degree 1) - Quick and perfect adjustment in all markets. In particular, when there is PURE profit (rents), the issue of the distribution of rents across agents arises. In this case, the factor payments can deviate from their marginal productivity.

b) Substitution and income effects in the labour market and heterogeneous workers W is the (opportunity) cost of 1 unit of leisure  it is the price of leisure. The behaviour is exactly as if the household earned W ( W  l  W with l  1 , wage corresponding to the total disposable income) and spent this earning in consumption goods bought at price P and in leisure bought at price W.

57

Income effect : Increase in the real wage (W/P)  Increase in the real income  The household increases both its consumption and leisure  The household lessens its labour supply (example : if the real wage increases by 10%, he increases its consumption by 5% and its leisure by 5%, i.e., he decreases his labour supply).

Substitution effect: Increase in the real wage (W/P)  Increases in the price of leisure relative to the price of consumption  The household substitutes consumption for leisure  The household increases its labour supply

 For an increase in the real wage to increase labour supply, the substitution effect must prevail over the income effect .

From the same model in which we insert (i) heterogeneous agents in terms of skill (productivity) and non-labour income and (ii) a minimum (vital or social) consumption, it is possible to determine: 1. 4 groups of households (rentiers, ‘classical’ workers, ‘non-classical’ workers, excluded) which differ in their labour supply. 2. For classical worker, labour supply increases with the real wage, whereas the opposite relation holds for non-classical workers. Rentiers and excluded do not work, the former because they prefer to live from their rents without

58

working, the latter because their pay would be to low to ensure the minimum consumption necessary to participate in the labour market. . 2. An increase in taxes reduces the ‘classical workers’ labour supply whereas it increases the non-classical workers labour supply. 3. An increase in social transfers lessens the labour supply of the working households, but it also make excluded to enter the labour market  the total effect is ambiguous (depending on the distribution of households in the four groups and on the consumption-leisure elasticity of substitution).

c) Economic policies: What for? If the classical model is an adequate representation of the economy, then stabilising economic policies are meaningless. Why are they implemented then ? Two possible answers: 1. The public decider is ignorant ; 2. The public decider has an interest in implementing such policies (‘public choice’).

59

2. Extensions

a) Expectations in an inter-temporal framework Problem: What intertemporal equilibrium when future is imperfectly known ?  Complete markets: impossible.  Adaptive expectations (M. Friedman): lasting errors.  rational expectations

b) The problem of dichotomy Don Patinkin and real cash demand  introduction of cash balances in the utility function. M   Yˆ

Dichotomy:

P

Solution:

ui  u  ci , i , mi / P 

Y   f P /W ,   Y   f  P / W , , M / P

60

c) Budget policy & public debt: Ricardo-Barro equivalence Recall: s . (1  r )t  The discounted value of a succession of sums perceived in the T following

The discounted value  of the sum s in t periods of time is:  

periods ( st at period t ) is:

st t t 1 (1  r ) T

S0  

Public expenditures G can be funded : (1) either by an immediate tax ( t0 for each individual), (2) or through borrowing on financial markets, which leads to future refunding, i.e., future taxes t1,..., t .





We compere the two situations, (1) and (2).

Behaviour of the representative household:

max u  c0 ,..., ct ,l0 ,...,lt , g  , such that: t

1 case: w0l0  t0   st

i 1

2nd case: 1st case: 2nd case:

(1  r )i wili

t

t

G

i 1

m

 p0c0   (1  r )i pici with t0 

t

 (1  r)i  wili  ti    (1  r )i pici

i 0

i 0

g 

t

with:

g

G

(1  r )i ti   g  m i 0

t

 (1  r)i  wili  pici   0

i 0

t

t

t

i 0

i 0

i 0

 (1  r )i ti   (1  r )i  wili  pici    g   (1  r )i  wili  pici   0

 (1) is equivalent to (2)

61

Interpretation: 1) Private agents know that today’s debt will be refunded by future taxes. Then, households increase their savings today and invest in (public) bonds so as to pay the future taxes, which is equivalent to immediate levies. 2) In the model with a representative household and a constant discount rate (= interest rate), there is an optimal intertemporal allocation of disposable income which is independent from when the taxes are paid. In addition paying taxes now or in the future does not modify the households’ behaviour (there is no transfer of charges to the future generations).

