3' National Income

1
3. National Income

• Agenda
• What determines the level of national income?
• How the income is distributed to households?
• By whom and how much the income is spent?
• What equilibrates the demand and supply for goods
  and services?

2
Features of the Classical Model

• Economy in the long run
• No price rigidities Prices are flexible.
• (vs. Ch. 9-13 Business cycle theory, Ch. 6
  Unemployment)
• Static Production function, amount of labor and
  capital are given, thus the output is fixed. (
  Unemployment is at the natural level.)
• (vs. Ch. 7-8 Growth theory, Ch. 9-13 Business
  cycle theory)
• Real Only relative prices matters. No money in
  the economy.
• (vs. Ch. 4 Money and inflation)
• Closed Output cannot be exported or imported,
  thus it must be spent in the economy.
• (vs. Ch. 5 Open Economy)

3
The Circular Flow
Actors Households, Firms, Government
Market Goods and Service, Factors of production,
Financial market
4
The Factors of Production

• What determines the output/income/total
  production (supply) of goods and services, that
  is, what are the factors of production?
• Capital (K)
• Set of machines and tools that workers use
• Labor (L)
• Time that people spend working
• Production function F(K, L)
• Given K and L, how much output (Y) is produced
• F(K, L) represents the technology used in the
  economy

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The Production Function

• Production function has the following properties
• Constant returns to scale (CRS)
• F(zK, zL) zF(K, L)
• If K and L increase z times, then Y also
  increases z times.
• Diminishing marginal product
• If only K or L increases, the increase rate of Y
  ( MPK or MPL) gradually decreases.
• MPK (marginal product of capital) is how much
  output increases if the capital increases by one
  extra unit while holding the labor fixed.
• MPL (marginal product of capital) is
  similarly defined.
• MPK F(K1, L ) - F(K, L)
• MPL F(K , L1) - F(K, L)

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Constant Returns to Scale
Economy total ? YyL ? KkL ? L

The number of small firms (workers and machines)L
Ly LF(k,1) F(Lk, L1) F(K, L) Y
constant returns to scale
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Diminishing Marginal Product
gt
gt
MPLF(k,2)-F(k,1)
MPLF(k,3)-F(k,2)
MPLF(k,4)-F(k,3)
lt
lt
lt

The number of workers L
The increase in output (MPL) gradually falls.
Diminishing marginal product
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The Supply of Goods and Services

• K and L are given, thus Y is given.
• No wasted recourses because the prices of labor
  (wage) and the rental price of capital are
  adjusted so that the labor and capital are fully
  supplied.
• This level of the output (Y) called the natural
  level (rate) of the output.
• In the long run means ( the classical
  theory assumes) the considered period is enough
  long to adjust prices, but not enough long to
  change the amount of labor and capital and
  available technology.

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How is National Income Distributed?

• Neoclassical theory of distribution
• The total output/production/income is distributed
  to the households.
• How much is the income distributed to households
  that supply their capital and ones that supply
  their labor?
• ? (Quantities supplied)(Factor Prices)
• How are the quantities and prices decided?
• Quantity The total amount of factors of
  production (i.e., capital and labor) held by
  households
• Prices they are decided by the factor markets
  (i.e., capital market and labor market).

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The Firms Demand for Factors (Labor market)

• How much labor do firms want to hire/demand?
• Firms aim to maximize their profits ( PY-WL-RK).
• So, each firm employs one unit of additional
  labor if the revenue brought by the additional
  labor exceeds the cost of employing it.
• The additional revenue PMPL
• P price of output (price level)
• MPL (marginal product of labor) extra amount of
  output the firm gets from one extra unit of
  labor, holding the amount of capital fixed.
• The additional cost W (wage)

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Profit Maximization

• If PMPL (additional revenue) gt W (additional
  cost)
• ? the firm increases its labor demand.
• If PMPL (additional revenue) lt W (additional
  cost)
• ? the firm decreases its labor demand.
• Therefore, firms demand labor so that PMPLW
• ? MPL W/P
• (W/P is called real wage)

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From the MPL to Labor Demand
1. The production function has the property of
diminishing marginal product The MPL decreases
as the labor increases, while holding the capital
constant.
The slope equals MPL
2. The firm hires labor until MPL Real wage
(W/P)
Labor demand is a decreasing function of the
real wage ? the labor demand curve is downward
sloping.
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Labor Supply

• How much labor do households to supply?
• The amount of labor supplied by households is
  fixed.
• The labor supply curve is vertical Line.
• (Note)
• According to microeconomics, given real wage,
  each household decides their labor supply based
  on its preference between income and leisure.
  Theoretically, as the real wage increases, the
  labor supply increases first, but gradually it
  turns into decrease. Practically, the labor
  supply curve can be considered as upward sloping.
  Note that upward curve does not affect the
  outcome of the model.

