Lecture II Longterm static model

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Lecture IILong-term static model

• Classical model

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II.1 Macroeconomic equilibrium
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General equilibrium

• On a single market DS
• General equilibrium DS on all markets
  simultaneously, model solution
• Walrasian general equilibrium market
  equilibrium, when each agent maximizes his target
  function, given his constraints
• Equilibrating mechanisms, flexible prices
• More general concept equilibrium as a state of
  rest
• D does not have to equal S, prices do not have to
  clear all markets

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Adjustment towards equilibrium (1)

• All agents behave rationally, maximizing profit
  or utility
• All markets fully competitive, decision of agents
  based on fully flexible prices
• Agents have full information about the market
  conditions and prices before the start of every
  transaction a all transactions take place only
  after all equilibrium prices are known on all
  markets
• Agents have stable expectations

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Adjustment towards equilibrium (2)

• All markets clear sufficiently quickly towards
  equilibrium (when DS)
• If disequilibrium happens (D?S), it is either
  because of external shock and/or due to the
  short-term position within an economic cycle

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Long-term concept

• The conditions above are almost never fulfilled
  in real world
• Price rigidities
• Asymmetric information
• Many other violations
• However a prevailing consensus among economists
  that these conditions fulfilled in a hypothetical
  long-term, when all prices have time to adjusts
  and when all information reaches all agents
• Hypothetical ideal long-term equilibrium hardly
  to be reached, dynamic changes in the meantime

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Long-term model

• This Lecture long-term, static, macroeconomic
  model
• Equilibrium (DS) on all 3 aggregate markets
  goods and services, labor, money (financial
  market)
• Assumptions (simplifications)
• Capital K fixed
• Amount of labor available fixed
• Time horizon long enough to allow for
  adjustment towards equilibrium on all markets
• Theoretical concept, in reality close to medium
  term
• Closed economy
• Distinguish from dynamic growth models (Lecture
  IX)

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II.2 Production function
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Simple version

• Production function
• two factors, substitution
• product Y, labor N, capital K
• F(.) technology,
• Y F(K,N)
• Primarily microeconomic concept
• Assumption of aggregation

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Basic properties

• constant returns to scale
• tYF(tK, tN), t gt 0
• marginal product of labor and capital
• co-operative factors
• MPL extra amount of output the firm gets from
  one extra unit of labor
• diminishing MPL holding K fixed, MPL decreases
  as N increases
• The same MPK

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Y
N
MPL
N
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Optimization behavior of the firm profit
maximization (1)

• Firm sells production at the price P, hires
  workers at wage W and finances capital at
  interest R
• Profit ? P.F(K,N) W.N R.K
• Profit maximization subject to N (K fixed)
• , ?
• and

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Optimization behavior of the firm profit
maximization (2)

• Same procedure when maximizing profit subject to
  capital (labor fixed)
• First-order condition FNW/P, FKR/P
• Interpretation firms hires the factor up the
  point when hiring the next unit ceases to
  profitable

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W.N
P.F W.N
P.F
A
N
Profit max at point A marginal revenue (slope of
WN) equals marginal costs (slope of P.F)
A
N
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II.3 Labour market
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Demand (1)

• First order condition for profit max.gt ?
  implicit relation between demand for labor and
  real wage
• Total derivative
• and

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Demand (2)

• With higher real wage firms demand for labor
  falls
• Partial derivative of labor demand with respect
  to real wage is
• and
• is an explicit expression of the labor demand ?
  decreasing function of real wage

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Supply of labor (1)

• Typical worker maximizing his utility to achieve
  a mix between consumption C and leisure H, knows
  the price P
• Utility
• Max UT subject to
• Analytical solution not so easy, graphical
  exposition

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C
B
A
H
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Supply of labor (2)

• Labor supply increasing function of real wage
• Aggregation over the whole labor market

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Equilibrium on the labor market

• Condition
• Employment , real wage
• Assumptions
• Real wage flexible
• Nominal wage adjusts
• Full information
• Important the concept of labour demand generally
  accepted by all, but macroeconomists
  fundamentally differ about supply of labour the
  above formalization very often refused

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E
N
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II.4 Components of aggregate demand
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National Income identity and CA

• Basic identity Y C I G CA
• CA X - M, current account, i.e. exports minus
  imports
• Domestic absorption C I G
• CA gt 0 - surplus, country lends abroad,
  foreigners borrow and will have to repay
• CA lt 0 - deficit, country borrows abroad, will
  have to repay
• Other interpretation of CA change of Net Foreign
  Wealth of the country

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Savings and current account

• National savings S Y - C - G, i.e. income less
  everything we spend either as private individuals
  or as government
• Closed economy S I
• Open economy S I CA
• Country can build up savings by lending abroad
• Another interpretation I S - CA, i.e. country
  can finance investment without increasing savings
  (i.e.lowering consumption) by borrowing abroad

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Private and Government Spending

