Download National Income: Where It Comes From and Where It Goes

National Income: Where It
Comes From and Where It Goes
Chapter 3 of Macroeconomics, 8th
edition, by N. Gregory Mankiw
ECO62 Udayan Roy
Chapter Outline
• In chapter 2, we saw that Y = C + I + G + NX
• In this chapter, we will see
– a long-run theory of Y, and
– a long-run theory of how Y is split between C, I
and G
• For simplicity, this chapter considers a “closed
economy”, which is an economy such that NX = 0
• I will skip section 3-2!
Two productive resources and one
produced good
• There are two productive resources:
– Capital, K
– Labor, L
• These two productive resources are used to
produce one
– final good, Y
The Production Function
• The production function is an equation that
tells us how much of the final good is
produced with specified amounts of capital
and labor
Y = 5K L
• Y = F(K, L)
0.3 0.7
– Example: Y =
– A represents technologycapital
– Y = 5K0.3L0.7, when A = 5
A∙K0.3L0.7
0
1
2
3
4
labor
0
0
0
0
0
0
10
0
25.06
30.85
34.84
37.98
20
0
40.71
50.12
56.60
61.70
30
0
54.07
66.57
75.18
81.95
Constant returns to scale
• Y = F(K, L) = 5K0.3L0.7
– Note:
• if you double both K and
L, Y will also double
• if you triple both K and L,
Y will also triple
• … and so on
– This feature of the Y =
5K0.3L0.7 production
function is called
constant returns to
scale
Y = 5K0.3L0.7
labor
0
capital
0
0
1
0
2
0
3
0
4
0
10
0
25.06
30.85
34.84
37.98
20
0
40.71
50.12
56.60
61.70
30
0
54.07
66.57
75.18
81.95
It is common in economics
to assume that production
functions obey constant
returns to scale
Constant returns to scale
• Definition: The production function F(K, L) obeys
constant returns to scale if and only if
– for any positive number z, F(z∙K, z∙L) = z∙F(K, L)
• Example: Suppose F(K, L) = 5K0.3L0.7.
– Then, for any z > 0, F(zK, zL) = 5(zK)0.3(zL)0.7 =
5z0.3K0.3z0.7L0.7 = 5z0.3 + 0.7K0.3L0.7 = z5K0.3L0.7 = z∙F(K, L)
– Therefore, F(K, L) = 5K0.3L0.7 obeys constant returns to
scale
GDP in the long run: assumptions
GDP in the long run: assumptions
K, L, F(K, L)
Y
Predictions Grid
GDP, Y
Capital, K
+
Labor, L
+
Technology
+
GDP in the long run: assumptions
• The assumption that K and L are exogenous is
significant
• It basically is the assumption that in the long
run, the amount of capital and labor used in
production depends only on how much capital
and labor the economy has
• This assumption is not made in short-run
theories
Consumption Expenditure
• Now that we know what determines total
output (Y), the next question is:
• What happens to that output?
• In particular, what determines how much of
that output is consumed?
– What determines C?
Consumption, C
• Net Taxes = Tax Revenue – Transfer Payments
– Denoted T and always assumed exogenous
• Disposable income (or, after-tax income) is total
income minus net taxes: Y – T.
• Assumption: Consumption expenditure is directly
related to disposable income
Predictions Grid
Y
C
Capital, K
+
+
Labor, L
+
+
Technology
+
+
Taxes, T
−
The Consumption Function
C
C (Y –T )
MPC
1
The slope of the
consumption function
is the MPC.
Y–T
Marginal propensity to consume (MPC) is the
increase in consumption (C) when disposable
income (Y – T) increases by one dollar
The MPC is usually a positive
fraction: 0 < MPC < 1.
I will denote it Cy
Consumption, C
• Assumption: Consumption expenditure
is directly related to disposable income
• Consumption function: C = C (Y – T)
• Specifically, C = Co + Cy × (Y – T)
• Co represents all other exogenous
variables that affect consumption, such
as asset prices, consumer optimism,
etc.
• Cy is the marginal propensity to
consume (MPC), the fraction of every
additional dollar of income that is
consumed
Predictions Grid
Y
C
Capital, K
+
+
Labor, L
+
+
Technology
+
+
Taxes, T
−
Co
+
The Consumption Function
C = Co2 + Cy∙(Y – T)
C
C = Co1 + Cy∙(Y – T)
Predictions Grid
F(K, L) – T2
Consumption shift factor: greater consumer optimism,
higher asset prices (Co↑)
C
+
+
Taxes, T
−
Co
+
T1 > T2
F(K, L) – T1
Y
Y–T
Consumption: example
• Suppose F(K, L) = 5K0.3L0.7 and K = 2 and L = 10.
Then Y = 30.85.
• Suppose T = 0.85. Therefore, disposable
income is Y – T = 30.
Private Saving is defined
• Now, suppose C = 2 + 0.8✕(Y – T). as disposable income
minus consumption,
which is Y – T – C = 30 –
• Then, C = 2 + 0.8 ✕ 30 = 26
26 = 4.
