Presentation on theme: "National Income: Where It Comes From and Where It Goes"— Presentation transcript:
1National Income: Where It Comes From and Where It Goes Chapter 3 of Macroeconomics, 8th edition, by N. Gregory MankiwECO62 Udayan Roy
2Chapter Outline In chapter 2, we saw that Y = C + I + G + NX In this chapter, we will seea long-run theory of Y, anda long-run theory of how Y is split between C, I and GFor simplicity, this chapter considers a “closed economy”, which is an economy such that NX = 0I will skip section 3-2!
3Two productive resources and one produced good There are two productive resources:Capital, KLabor, LThese two productive resources are used to produce onefinal good, Y
4The 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 laborY = F(K, L)Example: Y = A∙K0.3L0.7A represents technologyY = 5K0.3L0.7, when A = 5Y = 5K0.3L0.7labor102030capital125.0640.7154.07230.8550.1266.57334.8456.6075.18437.9861.7081.95
5Constant returns to scale Y = 5K0.3L0.7labor102030capital125.0640.7154.07230.8550.1266.57334.8456.6075.18437.9861.7081.95Y = F(K, L) = 5K0.3L0.7Note:if you double both K and L, Y will also doubleif you triple both K and L, Y will also triple… and so onThis feature of the Y = 5K0.3L0.7 production function is called constant returns to scaleIt is common in economics to assume that production functions obey constant returns to scale
6Constant returns to scale Definition: The production function F(K, L) obeys constant returns to scale if and only iffor 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
8GDP in the long run: assumptions K, L, F(K, L)YPredictions GridGDP, YCapital, K+Labor, LTechnology
9GDP in the long run: assumptions The assumption that K and L are exogenous is significantIt 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 hasThis assumption is not made in short-run theories
10Consumption 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?
11Consumption, C Net Taxes = Tax Revenue – Transfer Payments Denoted T and always assumed exogenousDisposable income (or, after-tax income) is total income minus net taxes: Y – T.Assumption: Consumption expenditure is directly related to disposable incomePredictions GridYCCapital, K+Labor, LTechnologyTaxes, T−
12The Consumption Function Y – TC (Y –T )The slope of the consumption function is the MPC.MPC1Marginal propensity to consume (MPC) is the increase in consumption (C) when disposable income (Y – T) increases by one dollarThe MPC is usually a positive fraction: 0 < MPC < 1. I will denote it Cy
13Consumption, CAssumption: Consumption expenditure is directly related to disposable incomeConsumption 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 consumedPredictions GridYCCapital, K+Labor, LTechnologyTaxes, T−Co
15Consumption: exampleSuppose 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 = 26Private Saving is defined as disposable income minus consumption, which is Y – T – C = 30 – 26 = 4.K, L, F(K, L)YCC(Y – T), T
16Marginal 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 GridYCY – CK, L, Technology+Taxes, T−Co
17Government 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
18National Saving and Investment In chapter 2, we saw that Y = C + I + G + NXIn this chapter, we study a closed economy: NX = 0Therefore, Y = C + I + GY − C − G = IY − C − G is defined as national saving (S)Therefore, S = IGK, L, F(K, L)YS = I = Y – C – GCC(Y – T), T
19Investment: exampleSuppose 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 = 26Suppose G = 3Then, I = S = Y – C – G = – 26 – 3 = 1.85Public Saving = T – G = 0.85 – 3 = –2.15At this point, you should be able to do problem 8 on page 80 of the textbook.
20Saving and Investment I = S = Y − C − G = Y − (C + G) C Y – T Y C + G C = Co + Cy(Y – T)GCTY = F(K, L)I = S = Y − C − G = Y − (C + G)
21Saving and Investment: Predictions Predictions GridYCY – CK, L, Technology+Taxes, T−CoPredictions GridYCY – CY – C – GK, L, Technology+Taxes, T−CoGovt, GPredictions GridYCS, IK, L, Technology+Taxes, T−CoGovt, G
22The Real Interest RateImagine that lending and borrowing take place in our economy, but in commodities, not cashThat 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 interestThe 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
23The 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 interestThe nominal interest rate is not adjusted for inflationI will discuss the long-run theory of the nominal interest rate in Chapter 5
24Investment and the real interest rate Assumption: investment spending is inversely related to the real interest rateI = I(r), such that r↑⇒ I↓rII (r )
25Investment and the real interest rate Specifically, I = Io − IrrHere Ir is the effect of r on I andIo represents all other factors that also affect business investment spendingsuch as business optimism, technological progress, etc.rIo2 − IrrIo1 − IrrI
26The 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 = 26Suppose G = 3. Then, I = S = Y – C – G = – 26 – 3 = 1.85Suppose I = – 2r is the investment functionThen, – 2r = Therefore, r = 5 percentAt this point, you should be able to do problems 9, 10, and 11 on page 80 of the textbook.