• Private savings disposable income (YD Y - T)
  minus personal consumption C Sp Y - T - C
• Government savings revenues (T) minus
  expenditures (G) Sg T - G
• S I CA (Y - T - C) (T-G) Sp Sg
• Define budget deficit BD - Sg G - T
• Private savings Sp I BD CA
• Crucial interpretation of private savings - it
  can take three forms a. investment in domestic
  capital, b. purchase of wealth from foreigners,
  c. purchase of the debt (newly issued) of the
  Government

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Consumption and savings

• Determinants of personal consumption
• Disposable income
• TT(Y)
• the larger YD, the larger consumption and savings
• Real interest rate
• reward for consumption postponement
• higher r ? lower consumption, higher savings (and
  vice versa)
• Consumption function
• Savings function

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Remark on consumption and savings

• There are many ways how even these simple
  specifications of consumption and savings
  functions are differently used in different
  models
• In discussing different models, we will
  interchangeably vary (simplify) specification,
  e.g. consumption being the function of YD only,
  or savings depending only on r

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Investment demand, governmental expenditure

• Interest measures the costs of investment
  financing, return must be higher than interest
• Higher interest ? few projects with return
  exceeding interest (and vice versa)
• Demand for investment

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Project 1
Project 2
Project 3
r
Project 4
I
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II.5 Aggregate demand and supply(market for
goods and services)
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Full employment productaggregate supply

• Equilibrium on labor market full employment
• Capital fixed in the short run K
• Full employment product is
• Changes in only if
• shift in labor demand/supply schedules
• shifts in production function

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E
N
Y
N
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Aggregate demand

• Consumption function
• Investment function
• Governmental expenditure G
• Aggregate demand

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Equilibrium

• Aggregate supply AS
• Labor market in equilibrium employment N
• Production function aggregate supply Y
• Aggregate demand
• Equilibrium ADAS, hence
• Classical question what ensures that if
  supply is determined by full employment from
  labor market AD exactly matches AS?

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II.6 Equilibrating mechanism.
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Jean - Baptist Say

• 1767 1832
• Gifted political thinker and economist
• 1803 Traité deconomie politique (Treatise of
  Political Economy)
• Many other works
• Professor at lAthénée and at Collège de France

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Says law

• Barter (no money or as a numeraire only)
• products are paid for by products or supply
  creates its own demand
• Sum of all supplies sum of all demands
• Monetary economy (n-1 goods, money as a store of
  value, John Stuart Mill, David Ricardo)
• Sum of n-1 supplies sum of n-1 demands ? supply
  of money equals demand for money
• People produce (and supply) goods to earn money
  to spend for other goods immediately

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Implications

• If aggregate supply reflects full employment then
  involuntary unemployment because of insufficient
  demand can not exist
• Aggregate supply always equals aggregate demand
• Change of the price level doesnt have an impact
  on particular demands and on relative prices
• Money as veil

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Equilibrium and real interest

• Basic identity (remember II.4 above)
• I S (T G) (closed economy, CA0)
• Remark on notation here S is used for personal
  savings only (Sp in II.4)
• For classical model
• and when output Y is given on the supply side,
  then real interest r is only variable that
  adjusts to bring the aggregate demand to be
  exactly equal to given aggregate supply
• Ex-ante, the identity becomes and equilibrium
  condition, with interest r as equilibrating
  variable rewrite it as

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r
r1
r0
r2
I(r)G
IG, ST
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Loanable funds interpretation

• Savings supply of loanable funds households
  and government postpone the consumption, creating
  funds that may be used for investment financing
• Investment plans demand for financing, demand
  for loanable funds
• Real interest price, that adjusts and
  equilibrates the model
• If rgtr0, then excess supply of loanable funds and
  r decreases
• If rltr0, then excess demand of loanble funds and
  r increases

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II.7 The quantity theory of money
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The Quantity Equation

• Total expenditures in an economy expressed in
  two ways
• P.TRN, where P is aggregate price, TRN is number
  of transactions in the economy
• M.V, where M is nominal quantity of money, V is
  the transactions velocity of money
• V rate, at which the money circulates in the
  economy (how many times a unit of money changes
  hands)
• Both expressions must be equal, quantity
  equation M.VP.TRN
• Ex-post always true, identity (it is not a
  theory)
• TRN impossible to measure, approximation by total
  income (product) Y M.V P.Y
• V income velocity of money

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The Quantity Theory

• Theory seeks to answer following questions
• How is the equilibrium amount of money in the
  economy determined?
• What is the impact of the money on the economy
  (does the change of amount of money influences
  output, price, employment, etc.).
• Two versions of QTM, here only Fishers (full
  explanation see Lecture V)

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Irving Fisher

• 1867-1947
• American
• Neoclassical Marginalist Revolution, mathematical
  methods
• Introduced Austrian economic school to the USA
  (Theory of capital and investment, 1896-1930),
  intertemporality
• Quantity theory of money (1911-1935)
• Loss of credibility during Great Depression

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Fishers QTM (1)

