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CHAPTER 3
National Income: Where It Comes
From and Where It Goes
Notes to the Instructor
Chapter Summary
Chapter 3 of the Mankiw text presents an important but relatively straightforward classical
model of the real side of the economy. Much of the material in the chapter (such as marginal
products, factor demands, consumption and investment functions, and the like) is likely to be a
review of materials covered in principles courses. The material can probably be presented in two
lectures to students with a suitable grounding from principles; three lectures might be more
appropriate for less-well-prepared students.
Production: Capital and labor stocks are fixed and, together with the production function,
determine GDP.
Distribution: GDP is paid to factors of production according to their marginal products.
Euler’s theorem ensures that these factor payments exactly exhaust GDP.
Allocation: GDP is allocated to consumption, investment, and government purchases
according to a consumption function [C = C(Y – T)]), an investment function [I = I(r)], and
fiscal policy. The real interest rate adjusts to ensure equilibrium in the goods (equivalently
the loans) market.
The model is long run in the sense that it assumes that prices are flexible and that markets
clear. At the same time, however, it presents only a snapshot of the economy at a point in time
because it assumes a fixed capital stock, labor force, and technology.
The chapter has three primary goals:
1. To introduce students to some of the basic terms and concepts that will be used
2. To provide long-run answers to four questions:
(a) What determines the level of real GDP?
(b) What determines how GDP is distributed to labor and owners of capital?
3. To develop a model that is both a basis for further analysis and a benchmark for
9), and the IS–LM model (Chapters 11 and 12).
Comments
The lecture notes introduce notation for private saving and public or government saving that
does not appear in the textbook: Sp and Sg, respectively. This facilitates presentation of
equilibrium in the loans market. Students must clearly understand the distinction between public
50 | CHAPTER 3 National Income: Where It Comes From and Where It Goes
and private saving. For example, students are often confused by the fact that decreases in taxes
decrease saving, because they focus on the effect on private saving and miss the effect on the
government deficit.
The lecture notes emphasize the circular flow as the reference point for the analysis. The
Like the text, the lecture notes emphasize the loanable funds interpretation of equilibrium.
As well as being simple to present and illustrate in terms of a savings/investment diagram, this
approach makes it clear why the real interest rate is the key equilibrating variable.
Use of the Web Site
Since the classical model does provide a benchmark, it is probably a good idea to give the
students many analytical exercises using this model. The curve-shifting exercises are relatively
simple so that the exercises of this chapter allow the students to familiarize themselves with the
software.
Use of the Dismal Scientist Web Site
Use the Dismal Scientist Web site to download data for the past 40 years on national income,
national saving, the government budget surplus, and the current account surplus. Compute
private saving by subtracting the government budget surplus and the current account surplus
from national saving. Now, express private saving, the government budget surplus, and the
current account surplus as a share of national income. Discuss how the shares have changed over
time.
Chapter Supplements
This chapter includes the following supplements:
3-1 How Long Is the Long Run? Part One
3-2 What Is Capital?
3-4 The Consumption Function
3-6 Public and Private Saving
3-8 A First Look at Nominal and Real Interest Rates
Lecture Notes | 51
Lecture Notes
Introduction
We now move from measurement to the deeper question of the explanation of the behavior of
the economy. This chapter develops a basic model of the long-run behavior of a well-functioning
economy (one in which prices are flexible, so all markets are always in equilibrium). This
classical model explains
1. The determinants of the level of output (income),
3. how output is allocated among alternative uses, and
4. what ensures that the supply of and demand for goods are equal.
The starting point is the circular flow of income from Chapter 2, complicated somewhat by the
addition of the government but kept simple by restricting attention to a closed economy (net
exports equals zero). Some accounting relationships from Chapter 2 show up here. From the
goods market (remembering that NX = 0),
Y = C + I + G.
3-1 What Determines the Total Production of Goods and Services?
The Factors of Production
The economy has certain resources, most notably its labor and its stock of machines and
factories (its capital stock). Firms in the economy use labor and capital as inputs to produce
goods and services (GDP). To keep things simple, we take K and L as fixed and exogenous (
K=K;L=L
). We do not yet wish to explain variations in employment or in the capital stock.
The Production Function
We express the economy’s ability to produce goods and services from its resources as
Y = F(K, L).
This says simply that the amount of GDP an economy can produce depends on its capital stock
K and its labor L. More capital or more labor allows the economy to produce more output. An
example of a production function is
!Supplement 3-1,
“How Long Is
the Long Run?
Part One”
!Figure 3-1
!Supplement 3-2,
“What Is
Capital?”
52 | CHAPTER 3 National Income: Where It Comes From and Where It Goes
should be changed by the same percentage. This means that the production function should
exhibit constant returns to scale. This is written mathematically as
zY = F(zK, zL)
The Supply of Goods and Services
Since we are supposing that K and L are fixed, it follows that we can calculate GDP immediately
from the production function
3-2 How Is National Income Distributed to the Factors of Production?