Limits: 1) Households with, infinite lifetime. This corresponds to a particular type of altruism. 2) If levies are not equally distributed across households, there is no equivalence. 3) The government must not sell public bonds abroad and cannot enforce an interest rate lower which differs from that in the financial market. 4) The distribution of taxes over time has no impact on the interest rate. 5) The utility function is identical at any period for all households.

62

63

Slide 7 The (neo) Keynesian approach with fixed prices in a closed economy: IS-LM

64

1. General framework Prices are fixed. To simplify : P = 1. Adjustment takes place ‘at the small side’, which is the demand side. In fact: Prices are DOWNWARD rigid, which is sufficient since the small side is the demand side.  DEMAND DETERMINES SUPPLY (production), and SUPPLY DETERMINES EMPLOYMENT.

Demand

Production

Employment L

What determines demand? - The IS-LM approach answer this question

Income Y

Taxes Savings Monetary policy M

Consumption C

Interest rate r

Investment I Demand Public expenditures G Production Budget policy Employment L

65

2. The IS-LM equilibrium a) The IS relationship  Y Y  Y   Y C  I G   C  c(1   )Y  C   Y  c(1   )Y  C  I ( r )  G  kI ( r )  kG  kC    I  I (r ) 

Y  k  I (r)  k  G  k  C , with: k 

1 . 1  (1   )c

 The IS relationship = decreasing relationship between Y and r. Y

G

r  I  I ( r) : Explanation for

Investment depends on the marginal efficiency of capital (MEC) compared to the interest rate r. Marginal efficiency of capital (e) for investment I, with the lifetime n, and the returns Ri , i  1...n : MEC such that : I 

Rn R1 R2   ...  2 1  e (1  e) (1  e)n

66

Investment: Investment projects ranked in decreasing order of return (marginal capital efficiency) EMC

r

b) The LM relatioship

    r  r( Y , M )  Y  Y ( r , M )

Y

M

r

67

c) Equilibrium For M and G given: IS and LM  Equilibrium values of Y and r. Y at the equilibrium + production function Y  F ( K , L)  L at the equilibrium

Y

Y

G

LM M

Y

IS L

r

r

L

L  L  Unemployment  Economic policies (M et G) can be utilised to reach full eemployment

68

3. Economic policy within the IS-LM approach 3.1. Multipliers

a) General presentation Simplest: Y  Y (I )   I  I ( r )   Y  Y I  r ( M )  r  r( M ) 



YI ' 



Y I r  0; I r '   0; rM '  0 I r M 





Differentiation  dY  YI '  I r '  rM '  dM multiplier With a backward effect:

Y  Y (I )   I  I ( r )   Y  Y I  r( M ,Y )  r  r( M ,Y ) 



rY ' 



r 0 Y







Differentiation  dY  YI ' I r ' rM ' dM  YI '  I r '  rY '  dY negative  backward effect

dY 

YI ' I r ' rM '  dM 1  YI ' I r ' rY ' multiplier

Backward effect  YI ' I r ' rY '  YI ' I r ' rM ' dM   0  

69

b) Policy multipliers in the IS-LM approach We analyse the impact of an economic policy tool (dG for a variation of G and dM for a variation of M) on the product. We start from the IS-LM relations:

(IS)

Y  kI (r)  kG  kC

(LM)

r  r(Y , M )

To make appear all the policy-related mechanisms, we firstly determine the reduced form (IS)-(LM) to have Y in relation to G and M:

Y  kI r(Y , M )  kG  kC We subsequently calculate the total differential of the reduced form (since we want to make appear all the ieffects of the changes dM and dG on dY) :

dY  k  I r  rM  dM  direct impact of

monetary policy

kdG direct impact of

budget policy



k  I r  rY  dY Crowding-out (for dG) or backward effect (for dM )

with: k  Y / I ; I r  I / r  0; rY  r / Y  0; rM  r / M  0 .

dY 

kI r ' rM ' k dM  dG 1  kI r ' rY ' 1  kI r ' rY '

To determine the impact of budget policy alone we assume dG  0 and dM  0 , and for the impact of monetary policy alone dM  0 and dG  0 .