• Two assumptions in the framework of classical
  model
• In equilibrium, real output determined by full
  employment labor (given at the cleared labor
  market). Real economy independent on money
  supply.
• Velocity of money is given by technical features
  of the markets and is not in any relation to
  amount of money in the economy
• Usual corollary (however, not stipulated by
  Fischer himself) around equilibrium (i.e. at
  least in the short-term) velocity V is constant

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Fishers QTM (2)

• How the quantity equation becomes a theory ? If
• V and Y is fixed with respect to money supply
• Money is required for transactions
• Money supply M is exogenous
• then M.V P.Y is an equation of the model
  (required to be valid ex-ante) which says that in
  equilibrium, when output Y is given in the real
  sector of the economy and V is constant, the
  supply of money, controlled by central bank,
  determines the price level P only (P is
  proportional to M)
• Corollary real variables (output and its
  components, unemployment, etc.) are independent
  on the amount of money or, change in the money
  supply has an impact on the price level only (but
  not on output)
• Fishers QTM develops from quantity equation,
  no explicit consideration of supply and demand
  for money

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II.8 Complete model(closed economy)
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The model

• Labor market and aggregate supply
• W/P FN(K,N) demand for labor
• N NS(W/P) supply of labor
• Y F(K,N) production function
• Market with goods and services
• Y C I G demand and equilibrium,
• consumption function
• I I(r) investment function
• Financial (money) market price equation
  (Fishers version)
• M.V P.Y equilibrium

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Technical features

• 7 equations and 7 endogenous variables
• Y, C, I, N, W/P, P, r
• 3 exogenous variables K, M, G
• 1 constant V
• Equilibrium on 3 markets
• Goods and services, labor (factor) and money
  (financial)
• 2 equation of labor market form an independent
  block, 3 equations of labor market and aggregate
  supply form another independent block

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Static, general equilibrium model

• Time horizon sufficiently short for capital and
  total labor force fixed.
• Time horizon sufficiently long for the
  adjustment of perfectly flexible prices, thus
  ensuring the simultaneous equilibrium on all
  markets
• In particular, this applies for labor market,
  where there is no possibility of involuntary
  unemployment
• Strong theoretical assumptions, but at the end of
  XIX. and beginning of XX. centuries generally
  accepted of more or less consistent with reality

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Dichotomy of the classical model

• Real sector labor market, flexible nominal wage,
  production function, Says law
• full employment equilibrium product
• supply side determines the product at given
  price and amount of money
• Classical dichotomy, money is neutral (veil)

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P
AS
P0
M0V
W0
W0/P0
Y0
Y
W/P
ND
N0
F(K,N)
NS
N
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II.9 Policies
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Multipliers - general

• Intuitive interpretation the change of (or a
  direction of change from) equilibrium value of an
  endogenous variable when value of exogenous
  variable changes
• Policy interpretation exogenous variable as
  policy instruments, e.g. if money supply or taxes
  increase, what is the impact on endogenous
  variables of the system
• Historically first Richard Kahn, a student of
  Keynes, for particular situation impact of
  governmental expenditure on output and
  consumption, see Lecture on Keynes
• Mathematical interpretation partial derivative
  of a reduced form of the model (here in
  graphically)

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Policy implications

• Different social demand and different policy
  goals
• Economic growth and full employment were not
  perceived as visible targets
• Governments were not perceived as being
  responsible
• Classical model - limited possibilities for
  macro-policies
• Fiscal policies crowding-out of the private
  investment (small governments anyway)
• Monetary policies only impact on general price
  level

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P
AS
M1gtM0
P1
M1V
W1
P0
M0V
W0
W0/P0
Y0
W0/P1
W1/P1
Y
W/P
ND
N0
F(K,N)
NS
N
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Crowding-out effect

• In the classical model, when output given on the
  supply side, increase of any component of
  aggregate demand can not cause increase of output
  (and employment)
• Zero efficiency of fiscal policy increase in
  governmental expenditures at the cost of decrease
  of investment/consumption
• Value of fiscal multiplier equals zero

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Money neutrality

• Change of money has an proportional impact on the
  price level
• Amount of money has not any consequence for real
  output and employment
• See graphical exposition on the next slide
• Value of money multiplier equals zero

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Literature to L.II

• Snowdon, B., Vane, H., Modern Macroeconomics,
  Edvard Elgar, 2005, Ch.2, pp.36-54
• Basic reading to this chapter and literature
  there (e.g. on Says law), with exception of gold
  standard
• Mankiw, G.N. Macroeconomics, Worth Publishers,
  New York, 1992 (and subsequent editions)
• In Ch. 3 and 7, most of the features of classical
  model are being discussed
• Sargent, T., Macroeconomic Theory, Academic Press
  1987 (2nd ed.), Ch. 1
• Very difficult, mathematical approach. However,
  if you struggle through (or even skip much of)
  mathematics, you get a very clear picture of the
  model, discussed in this chapter.
• Mishkin, F.S., The Economics of Money, Banking
  and Financial Markets, HarperCollinsPublishers,
  1993 (3rd ed.), Ch. 23, pp.523-530 (there is a
  Czech translation)
• Comprehensible explanation of QTM