The overall determination of income is straightforward. More interesting, perhaps, is the
question of how this income is divided up between workers, who supply labor and receive
wages, and the owners of capital, who supply capital and obtain profits. The modern economic
explanation is the neoclassical theory of distribution, which explains how much workers are
paid per unit of labor and how much owners of capital are paid per unit of capital.
Factor Prices
As all markets are in equilibrium in the classical model, the markets for labor and capital—
factors of production—determine factor prices. The price of each of these factors is determined
by demand and supply. Since factor supplies are fixed, the supply curves are vertical, so our
main task is to explain factor demands.
The Decisions Facing a Competitive Firm
The demand for factors comes from the firms in the economy that use them to produce goods.
We suppose that there are many identical competitive firms. This means that they are small
relative to the markets in which they trade, and so they take as given and as outside their control
both the price at which they can sell output and the cost of factors of production. Each firm has a
production function
The Firm’s Demand for Factors
Suppose that a firm with K units of capital and L units of labor hires an extra worker. The extra
output it obtains is called the marginal product of labor (MPL):
MPL = F(K, L + 1) – F(K, L).
!Figure 3-2
Lecture Notes | 53
If the number of machines is fixed but the firm employs more and more workers, each additional
worker will probably contribute less extra output. Production functions generally exhibit
diminishing marginal product.
Firms compare the extra revenue from one more worker (P × MPL) with the cost of that
worker, which is the nominal (dollar) wage (W). If P × MPL > W, the firm will want to hire more
workers, and conversely, if P × MPL < W, the firm will want to hire fewer workers. The firm has
the optimal number of workers when P × MPL = W, or when the marginal product of labor
equals the real wage (W/P):
The Division of National Income
Since each factor of production is paid an amount equal to its marginal contribution to output,
total real payments to labor equal (W/P) × L = MPL × L and total real payments to capital equal
(R/P) × K = MPK × K. Total output equals Y. Real economic profit is the difference between
real output and total real payments to factors of production; it equals the earlier expression for
profit divided through by P:
Case Study: The Black Death and Factor Prices
We can carry out comparative static experiments with this model. For example, suppose that a
major earthquake destroys some of the economy’s capital stock. Then the supply of capital in the
economy would shift to the left, and we would expect the rental price of capital to rise. A vivid
The Cobb–Douglas Production Function
One feature of U.S. data is that factor shares—the division of income between capital and
labor—have been more or less constant over time. This constancy of factor shares was noted in
1927 by economist Paul Douglas, who later went on to become a U.S. senator from Illinois.
Suppose that the economy is competitive so that factors are paid their marginal products. What
production function then implies that factor shares are constant?
!Figures 3-3, 3-4
!Figure 3-5
54 | CHAPTER 3 National Income: Where It Comes From and Where It Goes
Y = AKαL1–α,
where A is an arbitrary positive constant. Regardless of the actual values of K and L, this
function will satisfy the equations we wrote above. It became known as the Cobb–Douglas
production function and is widely used in economics. Since labor’s share of total output in the
United States is approximately 0.7, the production possibilities of the U.S. economy can be
approximated by the function
Case Study: Labor Productivity as the Key Determinant of Real
Wages
The neoclassical theory of distribution states that the marginal product of labor will equal the
real wage. The Cobb–Douglas production function has the property that the marginal product of
labor is proportional to average labor productivity (Y/L). So the theory predicts that real wages
should equal average labor productivity and thus should rise over time with average labor
The Growing Gap Between Rich and Poor
Income inequality between high-wage workers and low-wage workers is much greater today
than it was in the 1970s. As measured by the Gini coefficient, inequality among family incomes
fell from 1947 to 1968 but then reversed course and rose in subsequent decades. One
explanation argues that skill-biased technological change has increased the demand for skilled
3-3 What Determines the Demand for Goods and Services?
So far, we have looked at the top part of the circular flow, finding that, given factor supplies K
and L, total output is Y = F(K, L) and that the real wage and real rental rate of capital are
determined by the marginal product of labor and capital. We now examine the demand for
Consumption
Consumption is the largest source of demand and so is a natural starting point. Individuals
receive wage and profit income, totaling Y. Some of this income is paid to government in the
form of taxes. The government also gives transfer payments (for example, unemployment
!Table 3-1
United Kingdom”
Lecture Notes | 55
The consumption decision is a decision between consuming now or saving to consume at
some time in the future. Consequently, the decision depends on expectations about future
economic conditions as well as on current circumstances. For now, however, we postpone
detailed discussion of these issues until Chapter 16 and concentrate on the simplest story of
consumer behavior.
Investment
The main determinant of investment is the interest rate. (We suppose that there is a single
interest rate in the economy. This is a reasonable assumption because, although there are many
different interest rates in the economy, they tend to move fairly closely together.)
Investment depends on the interest rate because investment decisions are made with an eye
to the future. Firms face a number of different investment opportunities or projects with differing
returns. Firms compare the return on these projects with the cost of borrowing to finance them—
in other words, with the interest rate. The interest rate is the cost of investment.
The interest rates that are quoted in the newspapers are nominal interest rates, meaning
that they are quoted in dollar terms. A nominal interest rate of 10 percent means that if you
Government Purchases
The final component of expenditure is government spending. This is the purchase by federal,
state, and local governments of goods and services. It does not include transfer payments; these
contribute indirectly to the demand for goods and services through their effect on consumption.
Governments’ choices of G and T determine their fiscal policy. One measure of a government’s
fiscal policy stance is the deficit (DEF = G – T). If the government takes actions to increase the
deficit (increasing G or decreasing T), this is known as an expansionary policy; the converse is a
contractionary policy. The current analysis takes G and T as exogenous (
G=G, T=T
).
!Supplement 3-4,
“Economist’s
Terminology”
56 | CHAPTER 3 National Income: Where It Comes From and Where It Goes
FYI: The Many Different Interest Rates
The textbook speaks throughout of “the” interest rate. Yet we know that, in the real world, there
are many different interest rates. Interest rates differ because of term to maturity, credit risk, and
tax treatment. But for most macroeconomic analysis, we can ignore these distinctions because
different interest rates tend to move together.
3-4 What Brings the Supply and Demand for Goods and Services Into
Equilibrium?
From the circular flow diagram, the supply of goods, Y, equals the demand for goods (C + I +
G). But Y is determined by the technology, tog ether with the stocks of capital and labor, while
C, I, and G depend on the choices of households, firms, and government. What guarantees that
supply equals demand? From microeconomics, we should expect that some price will match up
supply and demand.
A natural candidate for the equilibrating price might seem to be P, since it represents the
price of a unit of GDP in terms of dollars. But in fact, neither the supply nor any component of
Equilibrium in the Market for Goods and Services: The Supply
and Demand for the Economy’s Output
The following equations summarize the demand and supply of goods and services for the
economy:
Since
Y=C+I+G
Using these equations and noting that G and T are fixed by policy and Y is fixed by the factors of
production and the production function, we can derive the following relationship:
Y=C(Y−T)+I(r)+G
Equilibrium in the Financial Markets: The Supply and Demand
for Loanable Funds
We can rewrite the equilibrium condition as
Y–C Y –T
( )
–G=I r
( )
.
Now add and subtract
T
:
Lecture Notes | 57
Y–C Y –T
( )
–T+T–G
( )
=I r
( )
.
This can be rewritten as:
Sp+Sg =I r
( )
.
Changes in Saving: The Effects of Fiscal Policy
We can now use our simple model to carry out comparative static experiments. Among the most
interesting are those that entail a change in government policy variables. Suppose that the
government carries out an expansionary fiscal policy by increasing spending or cutting taxes.
Then, the government deficit will increase, so Sg will fall. To restore equilibrium in the goods
market, the interest rate must rise: Since there is a greater demand for goods, but a fixed supply,
the interest rate has to rise to decrease investment demand. Expressed in terms of the loans
market, there is less saving available, so there will be less investment in equilibrium. This is
known as crowding out.
Changes in Investment Demand
The model emphasizes that investment is endogenous, since it depends on the interest rate, but
there may also be exogenous changes in investment demand. For example, a technological
innovation might lead firms to wish to invest in new capital goods (such as computers), or
governments might change the tax laws in ways that affect firms’ incentives to invest. These can
be represented as shifts in the demand for investment. Perhaps surprisingly, the model predicts
!Supplement 3-8,
“A First Look at
Nominal and
Real Interest
Rates”
3-5 Conclusion
Chapter 3 presents a classical long-run model of the economy in which the level of output is
LECTURE SUPPLEMENT
3-1 How Long Is the Long Run? Part One
The models of the economy presented in Parts II and III of the book are models of the long run, whereas
the models in Part IV are short-run models. So how long is the long run?
LECTURE SUPPLEMENT
3-2 What Is Capital?
The economist Robert Solow wrote, “If the Lord had intended us to analyze three variable systems, she
would have made the page three dimensional.”1 The classical model of Chapter 3 (influenced by God or
Solow?) indeed supposes that there are two factors of production— capital and labor. The decision as to
how many factors of production to include in a model is at the discretion and judgment of the economist
who is building the model. As always in economics, different assumptions are appropriate depending upon
the questions that the model is designed to address. We could write the production function for the
economy in terms of hundreds of different factors of production:
Y = F(Trucks, Personal Computers, Jackhammers, Sewing Machines, . . . , L).
But distinguishing between a jackhammer and a sewing machine is not important to the
macroeconomist who is trying to understand the overall workings of the economy, however relevant the
distinction might be to a seamstress or a construction worker.
