The classical model output, employment and real interest rate

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The classical model output, employment and real
interest rate

• Chap 3, Mankiw

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• The classical (neo-classical) macro model (Chaps
  3-6)
• assumes markets always clear hence often
  described as the long run theory of employment,
  output, prices and growth
• assumes long run employment, output, growth are
  driven by fundamentals of an economy factor
  endowments, technology, productivity, preferences
  etc.
• prices are a monetary phenomenon determined by
  quantity of money supply money is neutral in
  the long run changes in money supply has no
  real effect

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Chap 3 - the real economy.

• This chapter discusses-
• The supply side of the real economy
• factors determining the economys total supply of
  goods and services i.e.
• how are labor, land and capital owners
  compensated
• The demand side of the real economy
• factors determining the demand for goods and
  services, by households, firms and the govt.
• Equilibrium
• what ensures that total supply total demand
  how equilibrium in the goods market is achieved

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The circular flow model with government
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• The supply side of the real sector
• the economys total supply of goods and
  services/ total income is determined by,
• the economys supply of inputs/factors of
  production
• available technology
• factors of production
• K capital, tools, machines, and structures
  used in production
• L labor, the physical and mental efforts of
  workers
• N land,
• All non-renewable resources
• available technology the form of the production
  function

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The production function and its properties

• represented as Y F (K, L), N being fixed is
  ignored
• shows how much output (Y ) the economy can
  produce from K units of capital and L units of
  labor.
• F reflects the economys level of technology
  technological progress affects F.
• is increasing in each of the arguments, K and L,
  given the other
• exhibits diminishing returns to inputs
• exhibits constant returns to scale.

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Returns to scale

• Suppose initially, Y1 F (K1 , L1 ) where K1 ,
  L1 are given
• Scale all inputs by the same factor z
• K2 zK1 and L2 zL1
• (If z 1.25, then all inputs are increased by
  25)
• What happens to output, Y2 F (K2 , L2 ) ?
• If constant returns to scale, Y2 zY1
• If increasing returns to scale, Y2 gt zY1
• If decreasing returns to scale, Y2 lt zY1

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• Returns to inputs
• Marginal product of labor (MPL)
• The extra output the firm can produce using an
  additional unit of labor (holding other inputs
  fixed)
• MPL F (K, L 1) F (K, L)
• Diminishing marginal returns to labor
• As a factor input is increased, its marginal
  product falls (other things equal), because
• ?L while holding K fixed
• ? fewer machines per worker
• lower productivity
• Note definitions apply to all inputs

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Diminishing marginal returns and the production
function
Y output
MPL
L labor
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Assumptions about the supply of inputs/factors of
production

• Technology is given.
• The economys supplies of capital and labor are
  fixed at

Output is determined by the fixed factor supplies
and the fixed state of technology
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Pricing of factors of production and the
distribution of national income

• factor price the price per unit that firms pay
  for a factor of production.
• wage rate the price of L per unit,
• rental rate the price of K per unit.
• W nominal wage
• R nominal rental rate
• P price of output
• W /P real wage (measured in units of output)
• R /P real rental rate

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How factor prices are determined - labor

• Factor markets are assumed to be competitive.
  Hence, factor prices are determined by supply and
  demand of factor services.
• Supply of each factor fixed by assumption, (see
  slide 10).
• Demand for factor inputs each firm takes W, R,
  and P as given. A firm hires each unit of labor
  if the cost for that unit does not exceed the
  benefit.
• cost real wage
• benefit marginal product of labor

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MPL and the demand for labor the demand curve
is the same as the MPL curve
Each firm hires labor up to the point where MPL
W/P
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MPK and the demand curve for capital the demand
curve for capital is the same as the MPK curve

• We have just seen that at a given real wage rate
  the quantity demanded of labor is at the point at
  which, MPL W/P
• The same logic shows that quantity demanded of
  capital at a given real rental rate is at the
  point, MPK R/P
• diminishing returns to capital MPK ? as K ?
• The MPK curve is the firms demand curve for
  renting capital.