70

Multiplier of monetary policy: kM 

kG 

Multiplier of budget policy:

kI r ' rM ' 1 kI r ' rY '

k 1 kI r ' rY '

Analysis of the effects

- Monetary policy:

dY 





  k  I r  rM

 dM 

impact direct de la politique monétaire

Direct effect:

M

Backward effect:

Y

- Budget policy:

dY 

I Y I Y



k  dG



impact direct de la politique budgétaire

Direct effect :

G

Y

Crowding-out effect :

Y

r

 dY

Effet en retour

r r

   k I r  rY 

    k I r  rY

 dY

Effet d'éviction

I Y

71

Crowding-out and the backward effect are partial

Budget policy :

dY 



k  dG



direct impact of

budget policy

   k I r  rY 

 dY

crowding - out

Y

LM 2

1 = Increase in Y for r given

1

2 = Crowding-out effect IS'

IS r

Increase in G

Increase in Y partial crowding-out

Decrease in I

Increase in r

72

dY 

Monetary policy :





  k  I r  rM

 dM 

direct impact of monetary policy

   k I r  rY 

 dY

Backward effect

Y LM'

1 = decrease in r for Y given LM 3

2 = Increase in Y induced by the decrease in r

2 1

IS r

Increase in M

Decrease in r

Increase in I

Increase in Y

Decrease in I

Increase in r

backward effect

Decrease in Y

Comparison of the two policies: Crowding-out and the backward effect are identical  It depends on I r ' rM ' . Econometric estimates  I r ' is low  kM  kG

 Budget policy is more efficient in closed economy

73

3.2. Full employment Policy mix a) general case Full-employment production:

Y  F ( L)  Y  F ( L) Reduecd form with Y  Y :

Y  kI r(Y , M )  kG  kC 



Set of full-employment policy mix:

P  (G, M ) G  Y / k  I r (Y , M )  C  







b) Balanced budget When budget policy only considers the change in G, the related changes in budget balance and in public debt are ignored. In case of deficit, this leads to an increase in public debt ; in case of surplus by money destruction. What happens when budget policy is set under the condition of balanced budget? Let us write relation IS in the form Y  c(Y  T )  C  I  G where T is the sum of levies on private agents.

Y  c(Y  T )  C  I (r )  G    (1  c)Y  I (r )  (1  c)G  C G T   Hence:

Y  kI (r )  G  kC , avec : k  1 1 c

74

The rule:

When public budget is balanced, the budget policy multiplier is 1 1 lower than 1: kG  , avec k  . 1 c 1 kI r ' rY ' Proof: The reduced form of IS-LM is ;

Y  kI  r (Y , M )  G  kC By differentiating with dM = 0 :

dY  k  Ir ' rY ' dY  dG . Hence : 1 . kG  Y  G 1 k  I r ' rY '

kG  1 because k  Ir ' rY '  0 1 k  Ir ' rY '  1  kG  1

75

Slide 8 The Mundell-Fleming model

76

The Keynesian relations in open economy

Taxes Savings Imports IM Income Y Inflow & outflow of Capital

Monetary policy Consumption C

Money supply M Interest rate r

Exit & Entry of Money * Exchange rate **

Investment I Demand Y 

Production Y 

Employment N

Exports X Public expenditures G

Budget policy

* Fixed exchange rate ; ** flexible exchange rate

77

1. The model a) The market for goods & services The new variables linked to openness are in red ! We assume to simplify: P = P* = 1 Demand: Y   C  I  G  X  IM  Equality resources = entry : Y  IM  C  I  G  X The macro-functions IM  IM ( E ,Y ) ,

Imports and exports:

IM IM 0 , 0 ; E Y

X 0 , E

X 0 Y *

Investment:

I  I (r ) ,

I 0 r

Consumption:

Pc  C  c(1   ) P  Y  Pc  C  C  c(1   )

X  X ( E,Y *) ,

Pc   EP * Prix externes



P

1 

P Y C Pc

,

Prix Internes



  share of imports in consumption :    ( E )  C  c(1   ) E  Y  C We assume: c(1   ) 1/ E  

constant

Equality resources-entry in the market for G&S

 Function IS IS : Y  kI (r )  kG  k  X ( E,Y *)  IM (E ,Y )   kC , with k 

1 1  1/ E   (1   )c

78

b) Equilibrium in the market for money   LM : r  r (Y , M )

M  M CB  M EXT !!!!!!!!! M CB = money created by the domestic central bank still in the home country M EXT = money created by the Foreign central bank (Home country’s reserves)

c) External balance EE : BG  X (E,Y *)  E  IM (E,Y )  EC (r, r*)  SC (r, r*)  0 BE (Y ,E ) BC (r ) Flexible exchange rate the variation of E clears the currency market: BG = 0

 Adjustment operates through the exchange rate and trade balance. Fixed exchange rate Transitory variation: BG  E  dRES  dRES *  dM EXT monnaie étrangère entrante

monnaie nationale sortante

It is shown hereafter that the variation in money supply dM EXT reestablishes balanced external payments through its impact on capital flows.

