National Income: Where It Comes From and Where It Goes Chapter 3 of Macroeconomics, 8 th edition, by N. Gregory MankiwMacroeconomics ECO62ECO62 Udayan

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 = F(K, L)– Example: Y = A K∙ 0.3L0.7

– A represents technology– Y = 5K0.3L0.7, when A = 5

Y = 5K0.3L0.7

labor0 10 20 30

capital 0 0 0 0 01 0 25.06 40.71 54.072 0 30.85 50.12 66.573 0 34.84 56.60 75.184 0 37.98 61.70 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

labor0 10 20 30

capital 0 0 0 0 01 0 25.06 40.71 54.072 0 30.85 50.12 66.573 0 34.84 56.60 75.184 0 37.98 61.70 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


Predictions Grid

GDP, Y

Capital, K +

Labor, L +

Technology +

K, L, F(K, L) Y


• 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 FunctionC

Y – T

C (Y –T )

1

MPCThe slope of the consumption function is the MPC.

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 FunctionC

Y – T

C = Co1 + Cy∙(Y – T)

C = Co2 + Cy∙(Y – T)

Consumption shift factor: greater consumer optimism, higher asset prices (Co↑)

F(K, L) – T1 F(K, L) – T2

T1 > T2

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

K, L, F(K, L) Y

C(Y – T), T

C

Private Saving is defined as disposable income minus consumption, which is Y – T – C = 30 – 26 = 4.

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↑• Similarly, Y↓⇒ C↓ and Y – C↓ Predictions Grid

Y C Y – C

K, L, Technology + + +

Taxes, T − +

Co + −

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

C(Y – T), T

C

GS = 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.

• 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

At this point, you should be able to do problem 8 on page 80 of the textbook.

Public Saving = T – G = 0.85 – 3 = –2.15

Saving and Investment: Predictions

Predictions Grid

Y C Y – C


Taxes, T − +

Co + −

Predictions Grid

Y C Y – C Y – C – G

K, L, Technology + + + +

Taxes, T − + +

Co + − −

Govt, G −

Predictions Grid

Y C S, I


Taxes, T − +

Co + −

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

I (r )

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.

I

r

Io1 − Irr

Io2 − Irr

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

K, L, A (Technology) + + + −

Net Taxes, T − + −

Co + − +

Govt Spending, G − +

Io +


• 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

C(Y – T), T

C

GS = I = Y – C – G

I(r)r

I

r

I(r) = Io − Irr

I = Y – C(Y-T) – G

I = F(K, L) – C(F(K, L) – T) – G Predictions Grid

Y C S, I r

K, L, Technology + + + −

Taxes, T − + −

Co + − +

Govt, G − +

Io +


K, L, F(K, L) Y

C(Y – T), T

C

GS = I = Y – C – G

I(r)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 + − +

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?

Predictions Grid

Y C S, I r


Taxes, T − + −

Co + − +

Govt, G − +

Io +

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

I

r

Io1 − Irr

Io2 − Irr

I = F(K, L) – C(F(K, L) – T) – G

The long-run model’s predictions

• This is it!Predictions Grid

Y C S, I r


Taxes, T − + −

Co + − +

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 deficitsr

S, I

1S

I (r )

r1

I1

r22. …which causes the

real interest rate to rise…

2. …which causes the real interest rate to rise…

I2

3. …which reduces the level of investment.

3. …which reduces the level of investment.

1. The increase in the deficit reduces saving…

1. The increase in the deficit reduces saving…

2S

Are the data consistent with these results?

variable 1970s 1980sT – G –2.2 –3.9

S 19.6 17.4r 1.1 6.3I 19.9 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


• 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….


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


• 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)


• 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



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National Income: Where It Comes From and Where It Goes Chapter 3 of Macroeconomics, 8 th edition, by N. Gregory MankiwMacroeconomics ECO62ECO62 Udayan