Mankiw 5e Chapter 3: National Income

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CHAPTER THREE National IncomeWhere it Comes
From and Where it Goes
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A Model for National Income

• How national income is determined
• How the prices of the factors of production are
  determined
• How national income is distributed
• How equilibrium in the goods market is achieved
• This chapter will propose a simple model to
  address these issues

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Outline of model

• A closed economy, market-clearing model
• Supply side
• factor markets (supply, demand, price)
• determination of output/income
• Demand side
• determinants of C, I, and G
• Equilibrium
• goods market
• Financial market (loanable funds market)

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The Circular Flow
Factor payments
Market for factors of production
Income
Private Saving
Financial Markets
Public Saving
Investment
Taxes
Households
Firms
Households
Government
Government Purchases
Firm Revenue
Consumption
Market for goods and services
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Factors Production

• Assume that there are only two inputs in this
  economy capital (K) and labor (L)
• For now, assume full employment and that these
  inputs are in fixed supply

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Factors of production

• K capital, tools, machines, and structures
  used in production
• L labor, the physical and mental efforts of
  workers

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The production function

• denoted Y F (K, L)
• shows how much output (Y ) the economy can
  produce fromK units of capital and L units of
  labor.
• reflects the economys level of technology.
• exhibits constant returns to scale.

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Returns to scale a review

• Initially Y1 F (K1 , L1 )
• 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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Assumptions of the model

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

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Determining GDP

• Output is determined by the fixed factor supplies
  and the fixed state of technology

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Marginal product of labor

• Decreasing marginal products
• Marginal product of labor
• I.e., extra amount of output from one extra unit
  of labor, holding the amount of capital fixed

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Marginal product of labor

• MPL is the slope of this curve
• MPL is decreasing in L

Y
F(K,L)
Low MPL
High MPL
L
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Marginal product of capital

• Similarly
• Marginal product of capital
• I.e., extra amount of output from one extra unit
  of capital, holding the amount of labor fixed

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Marginal product of capital

• MPK is the slope of this curve
• MPK is decreasing in K

Y
F(K,L)
Low MPK
High MPK
K
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Cobb-Douglas Production Function

• A overall level of efficiency
• (relative importance of capital)
• Constant Returns to Scale

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Cobb-Douglas Production Function

• Diminishing marginal products
• (decreasing in L)
• (decreasing in K)

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Distribution of Income

• What determines capital and labor income?
• Neoclassical theory of distribution factor
  prices are determined such that factor demand
  equals factor supply

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Factor Demand

• We suppose that a typical firm in this economy is
  competitive, i.e., takes factor prices and output
  prices as given
• Given prices, firms choose capital and labor
  inputs such that their profit is maximized

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Notation

• 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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Factor Demand

• Firm revenues PY PF(K,L)
• Firm costs labor costs capital costs
• w L R K
• w wage rate R rental rate of capital
• Profits Revenues Costs

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Factor Demand

• Firms choose amounts of capital and labor such
  that profits are maximized, taking prices as
  given

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Factor Demand

• First-order conditions

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Factor Demand

• P x MPL revenue from an extra worker
• w cost of extra worker
• Firm hires labor until additional revenue equals
  additional cost. Similarly for capital.

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Factor Demand

• Rewriting
• Labor Demand
• (marginal product of labor real wage)
• Demand for Capital
• (marginal product of capital real rental rate)

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Demand for labor

• Basic ideaA firm hires each unit of labor if
  the cost does not exceed the benefit.
• cost real wage
• benefit marginal product of labor

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Labor Market Equilibrium
Labor supply
w/P
Equilibrium Real wage
Labor demand MPL w/P
L
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Labor Market Equilibrium

• An increase in the number of workers

Ls
w/P
Ld
L
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Labor Market Equilibrium

• An improvement in technology (which makes all
  factors equally more productive)

Ls
w/P
Ld
L
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Determining the rental rate

• We have just seen that MPL W/P
• The same logic shows that MPK R/P
• diminishing returns to capital MPK ? as K ?
• The MPK curve is the firms demand curve for
  renting capital.
• Firms maximize profits by choosing K such that
  MPK R/P .

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Division of Income

• Dollar value of output (P x Y) is divided between
  labor payments (w x L), capital payments (R x K)
  and profits (?)
• If technology is constant returns to scale,
  profits are zero

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Division of Income

• Or
• Output is divided between payments to capital and
  payments to labor, depending on their marginal
  products

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Division of Income

• Cobb-Douglas case
• Capital Share
• Labor Share
• In the Cobb-Douglas case, output is split between
  capital and labor, and the shares are constant.
•  

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Division of Income

• Indeed, labor share is roughly constant around
  70 for the U.S. (see figure 3-5, p.57)
• Because of this, the Cobb-Douglas production
  function is often used by macroeconomists (with
  parameter ? .3 or 1/3)

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Expenditure Side Demand for goods services

• Components of aggregate demand
• C consumer demand for g s
• I demand for investment goods
• G government demand for g s
• (closed economy no NX )

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Consumption, C

• def disposable income is total income minus
  total taxes Y T
• Consumption function C C (Y T )
• Shows that ?(Y T ) ? ?C
• def The marginal propensity to consume is the
  increase in C caused by a one-unit increase in
  disposable income.

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The consumption function
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Investment

• We assume that investment is a decreasing
  function of the real interest rate (r).
  Investment function
• r real interest rate cost of borrowing money
• High interest rate ? fewer profitable investment
  projects ? lower investment

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The investment function
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Government spending, G

• G includes government spending on goods and
  services.
• G excludes transfer payments
• Assume government spending and total taxes are
  exogenous

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The market for goods services

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

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Equilibrium in Financial Markets (loanable fund
market)

• Rewrite the above problem as an equilibrium in
  financial markets, i.e., supply and demand for
  funds
• National saving

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Equilibrium in Financial Markets

• Substituting expressions for C, I, G and T
• In equilibrium
• supply of funds demand for funds

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Equilibrium in Financial Markets

• The equilibrium interest rate is such that the
  market for funds clears

r
S
Equilibrium Interest rate
I(r)
I, S
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Fiscal Policy I An increase in G

• ? higher G implies lower S

r
S
I(r)
I, S
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Fiscal Policy I An increase in G

• Interest rate increases to restore equilibrium
  between savings and investment
• Government expenditures crowd out investment ?
  investment falls by the exact amount as the
  increase in G
• There is no change in income (GDP)

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(No Transcript)
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Fiscal Policy II A tax cut

• A fall in T leads to an increase in consumption
  (given that disposable income is higher) ? total
  saving falls
• As in the previous case, interest rate increases
  ? investment falls by the same amount as the
  increase in consumption

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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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Increase in the Demand for Investment

• The computer is invented

r
S
I(r)
I, S
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The special role of r

• r adjusts to equilibrate the goods market and
  the financial market simultaneously
• If financial 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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Saving and the interest rate

• Why might saving depend on r ?
• How would the results of an increase in
  investment demand be different?
• Would r rise as much?
• Would the equilibrium value of I change?

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An increase in investment demand when saving
depends on the interest rate