K, L, F(K, L)
Y
C
C(Y – T), T
Marginal Propensity to Consume
• The marginal propensity to consume is a
positive fraction (1 > MPC > 0)
• That is, when income (Y) increases,
consumption (C) also increases, but by only a
fraction of the increase in income.
• Therefore, Y↑⇒ C↑ and Y – C↑
Predictions Grid
• Similarly, Y↓⇒ C↓ and Y – C↓
Y
C
Y–C
+
+
+
Taxes, T
−
+
Co
+
−
K, L, Technology
Government Spending
• Assumption: government spending (G) is
exogenous
• Public Saving is defined as the net tax revenue
of the government minus government
spending, which is T – G
National Saving and Investment
• In chapter 2, we saw that Y = C + I + G + NX
• In this chapter, we study a closed economy:
NX = 0
• Therefore, Y = C + I + G
• Y−C−G=I
• Y − C − G is defined as national saving (S)
• Therefore, S = I
K, L, F(K, L)
Y
G
C
C(Y – T), T
S=I=Y–C–G
Investment: example
• Suppose F(K, L) = 5K0.3L0.7 and K = 2 and L = 10.
Then Y = 30.85.
• Suppose T = 0.85. Therefore, disposable
income is Y – T = 30.
Public Saving = T – G
• Now, suppose C = 2 + 0.8✕(Y – T). = 0.85 – 3 = –2.15
• Then, C = 2 + 0.8 ✕ 30 = 26
• Suppose G = 3
• Then, I = S = Y – C – G = 30.85 – 26 – 3 = 1.85
At this point, you should be able to do problem 8 on page 80 of the textbook.
Saving and Investment: Predictions
Predictions Grid
Predictions Grid
Y
C
Y–C
+
+
+
K, L, Technology
Taxes, T
−
+
Co
+
−
K, L, Technology
Y
C
Y–C
Y–C–G
+
+
+
+
Taxes, T
−
+
+
Co
+
−
−
Govt, G
−
Predictions Grid
Y
C
S, I
+
+
+
Taxes, T
−
+
Co
+
−
K, L, Technology
Govt, G
−
The Real Interest Rate
• Imagine that lending and borrowing take place
in our economy, but in commodities, not cash
– That is, you may borrow some amount of the final
good, as long as you pay back the quantity you
borrowed plus a little bit extra as interest
• The real interest rate (r) is the fraction of
every unit of the final good borrowed that the
borrower will have to pay to the lender as
interest
The nominal interest rate
• The interest rate that a bank charges you for a
cash loan is called the nominal interest rate (i)
– It is the fraction of every dollar borrowed that the
lender must pay in interest
• The nominal interest rate is not adjusted for
inflation
• I will discuss the long-run theory of the
nominal interest rate in Chapter 5
Investment and the real interest rate
• Assumption: investment spending is inversely
related to the real interest rate
• I = I(r), such that r↑⇒ I↓
r
I (r )
I
Investment and the real interest rate
• Specifically, I = Io − Irr
• Here Ir is the effect of r
on I and
• Io represents all other
factors that also affect
business investment
spending
– such as business
optimism, technological
progress, etc.
r
Io2 − Irr
Io1 − Irr
I
The Real Interest Rate: example
• Suppose F(K, L) = 5K0.3L0.7 and K = 2 and L = 10.
Then Y = 30.85. Suppose T = 0.85. Therefore,
disposable income is Y – T = 30.
• Now, suppose C = 2 + 0.8✕(Y – T). Then, C = 2 +
0.8 ✕ 30 = 26
• Suppose G = 3. Then, I = S = Y – C – G = 30.85 – 26
– 3 = 1.85
• Suppose I = 11.85 – 2r is the investment function
• Then, 11.85 – 2r = 1.85. Therefore, r = 5 percent
At this point, you should be able to do problems 9, 10, and 11 on page 80 of the textbook.
Whole chapter in one slide!
Predictions Grid
Y
C
S, I
r
+
+
+
−
Net Taxes, T
−
+
−
Co
+
−
+
−
+
K, L, A (Technology)
Govt Spending, G
Io
+
The Real Interest Rate
• Recall that the amount of investment has
already been determined
• The investment function can therefore be
used to determine the real interest rate
K, L, F(K, L)
Y
G
C
C(Y – T), T
I(r)
S=I=Y–C–G
r
The Real Interest Rate
r
I = Y – C(Y-T) – G
Predictions Grid
I = F(K, L) – C(F(K, L) – T) – G
Y
C
S, I
r
+
+
+
−
Taxes, T
−
+
−
Co
+
−
+
−
+
K, L, Technology
Govt, G
I(r) = Io − Irr
Io
+
I
K, L, F(K, L)
Y
G
C
C(Y – T), T
I(r)
S=I=Y–C–G
r
The Real Interest Rate: predictions
• As investment and
the real interest rate
are inversely related,
any exogenous
variable that affects
investment one way
will affect the real
interest rate the
other way!