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The Equilibrium of Labor Market
In the long run, the wage and prices are
flexible, so the real wage reaches the
equilibrium where the labor demand equals the
labor supply.
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The Capital Market

• The same argument as Labor market
• Capital demand each firm uses one unit of
  additional capital if the revenue brought by the
  additional capital exceeds the cost of using it.
• PMPK R
• Additional revenue Additional cost
• (MPK marginal product of capital, R rental
  price of capital)
• ? MPK R/P (real rental
  price of capital)
• The amount of capital supplied by households is
  fixed.

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The Division of National Income

• How is national income (output) distributed
  through the production factors markets?
• PY WL RK
  (the income remained)
• Alternatively,
• Y (W/P)L (R/P)K
  Economic Profit
• Total Output Labor owners share Capital
  owners share
• ? Y MPLL MPKK
  Economic Profit
• If production function is CRS, the Economic
  profit 0
• Total output is divided between the payments
  to capital and the payments to labor, depending
  on their marginal productivities.

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Cobb-Douglas Production Function

• The special function form
• Y AKaL1-a (0ltalt1, constant)
• (1) Cobb-Douglas function has the properties of
  constant returns to scale and diminishing
  marginal product
• (2) The MPK is proportional to output per unit of
  capital, and the MPL is proportional to output
  per worker.
• (3) The constant a is the ratio of capital
  owners share to output. (1-a is the ratio of
  labor owners share)

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What Determines the Demand for Goods and
Services?

• Recall the component of expenditure.

Y C I G NX

• Consumption (C)
• Spending by households for present satisfaction.
• Investment (I)
• Spending by households and firms to create new
  capital for future production (and thus, for
  future satisfaction).
• Government Purchase (G)
• The government just spends some portion of
  national income.
• Net Exports (NX)
• The economy may lend/borrow the income.

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Consumption

• C C(Y-T)
• Consumption depends positively on disposable
  income
• Disposable income (Y-T) income after the payment
  of all taxes.
• If the disposable income increases, the
  consumption increases.

The consumption function is upward sloping
The slope of the consumption function is the
marginal propensity to consume (MPC)
(0ltMPClt1)
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Investment Function

• I I(r)
• Investment depends negatively on real interest
  rate
• Nominal interest rate usually reported
• Real interest rate (r) corrected for the
  effects of inflation
• (real interest rate nominal interest rate
  inflation rate)

7
The investment function slopes downward because
fewer investment projects are profitable when the
interest rate rises.
5
3
1
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Government Purchase and Net Exports

• Government
• The level of government purchase and taxes are
  given by policy
• G G, T T
• If G T ? balanced budget
• If G gt T ? budget deficit
• If G lt T ? budget surplus
• Net Exports
• To simplify analysis, we assume a closed economy
  ( no trade)
• NX 0

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Equilibrium in the Market for Goods and Services

• We can summarize the discussions as follows

Y C I G NX (Components of expenditures)
C C(Y-T) (Consumption function)
I I(r) (Investment function)
NX 0 (Closed economy)
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Equilibrium in the Financial Markets

• By rearranging the last equation, we get

I(r) Y C G S (Saving)
(Y T C) (T G)
Private saving Public saving

• The resources for investment come from the
  output remaining after subtracting consumption
  and government purchases, that is (national)
  saving.

• These resources are traded in the financial
  markets.
• Financial markets the market for exchanging
  present consumption and future consumption.

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Saving, Investment and the Interest Rate
Saving the supply of loanable funds Investment
the demand for loanable funds
If r is above the equilibrium level, there exists
excess supply of loanable funds
and thus, r falls until the amount that firms
want to invest equals to the amount that
households want to save.
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Crowding Out - the Effect of Fiscal Policy
If Government purchases increase ? Saving
decreases If Taxes decrease ? Disposal income
increases ? Consumption increases ? Saving
decreases
A reduction in saving by a change in fiscal
policy
shifts the saving schedule to the left, and
raises the interest rate and lowers
investment. (crowding out)
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Summary

• The Classical Model says
• The capital, labor and the production technology
  determine the level of output.
• MPK and MPL determine its distribution to
  households.
• Output is used for consumption, investment, and
  government purchases.
• Consumption depends positively on the disposable
  income.
• Investment depends negatively on the real
  interest rate.
• Government purchases and taxes are given (
  exogenous).
• Real interest rate equilibrates the supply and
  demand for goods and services.

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(Optional) Mathematical notes

• (1) Firms profit maximization
• First Order Conditions (FOCs) are
• So,

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(Optional) Mathematical notes

• (2) Proof of Economic profit 0
• F(K, L) is constant returns to scale, so zF(K,
  L) F(zK, zL)
• Replace MzK and NzL, then differentiate
  both sides with respect to z
• So
• Evaluate at z1, then MK, NL, so
• So Y MPKK MPLL
• Thus, Economic Profit 0