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Calculus approach to the derivation of demand
curves for factor inputs firms choose a level of
employment and capital use to maximize profits,
given factor prices Profits revenue costs
P Y W L R K P F(L, K)
W L R K take partial derivatives of the
profit function with respect to L and K and set
them equal to zero (to be shown in class). P
FL(L, K) W 0 or rearranging terms FL(L, K)
W/P P Fk(L, K) R 0 or rearranging terms
FK(L, K) R/P
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Equilibrium in the factor markets equilibrium
real wage rate (rental rate) and employment
(capital use)
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• The neo-classical theory of income distribution
• each factor, in equilibrium, is paid according
  to its marginal product i.e the contribution made
  to output by the last unit employed
• if production function exhibits constant returns
  to scale, total factor payments in equilibrium is
  equal to total output, i.e. economic profits 0,
  in equilibrium
• The last statement is known as the Eulers
  theorem in calculus or as the product
  exhaustion theorem in economics.
• Economic profits output factor payments
• Accounting profits and economic profits are not
  the same.

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The neo-classical theory of income distribution

• total labor income

total capital income
If production function has constant returns to
scale, then
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The demand side of the economy - Demand for goods
services

• Components of aggregate demand
• C consumer demand for goods services
• I demand for investment goods
• G government demand for goods services
• (closed economy no exports or imports, NX 0
• Planned consumption or the consumption function
• C C (Y T ) is an increasing function,
  implying that a rise in (Y T) raises C
• Y T disposable income, total income minus
  total taxes
• the marginal propensity to consume is the
  increase in C caused by a one-unit increase in
  disposable income.

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The linear consumption function
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Planned investment or the Investment function

• The investment function is I I (r ),
• where r denotes the real interest rate, i.e.
  the nominal interest rate corrected for
  inflation.
• The real interest rate is the cost of borrowing
  for a borrowing firm the opportunity cost of
  using ones own funds to finance investment
  spending.
• So, I(r) is inversely related to r, ?r ? ?I
• Digression An alternative way of understanding
  the inverse relationship is to use the notion of
  PDV present discounted value of a project.
• Planned Government spending
• G (includes transfer payments) constant,
• T constant

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The investment function
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The market for goods services

• The real interest rate adjusts to equate demand
  with supply.

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Explaining equilibrium - relationship between
market for goods and the market for financial
assets

• A simple supply-demand model of the financial
  system.
• We have one asset loanable funds or bonds
• demand for loanable funds or supply of bonds
  investment
• supply of loanable funds or demand for bonds
  saving
• price of funds real interest rate, inverse
  of bond price
• Demand for funds comes from investment firms
  borrow to finance spending on plant equipment,
  new office buildings, etc consumers borrow to
  buy new houses is inversely related to r.
• supply of funds comes from savings by households
  (and government, so long as it is not incurring
  budget deficits

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Types of saving

• private saving (Y T ) C
• public saving T G
• national saving, S private saving public
  saving
• (Y T ) C T G
• Y C G
• When T gt G , budget surplus (T G )
  public saving
• When T lt G , budget deficit (G T ) and
  public saving is negative.
• When T G , budget is balanced and public
  saving 0.

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The U.S. Federal Government Budget
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The U.S. Federal Government Debt
Fun fact In the early 1990s, nearly 18 cents of
every tax dollar went to pay interest on the
debt. (Today its about 9 cents.)
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Equilibrium in the market for loanable funds
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The special role of r in ensuring equilibrium in
goods and financial markets

• r adjusts to equilibrate the goods market and
  the loanable funds market simultaneously
• If L.F. market in equilibrium, then
• Y C G I
• Add (C G ) to both sides to get
• Y C I G (goods market eqm)
• Thus,

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An increase in investment demand

• An increase in desired investment

r1
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An increase in investment demand when savings
depend on the interest rate
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