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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 RoyUdayan Roy

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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!

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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

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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 = AK 0.3 L 0.7 – A represents technology – Y = 5K 0.3 L 0.7, when A = 5 Y = 5K 0.3 L 0.7 labor 0102030 capital00000 1025.0640.7154.07 2030.8550.1266.57 3034.8456.6075.18 4037.9861.7081.95

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Constant returns to scale Y = F(K, L) = 5K 0.3 L 0.7 – 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 = 5K 0.3 L 0.7 production function is called constant returns to scale Y = 5K 0.3 L 0.7 labor 0102030 capital00000 1025.0640.7154.07 2030.8550.1266.57 3034.8456.6075.18 4037.9861.7081.95 It is common in economics to assume that production functions obey constant returns to scale

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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) = 5K 0.3 L 0.7. – Then, for any z > 0, F(zK, zL) = 5(zK) 0.3 (zL) 0.7 = 5z 0.3 K 0.3 z 0.7 L 0.7 = 5z 0.3 + 0.7 K 0.3 L 0.7 = z5K 0.3 L 0.7 = zF(K, L) – Therefore, F(K, L) = 5K 0.3 L 0.7 obeys constant returns to scale

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GDP in the long run: assumptions

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GDP in the long run: assumptions Predictions Grid GDP, Y Capital, K+ Labor, L+ Technology+ K, L, F(K, L)Y

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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

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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?

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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 YC Capital, K++ Labor, L++ Technology++ Taxes, T

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The Consumption Function C Y – T C (Y –T ) 1 MPC The 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 C y

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Consumption, C Assumption: Consumption expenditure is directly related to disposable income Consumption function: C = C (Y – T ) Specifically, C = C o + C y × (Y – T) C o represents all other exogenous variables that affect consumption, such as asset prices, consumer optimism, etc. C y is the marginal propensity to consume (MPC), the fraction of every additional dollar of income that is consumed Predictions Grid YC Capital, K++ Labor, L++ Technology++ Taxes, T CoCo +

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The Consumption Function C Y – T C = C o1 + C y (Y – T) C = C o2 + C y (Y – T) Consumption shift factor: greater consumer optimism, higher asset prices (C o ) F(K, L) – T 1 F(K, L) – T 2 T 1 > T 2 Predictions Grid YC ++ Taxes, T CoCo +

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Consumption: example Suppose F(K, L) = 5K 0.3 L 0.7 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.

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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 YCY – C K, L, Technology+++ Taxes, T+ CoCo +

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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

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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 G S = I = Y – C – G

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Investment: example Suppose F(K, L) = 5K 0.3 L 0.7 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

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Saving and Investment C Y – T C = C o + C y (Y – T) C + G Y I Y = F(K, L) I = S = Y C G = Y (C + G) T G C

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Saving and Investment: Predictions Predictions Grid YCY – C K, L, Technology+++ Taxes, T+ CoCo + Predictions Grid YCY – CY – C – G K, L, Technology++++ Taxes, T++ CoCo + Govt, G Predictions Grid YCS, I K, L, Technology+++ Taxes, T+ CoCo + Govt, G

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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

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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

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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 )I (r )

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Investment and the real interest rate Specifically, I = I o I r r Here I r is the effect of r on I and I o represents all other factors that also affect business investment spending – such as business optimism, technological progress, etc. I r I o1 I r r I o2 I r r

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The Real Interest Rate: example Suppose F(K, L) = 5K 0.3 L 0.7 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.

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Whole chapter in one slide! Predictions Grid YCS, Ir K, L, A (Technology)+++ Net Taxes, T+ CoCo ++ Govt Spending, G+ IoIo +

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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 C(Y – T), T C G S = I = Y – C – G I(r)I(r) r

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I r I(r) = I o I r r I = Y – C(Y-T) – G I = F(K, L) – C(F(K, L) – T) – G Predictions Grid YCS, Ir K, L, Technology+++ Taxes, T+ CoCo ++ Govt, G+ IoIo + The Real Interest Rate K, L, F(K, L)Y C(Y – T), T C G S = I = Y – C – G I(r)I(r) r

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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 YCS, Ir K, L, Technology+++ Taxes, T+ CoCo ++ Govt, G+ IoIo + 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?

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Predictions Grid YCS, Ir K, L, Technology+++ Taxes, T+ CoCo ++ Govt, G+ IoIo + 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 I o1 I r r I o2 I r r I = F(K, L) – C(F(K, L) – T) – G

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The long-run models predictions This is it! Predictions Grid YCS, Ir K, L, Technology+++ Taxes, T+ CoCo ++ Govt, G+ IoIo +

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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.

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U.S. Federal Government Surplus/Deficit, 1929-2011

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U.S. Federal Government Surplus/Deficit, 1940-2013 (% of GDP)

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U.S. Federal Government Debt

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U.S. Federal Government Debt, 1940-2012 (% of GDP)

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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:

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CASE STUDY: The Reagan deficits r S, I I (r )I (r ) r1r1 I1I1 r2r2 2.…which causes the real interest rate to rise… I2I2 3.…which reduces the level of investment. 1.The increase in the deficit reduces saving…

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Are the data consistent with these results? variable1970s1980s T – G–2.2–3.9 S19.617.4 r1.16.3 I 19.919.4 T–G, S, and I are expressed as a percent of GDP All figures are averages over the decade shown.

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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?

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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

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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….

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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

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NOMINAL AND REAL INTEREST RATES AND INFLATION EXPECTATIONS

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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

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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 (π = 0.03), then you paid the real interest rate of just 2% (r = i π = 0.02)

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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 π – and the ex ante real interest rate: r = i Eπ, where Eπ is the expected inflation rate over the loan period – See pages 110113 of the textbook for more on this

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Real Interest Rate

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Nominal Interest Rate Nominal Real

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Inflation Expectations, inferred Nominal Real Nominal – Real = Expected Inflation

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Inflation Expectations, direct

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Inflation Expectations, inferred and direct

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