27Whole chapter in one slide! Predictions GridYCS, IrK, L, A (Technology)+−Net Taxes, TCoGovt Spending, GIo
28The Real Interest RateRecall that the amount of investment has already been determinedThe investment function can therefore be used to determine the real interest rateI(r)GrK, L, F(K, L)YS = I = Y – C – GCC(Y – T), T
29The Real Interest Rate I = Y – C(Y-T) – G Predictions Grid Y C S, I r K, L, Technology+−Taxes, TCoGovt, GIorI = F(K, L) – C(F(K, L) – T) – GI(r) = Io − IrrII(r)GrK, L, F(K, L)YS = I = Y – C – GCC(Y – T), T
30The Real Interest Rate: predictions Predictions GridYCS, IrK, L, Technology+−Taxes, TCoGovt, GIoAs 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?
31The Real Interest Rate: predictions Predictions GridYCS, IrK, L, Technology+−Taxes, TCoGovt, GIoThe amount of business investment has already been determinedSo, any increase in business optimism must be cancelled out by an increase in the real interest raterI = F(K, L) – C(F(K, L) – T) – GIo2 − IrrIo1 − IrrI
33Budget 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.
34U.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.
35U.S. Federal Government Surplus/Deficit, 1940-2013 (% of GDP) From The Budget and Economic Outlook: Fiscal Years 2013 to 2023, CBO, February 5, 2013.
36U.S. Federal Government Debt Downloaded from on February 11, 2013.
37U.S. Federal Government Debt, 1940-2012 (% of GDP) From The Budget and Economic Outlook: Fiscal Years 2013 to 2023, CBO, February 2013.
38CASE STUDY: The Reagan deficits Reagan policies during early 1980s:increases in defense spending: G > 0big tax cuts: T < 0Both policies reduce national saving:
39CASE STUDY: The Reagan deficits 1. The increase in the deficit reduces saving…rS, II (r )r22. …which causes the real interest rate to rise…r13. …which reduces the level of investment.I2I1
40Are the data consistent with these results? variable 1970s 1980sT – G –2.2 –3.9SrIDisplay 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 GDPAll figures are averages over the decade shown.
41NOW 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.
42FYI: Markets, Intermediaries, the 2008 Crisis In the real world, firms have several options for raising funds they need for investment, including:borrow from bankssell bonds to saverssell shares of stock (ownership) to saversThe financial system includes:bond and stock markets, where savers directly provide funds to firms for investmentfinancial intermediaries, e.g. banks, insurance companies, mutual funds, where savers indirectly provide funds to firms for investmentThese 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.
43FYI: 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.
44FYI: 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 foreclosuresMany banks, financial institutions holding mortgages or mortgage-backed securities driven to near bankruptcyCongress authorized $700 billion to help shore up financial institutionsSources: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,
45Nominal and real interest rates and inflation expectations
46The Nominal Interest Rate Suppose you borrow $100 today and promise to pay back $110 a year from todayHere i = 0.10If 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 lossIf 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
47The Real Interest RateIn the case of cash loans, the real interest rate is the inflation-adjusted interest rateTo adjust the nominal interest rate for inflation, you simply subtract the inflation rate from the nominal interest rateIf 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)
48The Real Interest RateUnfortunately, when you are taking out a cash loan you don’t quite know what the inflation rate will be over the loan periodSo, economists distinguish betweenthe ex post real interest rate: r = i − πand the ex ante real interest rate: r = i − Eπ, where Eπ is the expected inflation rate over the loan periodSee pages 110−113 of the textbook for more on this
49Real Interest RateDownloaded from on February 11, 2013.
50Nominal Interest Rate Nominal Real Downloaded from and on February 11, 2013.Real
52Inflation Expectations, direct Downloaded from on February 11, Median expected price change next 12 months, Survey of Consumers.
53Inflation 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:
54Inflation 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.
55Inflation 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: