Macalester College Intermediate Macroeconomic Analysis

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Macalester CollegeIntermediate Macroeconomic
Analysis

• THE CLASSICAL MODEL

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Controversy in Macroeconomics

• Keynesian
• Short run
• Sticky prices
• Government intervention
• East Coast schools
• Econometrics
• Pragmatic
• Left
• Equality

• Classical
• Long run
• Market clearing
• Leave markets alone
• Chicago School
• Calibration
• Theoretically sound
• Right
• Freedom

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Outline of the 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
• loanable funds market

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The Production Function

• Two production factors Capital (K) and labor
  (L).
• The function Y F (K, L) shows how much output
  (Y) the economy can produce from K units of
  capital and L units of labor.
• The economys supplies of capital and labor are
  fixed at K K and L L. Thus, the supply of
  goods is fixed at Y F (K, L).

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Assumptions about F

• We assume constant returns to scale.
• F(zK, zL) z F(K, L)
• We assume increasing returns to the factors.
• ?F(K, L)/?L gt 0 and ?F(K, L)/?K gt 0
• We assume diminishing marginal returns to the
  factors.
• ?2F(K, L)/?L2 lt 0 and ?2F(K, L)/?K2 lt 0
• We assume that factors are complementary.
• ?2F(K, L)/?L?K gt 0 and ?2F(K, L)/?K?L gt 0

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Marginal product of labor (MPL)

• MPL is 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)
• MPL ?F(K, L)/?L

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The MPL and the production function
Y output
F(K, L)
MPL
L labor
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Labor and Capital Complement Each Other
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Cobb-Douglas Production Function
Y A K ? L1-a
Verify that the properties are satisfied.
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Factor Markets

• The wage (W) is the price of labor , the rental
  rate (R) is the price of capital.
• Factor prices are determined by supply and demand
  in factor markets.
• Supply of each factor is fixed.
• Demand of factors is determined by
  profit-maximizing behavior of the firms.
• Factor prices determine the distribution of
  income.

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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 (measured in
  units of output)

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Exercise
You can buy as many Twins tickets as you like at
a price of 6 each. You know that you can sell
them according to the following table. How many
tickets do you buy?

• of tickets Selling Price
• 0 0
• 1 10
• 2 19
• 3 27
• 4 34
• 5 40
• 6 45
• 7 49
• 8 52
• 9 54
• 10 55

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Exercise
You can hire as many workers as you like at a
wage of 6 each. You know that they will generate
income according to the following table. How many
workers do you demand?

• of workers Revenue
• 0 0
• 1 10
• 2 19
• 3 27
• 4 34
• 5 40
• 6 45
• 7 49
• 8 52
• 9 54
• 10 55

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Graphs
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Demand for labor

• Assume markets are competitive firms take W, R,
  and P as given.
• Firms hire more labor if the cost does not exceed
  the benefit.
• Maximize Profit P F(K, L) - W L - R K

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MPL and the demand for labor
Each firm hires labor up to the point where MPL
W/P
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The Labor Market
Labor supply
The real wage adjusts to equate labor demand
with supply.
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Determining the Rental Rate of K

• 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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The Capital Market
The real rental rate adjusts to equate demand
for capital with supply.
Supply of capital
K
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Income Distribution

• Total labor income (W / P) L MPL L

Total capital income (R / P) K MPK K
If production function has constant returns to
scale, Y MPL L MPK K OR P Y W L
R K Verify with the Cobb Douglas production
function.
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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 NX )

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Consumption

• Disposable income is total income minus total
  taxes Y T
• Consumption function C C (Y T ) ?(Y
  T ) ? ?C
• The marginal propensity to consume is the
  increase in C caused by a one-unit increase in
  disposable income.
• C MPC (Y T ) C0

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The consumption function
C (Y T )
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Investment, I

• The investment function is I I (r ), where r
  denotes the real interest rate, the nominal
  interest rate corrected for inflation.
• The real interest rate is
• the cost of borrowing
• the opportunity cost of using ones own funds to
  finance investment spending.
• So, ?r ? ?I

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The Investment Function
I (r )
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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 Loanable Funds Market

• A simple supply-demand model of the financial
  system.
• One asset loanable funds
• Demand for funds investment
• Supply of funds saving
• Price of funds real interest rate

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Supply of funds Saving

• The supply of loanable funds comes from saving
• Households use their saving to make bank
  deposits, purchase bonds and other assets.
• The Government also contributes to saving if it
  does not spend all of the tax revenue it
  receives.
• These funds become available to finance
  investment spending.

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Types of Saving

• Private saving (Y T ) C
• Public Saving T G
• National Saving S
• National Saving Private Saving Public Saving
• S (Y T ) C T
  G
• S Y C G

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Budget Surpluses and Deficits

• 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
• Balanced Budget is balanced and public saving
  0.

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The U.S. Federal Government Budget
(T-G) as a percent of GDP
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The U.S. Federal Government Debt
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Says Law
If S I
E C I G
C S G
C (SP SG) G
C (Y T C) (T G) G
Y
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Says Law the Loanable Funds Market
Says Law Implies
Y C I G
Y C G I
Thus SI and YCIG state the same result
(Y - T - C) (T G) I
SPrivate SGovernment S I
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Circular Flow
Factor Markets
Y
If SI
SPY-T-C
SSPSG
Financial Markets
SG T-G
T
Households
Firms
Government
I
G
C
Then YCIG
Goods markets
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Says Law in the Circular Flow Example
Factor Markets
Y 100
Financial Markets
SP20
S20
SG0
T10
Households
Firms
Government
G10
I20
C I G
C70
Goods markets
702010
100
Y
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Effect of Lower Consumption
What mechanism links higher savings to greater
investment?
Factor Markets
Y 100
30
30
SP20
S20
Financial Markets
SG0
T10
Households
Firms
Government
G10
I20
C I G
C70
Goods markets
30
603010
60
100
Y
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Effect of a Government Tax Cut
Factor Markets
Y 100
21
16
SP20
S20
Financial Markets
-5
SG0
5
T10
Households
Firms
Government
G10
I20
C I G
C70
Goods markets
16
741610
74
100
Y
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Demand for Loanable Funds
r
.07
.05
I I(r)
I
I0
I1
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Loanable funds supply curve
National saving does not depend on r, so the
supply curve is vertical.
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Loanable funds market equilibrium
I (r )
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The market for goods services

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

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Supply of Loanable Funds
r
S SPrivate SGovernment
.07
.05
S
S0
S1
? r
? ? return to saving (opportunity cost of cons.)
? ? desired savings
? ? desired consumption
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Loanable Funds Market Equilibrium
r
S SPrivate SGovernment
r
.07
.05
I I(r)
S I
I
S
SI
r equilibrium interest rate, which balances
supply of loanable funds (S) with demand for
loanable funds (I).
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Factors that Shift Demand for Loanable Funds
r
Technological boom
Optimism
.07
I I(r)
I
I1
I0
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Factors that Shift Supply of Loanable Funds
r
S SPrivate SGovernment
Rise in income
.07
Fall in wealth
Rise in taxes
Culture
S
S0
S1