 Adjustment operates through the entry/exit of money and the captal accounts. Equilibrium : Money supply :

BG = 0

M  MCB  M EXT

79

1) Flexible exchange rate and the Marshall-Lerner condition Global payment imbalance ( BG  0 )  imbalance in the currency market (supply  demand): BG  0  dE  0 (depreciation of the domestic currency) BG  0  dE  0 (appreciation of the domestic currency)

Move in the exchange rate  2 opposite effects on trade balance. Example : depreciation ( dE  0 )  without direct dE   BE (Y , E )  X ( E )  E  IM ( E ,Y )  

- Price competitiveness effect (PCE): Domestic currency depreciation = domestic price-competitiveness increases  Increase in the volume of exports and imports  Positive effect on trade balance. - Terms of trade effect (TTE): Domestic currency depreciation  Increase in the unit price of imports in national currency  Negative effect on trade balance.

PCE > TTE  The depreciation of the domestic currency improves trade balance. PCE < TTE  The depreciation of the domestic currency worsens trade balance.

80

Condition for exchange rate variations to adjust the global balance ?

 Marshall-Lerner condition Condition for PCE to dominate TTE : dE  0  dBE  0 : BE(Y , E)  X (E)  E  IM (E,Y )  BE  X  IM  E IM  0 E E E

X  IM  E IM  0  X  X / X  1  IM / IM  0 E E E  IM E / E E / E

 X  X / X E / E

 IM  IM / IM   IM / IM E / E



E / E

X , export / import ratio E  IM

 Marshall-Lerner condition for the exchange rate to adjust the foreign balance :

   X   IM  1

WE ASSUME THAT THE M-L CONDITION HOLDS. Then the adjustment in flexible exchange rate is as follows:

BG  0 

E

BE  BG  0

BG  0 

E

BE  BG  0

 Adjustment operates through the exchange rate and trade balance.

81

Remarks : 1) When trade is balanced, the M-L condition is:

 X   IM 1 2) When  X   IM  1, a depreciation of the currency improves the export/import ratio. 

X E  IM

E  IM  dX  X  IM  dE  E  dIM  X  E  IM  dE / E  E  IM  dIM / IM   dX  ( E  IM )2 ( E  IM )2 X  dX dE dIM  X  dE dE dE  d      M    X E  IM  X E IM  E  IM  E E E  d 

 d     X   M 1  dE   E



dE  0  d  0 E

iif

 X  M 1

3) When  X   IM  1 and   X   IM  1, trade balance is attained after a transitory deterioration of the trade account  J-curve. Reasoning : - As   X   IM  1, BG  0  -  X   IM  1  

E

BE  Higher deficit.

    X   IM  1 sooner or later.

82

solde des échanges temps

 In the long term, the M-L condition is:  X   IM  1 2) Fixed exchange rate

BG  0 

M

r

BC  BG  0

BG  0 

M

r

BC  BG  0

Adjustment is brought about through money supply, the interest rate and the capital account.

Remarks: Adjustment with flexible exchange rates is similar to that in the ‘classical’ approach.. Adjustment in fixed exchange rates is completely different because here the variation in money supply acts through its impact on the interest rate and the capital account, whereas it acts through prices and the trade balance in the classical approach.

83

3) Crowding out through imports In open economy, any increase in domestic income generates crowding-out by imports:

Increase in income Y

Increase in Imports IM

Decrease in income Y

With flexible exchange rates, the crowding-out through imports is fully offset by the impact of the exchange rate variation upon trade and production :

Increase in income Y

Increase in imports IM

Decrease in income Y

Deterioration of BE offset Depreciation of E Increase in X & decrease in IM Balanced BE

Increase in income Y

84

2. Global equilibrium

a) General presentation The 4 cases

Exchange rate

Flexible

Fixed

High

BCr '  0 et e  0

BCr '  0 et e  0

Low

BCr ' 0 et e  0

BCr ' 0 et e  0

Capital mobility

We analyse the relations IS, LM et EE.

Relation IS

Y  kI (r )  kG  k  X (E)  IM (E,Y )   kC ,

Y  k  Ir '  0 ; r

Relation LM r  r Y , M  ; r  0; Y

r  0  Y  0; M r

Y  0 M

  Y Y( r , M ) Y  0 :  M   r  For r constant, we must have  Y M

Y k 0 G

85

Relation EE It stipulates balanced global payments, BG = 0.