Predictions Grid
Y
C
S, I
r
+
+
+
−
Taxes, T
−
+
−
Co
+
−
+
−
+
K, L, Technology
Govt, G
Io
Q: Why is it that business
optimism or technological
progress shifts the investment
curve upwards, but does not
affect the amount of investment
in the long run?
+
The Real Interest Rate: predictions
• The amount of
business investment
has already been
determined
• So, any increase in
business optimism
must be cancelled
out by an increase in
the real interest rate
Predictions Grid
Y
C
S, I
r
+
+
+
−
Taxes, T
−
+
−
Co
+
−
+
−
+
K, L, Technology
Govt, G
Io
+
r
I = F(K, L) – C(F(K, L) – T) – G
Io2 − Irr
Io1 − Irr
I
The long-run model’s predictions
Predictions Grid
• This is it!
Y
C
S, I
r
+
+
+
−
Taxes, T
−
+
−
Co
+
−
+
−
+
K, L, Technology
Govt, G
Io
+
Budget surpluses and deficits
• If T > G, budget surplus = (T – G)
= public saving.
• If T < G, budget deficit = (G – T)
and public saving is negative.
• If T = G, “balanced budget,” public saving = 0.
• The U.S. government finances its deficit by
issuing Treasury bonds – i.e., borrowing.
U.S. Federal Government
Surplus/Deficit, 1929-2011
U.S. Federal Government
Surplus/Deficit, 1940-2013 (% of GDP)
U.S. Federal Government Debt
U.S. Federal Government Debt,
1940-2012 (% of GDP)
CASE STUDY:
The Reagan deficits
• Reagan policies during early 1980s:
– increases in defense spending: G > 0
– big tax cuts: T < 0
• Both policies reduce national saving:
S  Y  C (Y  T )  G
G   S
T   C   S
CASE STUDY:
The Reagan deficits
1. The increase in the
deficit reduces
saving…
2. …which causes the
real interest rate to
rise…
3. …which reduces
the level of
investment.
r
S2
S1
r2
r1
I (r )
I2
I1
S, I
Are the data consistent with these results?
variable
T–G
S
r
I
1970s
–2.2
19.6
1.1
19.9
1980s
–3.9
17.4
6.3
19.4
T–G, S, and I are expressed as a percent of GDP
All figures are averages over the decade shown.
NOW YOU TRY:
The effects of saving incentives
• Draw the diagram for the loanable funds model.
• Suppose the tax laws are altered to provide more
incentives for private saving.
(Assume that total tax revenue T does not change)
• What happens to the interest rate and investment?
FYI: Markets, Intermediaries, the 2008 Crisis
• In the real world, firms have several options for raising
funds they need for investment, including:
– borrow from banks
– sell bonds to savers
– sell shares of stock (ownership) to savers
• The financial system includes:
– bond and stock markets, where savers directly
provide funds to firms for investment
– financial intermediaries, e.g. banks, insurance
companies, mutual funds, where savers indirectly
provide funds to firms for investment
FYI: Markets, Intermediaries, the 2008 Crisis
• Intermediaries can help move funds to their
most productive uses.
• But when intermediaries are involved,
savers usually do not know what investments
their funds are financing.
• Intermediaries were at the heart of the
financial crisis of 2008….
FYI: Markets, Intermediaries, the 2008 Crisis
A few details on the financial crisis:
• July ’06 to Dec ’08: house prices fell 27%
• Jan ’08 to Dec ’08: 2.3 million foreclosures
• Many banks, financial institutions holding
mortgages or mortgage-backed securities
driven to near bankruptcy
• Congress authorized $700 billion to help shore
up financial institutions
NOMINAL AND REAL INTEREST RATES
AND INFLATION EXPECTATIONS
The Nominal Interest Rate
• Suppose you borrow $100 today and promise to
pay back $110 a year from today
– Here i = 0.10
• If prices are low a year from today, the
purchasing power of the $10 you pay in interest
will be high. So, you will regret the loss
• If prices are high a year from today, the
purchasing power of the $10 you pay in interest
will be low. You will not regret the loss as much
The Real Interest Rate
• In the case of cash loans, the real interest rate
is the inflation-adjusted interest rate
• To adjust the nominal interest rate for
inflation, you simply subtract the inflation
rate from the nominal interest rate
– If the bank charges you 5% interest rate on a cash
loan, that’s the nominal interest rate (i = 0.05).
– If the inflation rate turns out to be 3% during the
loan period (π = 0.03), then you paid the real
interest rate of just 2% (r = i − π = 0.02)
The Real Interest Rate
• Unfortunately, when you are taking out a cash
loan you don’t quite know what the inflation
rate will be over the loan period
• So, economists distinguish between
– the ex post real interest rate: r = i − π
– and the ex ante real interest rate: r = i − Eπ,
where Eπ is the expected inflation rate over the
loan period
– See pages 110−113 of the textbook for more on
this
Real Interest Rate
Nominal Interest Rate
Nominal
Real
Inflation Expectations, inferred
Nominal
Real
Nominal – Real = Expected Inflation
Inflation Expectations, direct
Inflation Expectations, inferred and
direct
Inflation Expectations, inferred and
direct
Inflation Expectations, inferred and
direct