# A closed economy, market-clearing model

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National Income: Where it Comes From and Where it Goes
3 National Income: Where it Comes From and Where it Goes The material in this chapter is the basis of much of the remaining material in this book. So, the time your students spend mastering this material will pay dividends throughout the semester. New to the 6th edition, the appendix on the Cobb-Douglas production function is now integrated into the chapter – and into this PowerPoint presentation. Also, if you used the previous edition of these PowerPoints, you will find that I have cleaned up and expanded the returns to scale section and the optional last section on the loanable funds model with an upward-sloping saving curve. As a result of these changes, this PowerPoint presentation is longer. I suggest you look through it before presenting it in class to determine whether there’s any material you might want to cut out or shorten.

A closed economy, market-clearing model
Outline of model A closed economy, market-clearing model Supply side factor markets (supply, demand, price) determination of output/income Demand side determinants of C, I, and G Equilibrium goods market loanable funds market It’s useful for students to keep in mind the “big picture” as they learn the individual components of the model in the following slides. CHAPTER 3 National Income

Factors of production K = capital: tools, machines, and structures used in production L = labor: the physical and mental efforts of workers In the simple model of this chapter, we think of capital as plant & equipment. In the real world, capital also includes inventories and residential housing, as discussed in Chapter 2. Students may have learned in their principles course that “land” or “land and natural resources” is an additional factor of production. In macro, we mainly focus on labor and capital, though. So, to keep our model simple, we usually omit land as a factor of production, as we can learn a lot about the macroeconomy despite the omission of land. CHAPTER 3 National Income

The production function
denoted Y = F(K, L) shows how much output (Y ) the economy can produce from K units of capital and L units of labor reflects the economy’s level of technology exhibits constant returns to scale CHAPTER 3 National Income

Returns to scale: A review
Initially Y1 = F (K1 , L1 ) Scale all inputs by the same factor z: K2 = zK1 and L2 = zL1 (e.g., if z = 1.25, then all inputs are increased by 25%) What happens to output, Y2 = F (K2, L2 )? If constant returns to scale, Y2 = zY1 If increasing returns to scale, Y2 > zY1 If decreasing returns to scale, Y2 < zY1 This material has been improved and expanded from the previous edition of these PowerPoints. However, it is longer: 7 slides instead of 2. To shorten your presentation, you might consider omitting one or two of the following three examples, and/or eliminating one of the two “now you try” in-class exercises. CHAPTER 3 National Income

try… Determine whether constant, decreasing, or increasing returns to scale for each of these production functions: (a) (b) CHAPTER 3 National Income

Assumptions of the model
Technology is fixed. The economy’s supplies of capital and labor are fixed at Emphasize that “K” and “L” (without bars on top) are variables - they can take on various magnitudes. On the other hand, “Kbar” and “Lbar” are specific values of these variables. Hence, “K = Kbar” means that the variable K equals the specific amount Kbar. Regarding the assumptions: In chapters 7 and 8 (the Economic Growth chapters), we will relax these assumptions: K and L will grow in response to investment and population growth, respectively, and the level of technology will increase over time. CHAPTER 3 National Income

Determining GDP Output is determined by the fixed factor supplies and the fixed state of technology: Again, emphasize that “F(Kbar,Lbar)” means we are evaluating the function at a particular combination of capital and labor. The resulting value of output is called “Ybar”. CHAPTER 3 National Income

The distribution of national income
determined by factor prices, the prices per unit that firms pay for the factors of production wage = price of L rental rate = price of K Recall from chapter 2: the value of output equals the value of income. The income is paid to the workers, capital owners, land owners, and so forth. We now explore a simple theory of income distribution. CHAPTER 3 National Income

Notation W = nominal wage R = nominal rental rate P = price of output
W /P = real wage (measured in units of output) R /P = real rental rate It might be worthwhile to refresh students’ memory about nominal and real variables. The nominal wage & rental rate are measured in currency units. The real wage is measured in units of output. To see this, suppose W = \$10/hour and P = \$2 per unit of output. Then, W/P = (\$10/hour) / (\$2/unit of output) = 5 units of output per hour of work. It’s true, the firm is paying the workers in money units, not in units of output. But, the real wage is the purchasing power of the wage - the amount of stuff that workers can buy with their wage. CHAPTER 3 National Income

How factor prices are determined
Factor prices are determined by supply and demand in factor markets. Recall: Supply of each factor is fixed. What about demand? Since the distribution of income depends on factor prices, we need to see how factor prices are determined. Each factor’s price is determined by supply and demand in a market for that factor. For instance, supply and demand for labor determine the wage. CHAPTER 3 National Income

Demand for labor Assume markets are competitive: each firm takes W, R, and P as given. Basic idea: A firm hires each unit of labor if the cost does not exceed the benefit. cost = real wage benefit = marginal product of labor CHAPTER 3 National Income

Marginal product of labor (MPL )
definition: The extra output the firm can produce using an additional unit of labor (holding other inputs fixed): MPL = F (K, L +1) – F (K, L) CHAPTER 3 National Income

MPL and the production function
Y output 1 MPL As more labor is added, MPL  1 MPL (Figure 3-3 on p.51) It’s straightforward to see that the MPL = the prod function’s slope: The definition of the slope of a curve is the amount the curve rises when you move one unit to the right. On this graph, moving one unit to the right simply means using one additional unit of labor. The amount the curve rises is the amount by which output increases: the MPL. Slope of the production function equals MPL MPL 1 L labor CHAPTER 3 National Income

Diminishing marginal returns
As a factor input is increased, its marginal product falls (other things equal). Intuition: Suppose L while holding K fixed  fewer machines per worker  lower worker productivity Tell class: Many production functions have this property. This slide introduces some short-hand notation that will appear throughout the PowerPoint presentations of the remaining chapters: The up and down arrows mean increase and decrease, respectively. The symbol “” means “causes” or “leads to.” Hence, the text after “Intuition” should be read as follows: “An increase in labor while holding capital fixed causes there to be fewer machines per worker, which causes lower productivity.” Many instructors use this type of short-hand (or something very similar), and it’s much easier and quicker for students to write down in their notes. CHAPTER 3 National Income

MPL and the demand for labor
Units of output Units of labor, L Each firm hires labor up to the point where MPL = W/P. MPL, Labor demand Real wage Quantity of labor demanded It’s easy to see that the MPL curve is the firm’s L demand curve. Let L* be the value of L such that MPL = W/P. Suppose L < L*. Then, benefit of hiring one more worker (MPL) exceeds cost (W/P), so firm can increase profits by hiring one more worker. Instead, suppose L > L*. Then, the benefit of the last worker hired (MPL) is less than the cost (W/P), so firm should reduce labor to increase its profits. When L = L*, then firm cannot increase its profits either by raising or lowering L. Hence, firm hires L to the point where MPL = W/P. This establishes that the MPL curve is the firm’s labor demand curve. CHAPTER 3 National Income

The equilibrium real wage
Units of output Units of labor, L Labor supply The real wage adjusts to equate labor demand with supply. MPL, Labor demand equilibrium real wage The labor supply curve is vertical: We are assuming that the economy has a fixed quantity of labor, Lbar, regardless of whether the real wage is high or low. Combining this labor supply curve with the demand curve we’ve developed in previous slides shows how the real wage is determined. CHAPTER 3 National Income

Determining the rental rate
We have just seen that MPL = W/P. The same logic shows that MPK = R/P : diminishing returns to capital: MPK  as K  The MPK curve is the firm’s demand curve for renting capital. Firms maximize profits by choosing K such that MPK = R/P . In our model, it’s easiest to think of firms renting capital from households (the owners of all factors of production). R/P is the real cost of renting a unit of K for one period of time. In the real world, of course, many firms own some of their capital. But, for such a firm, the market rental rate is the opportunity cost of using its own capital instead of renting it to another firm. Hence, R/P is the relevant “price” in firms’ capital demand decisions, whether firms own their capital or rent it. CHAPTER 3 National Income

The equilibrium real rental rate
Units of output Units of capital, K Supply of capital The real rental rate adjusts to equate demand for capital with supply. MPK, demand for capital equilibrium R/P The previous slide used the same logic behind the labor demand curve to assert that the capital demand curve is the same as the downward-sloping MPK curve. The supply of capital is fixed (by assumption), so the supply curve is vertical. The real rental rate (R/P) is determined by the intersection of the two curves. CHAPTER 3 National Income

The Neoclassical Theory of Distribution
states that each factor input is paid its marginal product is accepted by most economists When I teach this theory, after saying “accepted by most economists” I append “at least, as a starting point.” This theory is fine for macro models with only one type of labor. But taken literally, it implies that people who earn low wages have low marginal products. Thus, this theory would attribute the entire observed wage gap between white males and minorities to productivity differences, a conclusion that most would find objectionable. CHAPTER 3 National Income

How income is distributed:
total labor income = total capital income = If production function has constant returns to scale, then The last equation follows from Euler’s theorem, discussed in text on p. 54. national income labor income capital income CHAPTER 3 National Income

The ratio of labor income to total income in the U.S.
Labor’s share of total income Labor’s share of income is approximately constant over time. (Hence, capital’s share is, too.) This graph appears in the textbook as Figure 3-5 on p.57. This and the next two slides cover the Cobb-Douglas production function. In the textbook’s previous edition, this material was covered in an appendix. Source: CHAPTER 3 National Income

A closed economy, market-clearing model
Outline of model A closed economy, market-clearing model Supply side factor markets (supply, demand, price) determination of output/income Demand side determinants of C, I, and G Equilibrium goods market loanable funds market DONE  DONE  Next  We’ve now completed the supply side of the model. CHAPTER 3 National Income

Demand for goods & services
Components of aggregate demand: C = consumer demand for g & s I = demand for investment goods G = government demand for g & s (closed economy: no NX ) “g & s” is short for “goods & services” CHAPTER 3 National Income

Consumption, C def: Disposable income is total income minus total taxes: Y – T. Consumption function: C = C (Y – T ) Shows that (Y – T )  C def: Marginal propensity to consume (MPC) is the increase in C caused by a one-unit increase in disposable income. Again, we are using the short-hand notation that will appear throughout the remaining PowerPoints: X  Y means “an increase in X causes a decrease in Y.” Please feel free to edit slides if you wish to substitute other notation. CHAPTER 3 National Income

The consumption function
Y – T C (Y –T ) The slope of the consumption function is the MPC. MPC 1 CHAPTER 3 National Income

Investment, I The investment function is I = I (r ),
where r denotes the real interest rate, the nominal interest rate corrected for inflation. The real interest rate is the cost of borrowing the opportunity cost of using one’s own funds to finance investment spending. So, r  I CHAPTER 3 National Income

The investment function
r I Spending on investment goods depends negatively on the real interest rate. I (r ) CHAPTER 3 National Income

Government spending, G G = govt spending on goods and services.
G excludes transfer payments (e.g., social security benefits, unemployment insurance benefits). Assume government spending and total taxes are exogenous: It might be useful to remind students of the meaning of the terms “exogenous” and “transfer payments.” CHAPTER 3 National Income

The market for goods & services
Aggregate demand: Aggregate supply: Equilibrium: The real interest rate adjusts to equate demand with supply. Note the only variable in the equilibrium condition that doesn’t have a “bar” over it is the real interest rate. When the full slide is showing, before you advance to the next one, you might want to note that the interest rate is important in financial markets as well, so we will next develop a simple model of the financial system. CHAPTER 3 National Income

The loanable funds market
A simple supply-demand model of the financial system. One asset: “loanable funds” demand for funds: investment supply of funds: saving “price” of funds: real interest rate CHAPTER 3 National Income

Demand for funds: Investment
The demand for loanable funds… comes from investment: Firms borrow to finance spending on plant & equipment, new office buildings, etc. Consumers borrow to buy new houses. depends negatively on r, the “price” of loanable funds (cost of borrowing). CHAPTER 3 National Income

Loanable funds demand curve
I The investment curve is also the demand curve for loanable funds. I (r ) CHAPTER 3 National Income

Supply of funds: Saving
The supply of loanable funds comes from saving: Households use their saving to make bank deposits, purchase bonds and other assets. These funds become available to firms to borrow to finance investment spending. The government may also contribute to saving if it does not spend all the tax revenue it receives. CHAPTER 3 National Income

Types of saving private saving = (Y – T ) – C public saving = T – G
national saving, S = private saving + public saving = (Y –T ) – C T – G = Y – C – G After showing definition of private saving, - give the interpretation of the equation: private saving is disposable income minus consumption spending - explain why private saving is part of the supply of loanable funds: Suppose a person earns \$50,000/year, pays \$10,000 in taxes, and spends \$35,000 on goods and services. There’s \$5000 remaining. What happens to that \$5000? The person might use it to buy stocks or bonds, or she might put it in her savings account or money market deposit account. In all of these cases, this \$5000 becomes part of the supply of loanable funds in the financial system. After displaying public saving, explain the equation’s interpretation: public saving is tax revenue minus government spending. Notice the analogy to private saving – both concepts represent income less spending: for the private household, income is (Y-T) and spending is C. For the government, income is T and spending is G. CHAPTER 3 National Income

EXERCISE: Calculate the change in saving
Suppose MPC = 0.8 and MPL = 20. For each of the following, compute S : a. G = 100 b. T = 100 c. Y = 100 d. L = 10 This problem reinforces the concepts with concrete numerical examples. It’s also a good way to break up the lecture and get students actively involved with the material. CHAPTER 3 National Income

First, in the box at the top of the slide, we plug the given value for the MPC into the expression for S and simplify. Then, finding the answers is straightforward: just plug in the given values into the expression for S. CHAPTER 3 National Income

digression: 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. CHAPTER 3 National Income

U.S. Federal Government Surplus/Deficit, 1940-2005
Notes: 1. The huge deficit in the early 1940s was due to WW2: wars are expensive. 2. The budget is closed to balanced in the ’50s and ’60s, and begins a downward trend in the ’70s. 3. The early ’80s saw the largest deficits (as % of GDP) of the post-WW2 era, due to the Reagan tax cuts, defense buildup, and growth in entitlement program outlays. 4. The budget begins a positive trend in the early 1990s, and a surplus emerges in the late 1990s. There are several possible explanations for the improvement. First, President Bush (the first one) broke his campaign promise not to raise taxes. Second, the Clinton administration barely squeaked a deficit reduction deal through Congress (with Al Gore casting the tie-breaking vote in the Senate). And third, and probably most important, there was a swelling of tax revenues due to the surge in economic growth and the stock market boom. (A stock market boom leads to large capital gains, which leads to large revenues from the capital gains tax.) 5. The budget swings to deficit again in 2001, due to the Bush tax cuts and a recession. 6. Recently, the budget deficit has reached all-time highs, when measured in current dollars. As a percentage of GDP, though, the deficit does not seem quite as worrisome relative to the time period captured in this graph. Source of data: U.S. Department of Commerce, Bureau of Economic Analysis. CHAPTER 3 National Income

U.S. Federal Government Surplus/Deficit, 1940-2011
Notes: 1. The huge deficit in the early 1940s was due to WW2: wars are expensive. 2. The budget is closed to balanced in the ’50s and ’60s, and begins a downward trend in the ’70s. 3. The early ’80s saw the largest deficits (as % of GDP) of the post-WW2 era, due to the Reagan tax cuts, defense buildup, and growth in entitlement program outlays. 4. The budget begins a positive trend in the early 1990s, and a surplus emerges in the late 1990s. There are several possible explanations for the improvement. First, President Bush (the first one) broke his campaign promise not to raise taxes. Second, the Clinton administration barely squeaked a deficit reduction deal through Congress (with Al Gore casting the tie-breaking vote in the Senate). And third, and probably most important, there was a swelling of tax revenues due to the surge in economic growth and the stock market boom. (A stock market boom leads to large capital gains, which leads to large revenues from the capital gains tax.) 5. The budget swings to deficit again in 2001, due to the Bush tax cuts and a recession. 6. Recently, the budget deficit has reached all-time highs, when measured in current dollars. As a percentage of GDP, though, the deficit does not seem quite as worrisome relative to the time period captured in this graph. Source of data: U.S. Department of Commerce, Bureau of Economic Analysis. CHAPTER 3 National Income

U.S. Federal Government Debt, 1940-2005
Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt (Today it’s about 9 cents.) A later chapter will give more details, but for now, tell students that the government finances its deficits by borrowing from the public. (This borrowing takes the form of selling Treasury bonds). Persistent deficits over time imply persistent borrowing, which causes the debt to increase. After WW2, occasional budget surpluses allowed the government to retire some of its WW2 debt; also, normal economic growth increased the denominator of the debt-to-GDP ratio. Starting in the early 1980s, corresponding to the beginning of huge and persistent deficits, we see a huge increase in the debt-to-GDP ratio, from 32% in 1981 to 66% in In the mid 1990s, budget surpluses and rapid growth started to reduce the debt-to-GDP ratio, but it started rising again in 2001 due to the economic slowdown, the Bush tax cuts, and higher spending (Afghanistan & Iraq, war on terrorism, 2002 airline bailout, etc). Students are typically shocked when they realize how much extra we are paying in taxes just to service the debt; if it weren’t for the debt, we’d either pay much lower taxes, or have a lot of revenue available for other purposes, like financial aid for college students, AIDS and cancer research, national defense, Social Security reform, etc. Source of data: U.S. Dept of Commerce Bureau of Economic Analysis. CHAPTER 3 National Income

Loanable funds supply curve
S, I National saving does not depend on r, so the supply curve is vertical. At the end of this chapter, we will briefly consider how things would be different if Consumption (and therefore Saving) were allowed to depend on the interest rate. For now, though, they do not. CHAPTER 3 National Income

Loanable funds market equilibrium
S, I I (r ) Equilibrium real interest rate Equilibrium level of investment CHAPTER 3 National Income

The special role of r Eq’m in L.F. market Eq’m in goods market
r adjusts to equilibrate the goods market and the loanable funds market simultaneously: If L.F. market in equilibrium, then Y – C – G = I Add (C +G ) to both sides to get Y = C + I + G (goods market eq’m) Thus, This slide establishes that we can use the loanable funds supply/demand diagram to see how the interest rate that clears the goods market is determined. Explain that the symbol  means each one implies the other. The thing on the left implies the thing on the right, and vice versa. More short-hand: “eq’m” is short for “equilibrium” and “LF” for “loanable funds.” Eq’m in L.F. market Eq’m in goods market CHAPTER 3 National Income

Digression: Mastering models
To master a model, be sure to know: 1. Which of its variables are endogenous and which are exogenous. 2. For each curve in the diagram, know a. definition b. intuition for slope c. all the things that can shift the curve 3. Use the model to analyze the effects of each item in 2c. This is good general advice for students. They will learn many models in this course. Many exams include questions requiring students to show how some event shifts a curve, and then use the model to analyze its effect on the endogenous variables. If students methodically follow the steps presented on this slide for each model they learn in this course (and other economics courses), they will likely do better on the exams and get more out of the course. CHAPTER 3 National Income

Mastering the loanable funds model
Things that shift the saving curve public saving fiscal policy: changes in G or T private saving preferences tax laws that affect saving 401(k) IRA replace income tax with consumption tax Continuing from the previous slide, let’s look at all the things that affect the S curve. Then, we will pick one of those things and use the model to analyze its effects on the endogenous variables. Then, we’ll do the same for the I curve. CHAPTER 3 National Income

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: CHAPTER 3 National Income

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 CHAPTER 3 National Income

Mastering the loanable funds model, continued
Things that shift the investment curve some technological innovations to take advantage of the innovation, firms must buy new investment goods tax laws that affect investment investment tax credit CHAPTER 3 National Income

An increase in investment demand
S, I I2 I1 …raises the interest rate. An increase in desired investment… r2 r1 But the equilibrium level of investment cannot increase because the supply of loanable funds is fixed. CHAPTER 3 National Income

Saving and the interest rate
Why might saving depend on r ? How would the results of an increase in investment demand be different? Would r rise as much? Would the equilibrium value of I change? Suggestion: Display these questions and give your students 3-4 minutes, working in pairs, to try to find the answers. Then display the analysis on the next slide. CHAPTER 3 National Income

An increase in investment demand when saving depends on r
S, I An increase in investment demand raises r, which induces an increase in the quantity of saving, which allows I to increase. I(r)2 I(r) r2 I2 r1 I1 CHAPTER 3 National Income

Chapter Summary Total output is determined by
the economy’s quantities of capital and labor the level of technology Competitive firms hire each factor until its marginal product equals its price. If the production function has constant returns to scale, then labor income plus capital income equals total income (output). CHAPTER 3 National Income slide 53

Chapter Summary A closed economy’s output is used for
consumption investment government spending The real interest rate adjusts to equate the demand for and supply of goods and services loanable funds CHAPTER 3 National Income slide 54

Chapter Summary A decrease in national saving causes the interest rate to rise and investment to fall. An increase in investment demand causes the interest rate to rise, but does not affect the equilibrium level of investment if the supply of loanable funds is fixed. CHAPTER 3 National Income slide 55

In this chapter, you will learn…
The classical theory of inflation causes effects social costs “Classical” – assumes prices are flexible & markets clear Applies to the long run CHAPTER 4 Money and Inflation 56

U.S. inflation and its trend, 1960-2007
% change in CPI from 12 months earlier 0% 3% 6% 9% 12% 15% 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 long-run trend In this chapter, we learn about the long-run trend behavior of prices and inflation. The factors that make inflation deviate from its trend in the short run will be studied in chapter 13 (on Aggregate Supply and the Phillips Curve). source: BLS obtained from slide 57 57

The connection between money and prices
Inflation rate = the percentage increase in the average level of prices. Price = amount of money required to buy a good. Because prices are defined in terms of money, we need to consider the nature of money, the supply of money, and how it is controlled. CHAPTER 4 Money and Inflation 58

Money: Definition Money is the stock of assets that can be readily used to make transactions. CHAPTER 4 Money and Inflation 59

Money: Functions medium of exchange we use it to buy stuff
store of value transfers purchasing power from the present to the future unit of account the common unit by which everyone measures prices and values If your students have taken principles of economics, they will probably be familiar with the material on this slide. It might be worthwhile, though, to take an extra moment to be sure that students understand that the definition of store of value (an item that transfers purchasing power from the present to the future) simply means that money retains its value over time, so you need not spend all your money as soon as you receive it. The idea should be familiar, even though Mankiw’s wording is a bit more sophisticated than most other texts. CHAPTER 4 Money and Inflation 60

Money: Types has no intrinsic value example: the paper currency we use
1. fiat money has no intrinsic value example: the paper currency we use 2. commodity money has intrinsic value examples: gold coins, cigarettes in P.O.W. camps Again, this material should be review for most students. Note: Many students have seen the film The Shawshank Redemption starring Tim Robbins and Morgan Freeman. Most of this film takes place in a prison. The prisoners have an informal “underground economy” in which cigarettes are used as money, even by prisoners who don’t smoke. Students who have seen the film will better understand “commodity money” if you mention this example. Also, the textbook (p.79) has a case study on cigarettes being used as money in POW camps during WWII. CHAPTER 4 Money and Inflation 61

The money supply and monetary policy definitions
The money supply is the quantity of money available in the economy. Monetary policy is the control over the money supply. Again, this is mostly review. CHAPTER 4 Money and Inflation 62

The Federal Reserve Building Washington, DC
The central bank Monetary policy is conducted by a country’s central bank. In the U.S., the central bank is called the Federal Reserve (“the Fed”). The Federal Reserve Building Washington, DC Again, this is mostly review. CHAPTER 4 Money and Inflation 63

Money supply measures, May 2007
symbol assets included amount (\$ billions) \$755 Currency C \$1377 C + demand deposits, travelers’ checks, other checkable deposits M1 Source: Federal Reserve Board, H.6 release. Figures are seasonally adjusted. This table is an updated version of Table 4-1 on p.82 of the textbook, with one change: This slide excludes M3, which the Federal Reserve discontinued in March For more info, see The most important thing that students should get from this slide is the following: Each successive measure of the money supply is BIGGER and LESS LIQUID than the one it follows. I.e., checking account deposits (in M1 but not C) are less liquid than currency. Money market deposit account and savings account balances (in M2 but not M1) are less liquid than demand deposits. Whether you require your students to learn the definitions of every component of each monetary aggregate is up to you. Most professors agree that students should learn the definitions of M1, M2, demand deposits, and time deposits. Some professors feel that, since the quantity of information students can learn in a semester is finite, it is not worthwhile to require students to learn such terms as “repurchase agreements.” However, you might verbally state the definitions of such terms to help students better understand the nature of the monetary aggregates. \$7227 M1 + small time deposits, savings deposits, money market mutual funds, money market deposit accounts M2 CHAPTER 4 Money and Inflation 64

The Quantity Theory of Money
A simple theory linking the inflation rate to the growth rate of the money supply. Begins with the concept of velocity… CHAPTER 4 Money and Inflation 65

Velocity basic concept: the rate at which money circulates
definition: the number of times the average dollar bill changes hands in a given time period example: In 2007, \$500 billion in transactions money supply = \$100 billion The average dollar is used in five transactions in 2007 So, velocity = 5 In order for \$500 billion in transactions to occur when the money supply is only \$100b, each dollar must be used, on average, in five transactions. CHAPTER 4 Money and Inflation 66

Velocity, cont. where V = velocity T = value of all transactions
This suggests the following definition: where V = velocity T = value of all transactions M = money supply CHAPTER 4 Money and Inflation 67

Velocity, cont. Use nominal GDP as a proxy for total transactions.
Then, where P = price of output (GDP deflator) Y = quantity of output (real GDP) P Y = value of output (nominal GDP) You might ask students if they know the difference between nominal GDP and the value of transactions. Answer: nominal GDP includes the value of purchases of final goods; total transactions also includes the value of intermediate goods. Even though they are different, they are highly correlated. Also, our models focus on GDP, and there’s lots of great data on GDP. So from this point on, we’ll use the income version of velocity. CHAPTER 4 Money and Inflation 68

The quantity equation The quantity equation M V = P Y follows from the preceding definition of velocity. It is an identity: it holds by definition of the variables. CHAPTER 4 Money and Inflation 69

Money demand and the quantity equation
M/P = real money balances, the purchasing power of the money supply. A simple money demand function: (M/P )d = k Y where k = how much money people wish to hold for each dollar of income (k is exogenous) CHAPTER 4 Money and Inflation 70

Money demand and the quantity equation
money demand: (M/P )d = k Y quantity equation: M V = P Y The connection between them: k = 1/V When people hold lots of money relative to their incomes (k is high), money changes hands infrequently (V is low). CHAPTER 4 Money and Inflation 71

Back to the quantity theory of money
starts with quantity equation assumes V is constant & exogenous: With this assumption, the quantity equation can be written as CHAPTER 4 Money and Inflation 72

The quantity theory of money, cont.
How the price level is determined: With V constant, the money supply determines nominal GDP (P Y ). Real GDP is determined by the economy’s supplies of K and L and the production function (Chap 3). The price level is P = (nominal GDP)/(real GDP). It’s worthwhile to underscore the order (logical order, though not necessarily chronological order) in which variables are determined in this model (as well as the other models students will learn in this course). First, real GDP is already determined outside this model (real GDP is determined by the model from chapter 3, which was completely independent of the money supply or velocity or other nominal variables). Second, the Quantity Theory of money determines nominal GDP. Third, the values of nominal GDP (PY) and real GDP (Y) together determine P (as a ratio of PY to Y). If, on an exam or homework problem, students forget the logical order in which endogenous variables are determined --- or on a more fundamental level, forget which variables are endogenous and which are exogenous --- then they are much less likely to earn the high grades that most of them desire. [Note the similarity between the way P is determined and the definition of the GDP deflator from chapter 2.] CHAPTER 4 Money and Inflation 73

The quantity theory of money, cont.
Recall from Chapter 2: The growth rate of a product equals the sum of the growth rates. The quantity equation in growth rates: CHAPTER 4 Money and Inflation 74

The quantity theory of money, cont.
 (Greek letter “pi”) denotes the inflation rate: The result from the preceding slide was: Solve this result for  to get CHAPTER 4 Money and Inflation 75

The quantity theory of money, cont.
Normal economic growth requires a certain amount of money supply growth to facilitate the growth in transactions. Money growth in excess of this amount leads to inflation. The text on this slide is an intuitive way to understand the equation. For students that are more comfortable with concrete numerical examples, you could offer the following: Suppose real GDP is growing by 3% per year over the long run. Thus, production, income, and spending are all growing by 3%. This means that the volume of transactions will be growing as well. The central bank can achieve zero inflation (on average over the long run) simply by setting the growth rate of the money supply at 3%, in which case exactly enough new money is being supplied to facilitate the growth in transactions. CHAPTER 4 Money and Inflation 76

The quantity theory of money, cont.
Y/Y depends on growth in the factors of production and on technological progress (all of which we take as given, for now). Hence, the Quantity Theory predicts a one-for-one relation between changes in the money growth rate and changes in the inflation rate. Note: the theory doesn’t predict that the inflation rate will equal the money growth rate. It *does* predict that a change in the money growth rate will cause an equal change in the inflation rate. CHAPTER 4 Money and Inflation 77

Confronting the quantity theory with data
The quantity theory of money implies 1. countries with higher money growth rates should have higher inflation rates. 2. the long-run trend behavior of a country’s inflation should be similar to the long-run trend in the country’s money growth rate. Are the data consistent with these implications? CHAPTER 4 Money and Inflation 78

U.S. inflation and money growth, 1960-2007
Over the long run, the inflation and money growth rates move together, as the quantity theory predicts. 0% 3% 6% 9% 12% 15% 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 M2 growth rate The quantity theory of money is intended to explain the long-run relation of inflation and money growth, not the short-run relation. In the long run, inflation and money growth are positively related, as the theory predicts. (In the short run, however, inflation and money growth appear highly negatively correlated! One possible reason is that the causality is reversed in the short run: when inflation rises – or is expected to rise – the Fed cuts back on money growth. If the economy slumps and inflation falls, the Fed increases money growth. It might be appropriate to discuss this when covering the chapters on short-run fluctuations.) sources: CPI - BLS Money supply - Board of Governors of the Federal Reserve obtained from inflation rate slide 79 79

Seigniorage To spend more without raising taxes or selling bonds, the govt can print money. The “revenue” raised from printing money is called seigniorage (pronounced SEEN-your-idge). The inflation tax: Printing money to raise revenue causes inflation. Inflation is like a tax on people who hold money. Introduction of abbreviation “govt” for “government” It’s quicker and easier for students to write “govt” in their notes. In the U.S., seigniorage accounts for only about 3% of total government revenue. In Italy and Greece, seigniorage has often been more than 10% of total revenue. In countries experiencing hyperinflation, seigniorage is often the government’s main source of revenue, and the need to print money to finance government expenditure is a primary cause of hyperinflation. See Case Study on p.90 “Paying for the American Revolution.” CHAPTER 4 Money and Inflation 80

Inflation and interest rates
Nominal interest rate, i not adjusted for inflation Real interest rate, r adjusted for inflation: r = i   This is probably review, if your students have taken an introductory course in economics. CHAPTER 4 Money and Inflation 81

The Fisher effect The Fisher equation: i = r + 
Chap 3: S = I determines r . Hence, an increase in  causes an equal increase in i. This one-for-one relationship is called the Fisher effect. Note that S and I are real variables. In chapter 3, we learned about the factors that determine S and I. These factors did not include the money supply, velocity, inflation, or other nominal variables. Hence, in the classical (long-run) theory we are learning, changes in money growth or inflation do not affect the real interest rate. This is why there’s a one-for-one relationship between changes in the inflation rate and changes in the nominal interest rate. (Again, the Fisher effect does not imply that the nominal interest rate EQUALS the inflation rate. It implies that CHANGES in the nominal interest rate equal CHANGES in the inflation rate, given a constant value of the real interest rate.) CHAPTER 4 Money and Inflation 82

Inflation and nominal interest rates in the U.S., 1955-2007
percent per year nominal interest rate 15% inflation rate 12% 9% 6% A replica of Fig 4-3, p.92 The data are consistent with the Fisher effect: inflation and the nominal interest rate are very highly correlated. However, they are not perfectly correlated, which absolutely does not invalidate the Fisher effect. Over time, the saving and investment curves move around, causing the real interest rate to move, which, in turn, causes the nominal interest rate to change for a given value of inflation. About the data: The inflation rate is the percentage change in the (not seasonally adjusted) CPI from 12 months earlier. The nominal interest rate is the (not seasonally adjusted) 3-month Treasury bill rate in the secondary market. Data obtained from 3% 0% -3% 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 slide 83 83