BG  BE(Y , E)  BC(r)  0,

with: BEY '  0,

The Marshall-Lerner condition holds

 BEE '  0

Y-r relationship:

 BCr ' BEY ' dY  BCr ' dr  0  Y   0 r BEY ' 

If r increases, BC is better off and an increase in Y is necessary to reestablish the global balance by worsening BE.

Relation between Y and E : BE ' BEY ' dY  BEE ' dE  0  Y   E E BEY '



Y   BEE '  0 E BEY '

86

b) Diagrammatic resolution

IS :

  Y  kI ( r )  k G  k  X ( E )  IM ( E,Y )   kC  Y  Y ( r , E )

LM :

    r  r(Y , M )  Y  Y ( r , M )





  EE : BG  BE(Y , E)  BC( r)  0  Y  Y ( r , E )

Y M

LM

G EE

Yˆ

E

IS

rˆ

r

Remark: At the equilibrium, the 3 curves intersect in the same point.

87

3. Policies a) The issue of selecting a 'policy mix' Diagrammatic presentation

Y  F (L) the full employment production We start from an equilibrium with unemployment: Y M

LM

G EE

Y E

IS r

Flexible exchange rate : The 3 curves can move  Infinity of triplets (M , G, E) leading to full employment. Remark: The full employment target once determined ( Y  Y ), defining one tool (M or G) also determines the additional two variables.

88

Example with a given monetary policy: M  M  LM unchanged Y

LM G

E EE

Y

IS r

Fixed echange rate: Curve EE does not move (E constant)  There is a single Policy mix (M,G) consistent with full-employment. Money supply must bring curve LM, and budget policy curve IS, to this point: Y LM EE

Y Y

EE G IS M

r

r

89

Formal presentation The model is comprised of 3 equations: Y  kI (r)  kG  k  X ( E )  IM ( E,Y )   kC

r  r Y , M  BG  BE(Y , E)  BC(r )  0

In flexible exchange rate regime, for Y  Y , we have 3 equations with 4 unknown variable: r, M, G, E  1 degree of freedom  Infinity of triplet (M,G,E) permitting to reach full employment. In fixed exchange rate regime, for Y  Y , we have 3 equations with 3 unknown variables: r, M, G  NO degree of freedom  A single (M,G) permits to reach full employment.

Defining economic policy Flexible exchange rate: Infinity of triplet (M,G,E) consistenwith fullemployment  As the exchange rate automatically adjusts the external (global) account, the issue is to define the most efficient policy.

Fixed exchange rate: A single couple (M,G) consistent with fullemployment  As money supply (flows) adjusts external payments: Shall we utilise both instruments M and G, or set G only and let the automatic adjustment of M to operate ? b) Full employment equilibrium with flexible exchange rate

90

We start from : Yˆ  Y , Y  F ( L) being the full-employment product. 2 tools: Monetary policy (M) and budget policy (G). The selected Policy mix depends on the efficiency of each policy. We present the global macro-mechanisms generated by each policy Monetary policy

Increase in M decrease in r Backward effect

External effect Deficit BC

Increase in I

Deficit BG

Increase in Y

Deficit BE Depreciation of E

Internal effect Increase in X

Improved BE

&

Decrease in IM BG = 0

We know that the internal effect is weak.

91

The external effect depends on capital mobility: 1) High mobility ( BCr '  0 )  Important capital outflows  strong depreciation of the national currency  Forte hausse des exportations et baisse des importations  Forte hausse de Y

2) Low mobility ( BCr ' 0 )  Limited outflows of capital  Low depreciation of the national currency  Low increase in exports and low decrease in imports  Limited increase in Y

Diagnosis: High mobility  High efficiency of monetary policy. Low mobility  Low efficiency of monetary policy.

92

Budget policy

Increase in G External effect Increase in Y

Improvement in BC

Worsening BE

crowding-out

Increase in r Internal effect

High mobility

Low mobility

Improving BG

Worsening BG

Appreciation of E

Depreciation of E

Decreasing X & increasing IM

+

Increasing X & decreasing IM

BG = 0

Diagnosis: Budget policy is highly efficient when capital mobility is low, and weakly efficient when capital mobility is high.

93

c) Full employment equilibrium with fixed exchange rate

We know that there is a single policy mix (M,G) consistent with full employment. This policy mix can be easily determined from the 3 equations IS, LM and EE.





