National Income: Where It Comes From and Where It Goes

1
National Income Where It Comes From and Where It
Goes

• Chapter 3 of Macroeconomics, 8th edition, by N.
  Gregory Mankiw
• ECO62 Udayan Roy

2
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!

3
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

4
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 F(K, L)
• Example Y AK0.3L0.7
• A represents technology
• Y 5K0.3L0.7, when A 5

Y 5K0.3L0.7 Y 5K0.3L0.7
labor
0 10 20 30
capital 0 0 0 0 0
1 0 25.06 40.71 54.07
2 0 30.85 50.12 66.57
3 0 34.84 56.60 75.18
4 0 37.98 61.70 81.95
5
Constant returns to scale
Y 5K0.3L0.7 Y 5K0.3L0.7
labor
0 10 20 30
capital 0 0 0 0 0
1 0 25.06 40.71 54.07
2 0 30.85 50.12 66.57
3 0 34.84 56.60 75.18
4 0 37.98 61.70 81.95

• 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

It is common in economics to assume that
production functions obey constant returns to
scale
6
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(zK, zL) zF(K,
  L)
• Example Suppose F(K, L) 5K0.3L0.7.
• Then, for any z gt 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 zF(K, L)
• Therefore, F(K, L) 5K0.3L0.7 obeys constant
  returns to scale

7
GDP in the long run assumptions

•  

8
GDP in the long run assumptions

•  

Predictions Grid Predictions Grid
GDP, Y
Capital, K
Labor, L
Technology
9
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

10
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?

11
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 Predictions Grid Predictions Grid
Y C
Capital, K
Labor, L
Technology
Taxes, T -
12
The Consumption Function
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 lt MPC lt
1. I will denote it Cy
13
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 Predictions Grid Predictions Grid
Y C
Capital, K
Labor, L
Technology
Taxes, T -
Co
14
The Consumption Function
C Co2 Cy(Y T)
Predictions Grid Predictions Grid Predictions Grid
Y C

Taxes, T -
Co
T1 gt T2
F(K, L) T1
F(K, L) T2
Consumption shift factor greater consumer
optimism, higher asset prices (Co?)
15
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.
• Now, suppose C 2 0.8?(Y T).
• Then, C 2 0.8 ? 30 26

Private Saving is defined as disposable income
minus consumption, which is Y T C 30 26
4.
K, L, F(K, L)
Y
C
C(Y T), T
16
Marginal Propensity to Consume

• The marginal propensity to consume is a positive
  fraction (1 gt MPC gt 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?
• Similarly, Y?? C? and Y C?

Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C Y C
K, L, Technology
Taxes, T -
Co -
17
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

18
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

G
K, L, F(K, L)
Y
S I Y C G
C
C(Y T), T
19
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.
• 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

Public Saving T G 0.85 3 2.15
At this point, you should be able to do problem 8
on page 80 of the textbook.
20
Saving and Investment
Y
C G
I
G
C
T
Y F(K, L)
I S Y - C - G Y - (C G)
21
Saving and Investment Predictions
Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C Y C
K, L, Technology
Taxes, T -
Co -
Predictions Grid Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C Y C Y C G
K, L, Technology
Taxes, T -
Co - -
Govt, G -
Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C S, I
K, L, Technology
Taxes, T -
Co -
Govt, G -
22
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

23
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

24
Investment and the real interest rate

• Assumption investment spending is inversely
  related to the real interest rate
• I I(r), such that r?? I?

25
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
26
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.
27
Whole chapter in one slide!

•  

Predictions Grid Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C S, I r
K, L, A (Technology) -
Net Taxes, T - -
Co -
Govt Spending, G -
Io
28
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

I(r)
G
r
K, L, F(K, L)
Y
S I Y C G
C
C(Y T), T
29
The Real Interest Rate
I Y C(Y-T) G
Predictions Grid Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C S, I r
K, L, Technology -
Taxes, T - -
Co -
Govt, G -
Io
r
I F(K, L) C(F(K, L) T) G
I(r) Io - Irr
I
I(r)
G
r
K, L, F(K, L)
Y
S I Y C G
C
C(Y T), T
30
The Real Interest Rate predictions
Predictions Grid Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C S, I r
K, L, Technology -
Taxes, T - -
Co -
Govt, G -
Io

• 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!

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?
31
The Real Interest Rate predictions
Predictions Grid Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C S, I r
K, L, Technology -
Taxes, T - -
Co -
Govt, G -
Io

• 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

r
I F(K, L) C(F(K, L) T) G
Io2 - Irr
Io1 - Irr
I
32
The long-run models predictions
Predictions Grid Predictions Grid Predictions Grid Predictions Grid Predictions Grid
Y C S, I r
K, L, Technology -
Taxes, T - -
Co -
Govt, G -
Io

• This is it!

33
Budget surpluses and deficits

• If T gt G, budget surplus (T G ) public
  saving.
• If T lt 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.

34
U.S. Federal Government Surplus/Deficit,
1929-2011
35
U.S. Federal Government Surplus/Deficit,
1940-2013 ( of GDP)
36
U.S. Federal Government Debt
37
U.S. Federal Government Debt, 1940-2012 ( of
GDP)
38
CASE STUDY The Reagan deficits

• Reagan policies during early 1980s
• increases in defense spending ?G gt 0
• big tax cuts ?T lt 0
• Both policies reduce national saving

39
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.
I2
I1
40
Are the data consistent with these results?

• variable 1970s 1980s
• T G 2.2 3.9
• S 19.6 17.4
• r 1.1 6.3
• I 19.9 19.4

TG, S, and I are expressed as a percent of
GDP All figures are averages over the decade
shown.
41
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?
  

42
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

43
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.

44
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

45
Nominal and real interest rates and inflation
expectations
46
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

47
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, thats the nominal interest rate (i
  0.05).
• If the inflation rate turns out to be 3 during
  the loan period (p 0.03), then you paid the
  real interest rate of just 2 (r i - p 0.02)

48
The Real Interest Rate

• Unfortunately, when you are taking out a cash
  loan you dont quite know what the inflation rate
  will be over the loan period
• So, economists distinguish between
• the ex post real interest rate r i - p
• and the ex ante real interest rate r i - Ep,
  where Ep is the expected inflation rate over the
  loan period
• See pages 110-113 of the textbook for more on this

49
Real Interest Rate
50
Nominal Interest Rate
Nominal
Real
51
Inflation Expectations, inferred
Nominal
Real
Nominal Real Expected Inflation
52
Inflation Expectations, direct
53
Inflation Expectations, inferred and direct
54
Inflation Expectations, inferred and direct
55
Inflation Expectations, inferred and direct