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

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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∙K0.3L0.7 A represents technology Y = 5K0.3L0.7, when A = 5 Y = 5K0.3L0.7 labor 10 20 30 capital 1 25.06 40.71 54.07 2 30.85 50.12 66.57 3 34.84 56.60 75.18 4 37.98 61.70 81.95

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

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 = 5z K0.3L0.7 = 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
Y – T C (Y –T ) The slope of the consumption function is the MPC. MPC 1 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
Y – T C = Co2 + Cy∙(Y – T) C = Co1 + Cy∙(Y – T) Predictions Grid Y C + Taxes, T Co T1 > T2 F(K, L) – T1 F(K, L) – T2 Consumption shift factor: greater consumer optimism, higher asset prices (Co↑)

Consumption: example Suppose F(K, L) = 5K0.3L0.7 and K = 2 and L = 10. Then Y = Suppose T = Therefore, disposable income is Y – T = 30. Now, suppose C = ✕(Y – T). Then, C = ✕ 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

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 G K, L, F(K, L) Y S = I = Y – C – G C C(Y – T), T

Investment: example Suppose F(K, L) = 5K0.3L0.7 and K = 2 and L = 10. Then Y = Suppose T = Therefore, disposable income is Y – T = 30. Now, suppose C = ✕(Y – T). Then, C = ✕ 30 = 26 Suppose G = 3 Then, I = S = Y – C – G = – 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.

Saving and Investment I = S = Y − C − G = Y − (C + G) C Y – T Y C + G
C = Co + Cy(Y – T) G C T Y = F(K, L) I = S = Y − C − G = Y − (C + G)

Saving and Investment: Predictions
Predictions Grid Y C Y – C K, L, Technology + 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 K, L, Technology + 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. 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 = Suppose T = Therefore, disposable income is Y – T = 30. Now, suppose C = ✕(Y – T). Then, C = ✕ 30 = 26 Suppose G = 3. Then, I = S = Y – C – G = – 26 – 3 = 1.85 Suppose I = – 2r is the investment function Then, – 2r = 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

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

The Real Interest Rate I = Y – C(Y-T) – G 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

The Real Interest Rate: predictions
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?

The Real Interest Rate: predictions
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

The long-run model’s predictions
Predictions Grid Y C S, I r K, L, Technology + Taxes, T Co Govt, G Io This is it!

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
Downloaded from on February 11, The years are fiscal years, which begin on October 1 and end on September 30.

U.S. Federal Government Surplus/Deficit, 1940-2013 (% of GDP)
From The Budget and Economic Outlook: Fiscal Years 2013 to 2023, CBO, February 5, 2013.

U.S. Federal Government Debt

U.S. Federal Government Debt, 1940-2012 (% of GDP)
From The Budget and Economic Outlook: Fiscal Years 2013 to 2023, CBO, February 2013.

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:

CASE STUDY: The Reagan deficits
1. The increase in the deficit reduces saving… r S, I I (r ) r2 2. …which causes the real interest rate to rise… r1 3. …which reduces the level of investment. I2 I1

Are the data consistent with these results?
variable 1970s 1980s T – G –2.2 –3.9 S r I Display the data line by line, noting that it matches the model’s predictions---UNTIL YOU GET TO Investment. The model says that investment should have fallen as much as savings. Ask students why they think it didn’t. Answer: in our closed economy model of chapter 3, the only source of loanable funds is national saving. But the U.S. is actually an open economy. In the face of a fall in national saving (i.e. the domestic supply of loanable funds), firms can finance their investment spending by importing foreign loanable funds. More on this in an upcoming chapter. 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? Students may be confused because we are (somehow) changing taxes, but assuming T is unchanged. Taxes have different effects. The total amount of taxes (T ) affects disposable income. But even if we hold total taxes constant, a change in the structure or composition of taxes can have effects. Here, by holding total taxes constant, we ensure that neither disposable income nor public saving change, yet the composition of taxes changes to give consumers an incentive to increase their saving.

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 These slides correspond to a new FYI box on p.69. This material gives more detail about the financial system. While it ends with some information on the financial crisis, which will be explored in later chapters, the point here is that our loanable funds model, while abstracting from most of this detail, is fine for our present purposes.

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…. These slides correspond to a new FYI box on p.69. This material gives more detail about the financial system. While it ends with some information on the financial crisis, which will be explored in later chapters, the point here is that our loanable funds model, while abstracting from most of this detail, is fine for our present purposes.

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 Sources: House price data is the Case-Shiller U.S. national home price index and Case-Shiller 20-city composite index, obtained from: Foreclosure data is from realtytrac.com,

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

Nominal Interest Rate Nominal Real

Inflation Expectations, inferred
Nominal Nominal Interest Rate – Real Interest Rate = Expected Inflation. Image URL: . Real Nominal – Real = Expected Inflation

Inflation Expectations, direct
Downloaded from on February 11, Median expected price change next 12 months, Survey of Consumers.

Inflation Expectations, inferred and direct
Here the red line shows expected inflation over next 10 years, whereas the blue line shows expected inflation over next 12 months. Although there are 1-year Treasury rates – for example at – I could not find corresponding inflation-adjusted rates. Image URL:

Inflation Expectations, inferred and direct
Here the blue line shows expected inflation over next 5 years, whereas the red line shows expected inflation over next 12 months. Although there are 1-year Treasury rates – for example at – I could not find corresponding inflation-adjusted rates.

Inflation Expectations, inferred and direct
Here the blue line shows expected inflation over next 5 years, whereas the red line shows expected inflation over next 12 months. Although there are 1-year Treasury rates – for example at – I could not find corresponding inflation-adjusted rates. Image URL:

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