BG  BE (Y , E )  BC r(Y , M )  0

 determining of M  M  determining of r  r Y , M  

determining of G  Y / k  I (r )   X ( E )  IM ( E,Y )   C .

In addition, we know that the money supply automatically adjusts through money inflows and outflows.

Nevertheless, we show that this adjustment can be difficult, particularly when capital mobility is low.

94

Budget policy G  G

Increase in G External effect Increase in Y Improving BC

Worsening BE

High mobility

low mobility

crowding-out

Increase in r Internal effect

+ Increase in I

BG > 0

BG < 0

Money inflows

Money outflows

decrease in r Increase in r

Decrease in I Worsening BC

Improving BC BG = 0

1) Budget policy is more efficient in high than in low mobility of capital. 2) Budget policy can be difficuklt to implement when capital mobility is low if the country does not have a sufficient amount reserves to pay its deficit in foreign currency.  In the case of low mobility, the public policy maker can prefer to implement a restrictive monetary policy which prevents capital and money outflows so as to maintain the foreign currency reserves. As there is a single policy mix for obtaining a given production, the determining of G defines a single Y and a single M.

95

 Any monetary policy implemented alone is fully inefficient.

There is an automatic return to the initial equilibrium when monetary policy is set alone.

Increase in M Decrease in r Increase in I

Worsening of BC

Deficit of BG

Money outflows

Worsening of BE

Decrease in M

Increase in Y

c) Summary

Most efficient policy depending on the exchange rate regime and capital mobility* Exchange rate regime capital mobility

Flexible

Fixed

High

M+

G+

Low

G+

(M-, G+)

* The goal is to increase production

96

4. Destabilizing speculation

Speculators determine the market  Speculation determine the mrket price, at least in the short and middle terms. .

 The rational behaviour of speculators no longer consists in lying on the equilibrium price corresponding to ‘fundamentals’, but on their perception of the behaviour of other speculators  Mimetic behaviours  Destabilizing speculation with brutal tirnarounds.

Simple modelling : esa (t )    e(t  1)  (1   )



Eˆ  E (t  1) E (t  1)



e(t )  esa (t )  E (t )  1  esa (t )  E (t  1)

(1) (2)

Equation (1) show that the speculators’ behaviour is based on two elements : 1) Changes observed in the short term (preceding period), which depicts the mimetic behaviour, and 2) the gap with the equilibrium value corresponding to fundamentals, Eˆ . Eˆ  E (t  1) acts alone (   0 ), the market immediately comes back to E (t  1) the ‘normal’ equilibrium :

When

 Eˆ  E (t  1)  E (t )  E (t  1)  1    Eˆ   E ( t  1)  

Equation (2) stipulates that ‘speculators determine the market’.

97

Modelling with ‘self-fulfilling prophecies’: esa (t )    e(t  1)  (1   )



Eˆ  E (t  1)  Cr (t ) E (t  1)



e(t )  esa (t )  E (t )  1  esa (t )  E (t  1)

(1’) (2’)

98

99

Slide 9 Limits of the Keynesian model with fixed prices

100

a) Fixed prices 1. Prices and wages are rarely fixed, even downward. In addition, when productivity grows, prices can move down without decrease in wages.

2. Contradiction fixed price-flexible exchange rate in the MF model: a) Imported inputs b) Wage indexation to prices  Moves in the exchange rate impact prices through costs.  Contradiction fixed price and wages-flexible exchange rate.

b) Expectations 1. In the investment function I  I (expected returns, interest rate)

2. In capital flows

       EC  EC ( r , r* , eta,t 1 )  BC  EC  SC  BC ( r , r* , eta,t 1 )     SC  SC ( r , r* , eta,t 1 )  

101

c) Debts 1. Budget policy and public debt G  Y  public deficit  Public debt.

Cumulative deficit: Deficit



Debt  Deficit  Debt  Deficit.. .

Gˆ  G  r  DG DG (t )  G  r  DG (t 1)  Y  DG (t 1) si G   Y

2. Capital flows and external debt

BG  BE(Y , E)  BC(r )  0

BE(Y , E)  0  BC(r)  0  External debt BG  BE(Y , E)  BC(r)  r  DEXT  0 ,

t

DEXT   BC (i) 0

BC(r)  BE(Y , E)  r  DEXT (t ) exponentially growing when DEXT (t ) rises

Conclusion: even in the short term, correcting those shortcomings is necessary...