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.
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1
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.
2
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.
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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.
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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.
12
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”.
13
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.
14
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.
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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.
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This exercise is pretty basic review. It’s good for students who have not
had principles of economics in a few years, and students whose
graphing skills could benefit from some remedial attention. Many
instructors could probably “hide” or omit this and the next slide from
their presentations.
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(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.
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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.
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Answers:
(a) does NOT have diminishing MPL. MPL = 15, regardless of the value of L.
(b) and (c) both feature diminishing MPL
To get the answers:
- using calculus: take the derivative of F( ) with respect to L. The resulting
expression is the MPL. Looking at this expression, determine whether
MPL falls as L rises. (Or, take derivative of your MPL function w.r.t. L and
see whether it’s positive, negative, or zero.)
- using algebra: plug in any value for K and another value for L.
See what happens if you increase L, then increase it again, and again.
This may require a calculator.
- finally, you can sketch the graph of these production functions (Y on the
vertical, L on the horizontal, assuming a given value of K). If you know the
general shape of the square root function, then it’s easy to tell that (b) and
(c) have diminishing marginal returns.
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If L=3, then the benefit of hiring the fourth worker (MPL=7) exceeds the
cost of doing so (W/P = 6), so it pays the firm to increase L.
If L=7, then the firm should hire fewer workers: the 7th worker adds only
MPL=4 units of output, yet cost W/P = 6.
The point of this slide is to get students to see the idea behind the labor
demand = MPL curve.
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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.
25
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.
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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.
27
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.
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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.
29
The last equation follows from Euler’s theorem, discussed in text on p.
54.
30
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: www.bea.gov
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These formulas can be derived with basic calculus and algebra.
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We’ve now completed the supply side of the model.
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“g & s” is short for “goods & services”
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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.
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It might be useful to remind students of the meaning of the terms
“exogenous” and “transfer payments.”
40
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.
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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.
46
The Delta notation will be used throughout the text, so it would be very
helpful if your students started getting accustomed to it now.
If your students have taken a semester of calculus, tell them that X is
(practically) the same thing as dX (if X is small). Furthermore, some
basic rules from calculus apply here with s:
• The derivative of a sum is the sum of the derivatives:
(X+Y) = X + Y
• The product rule:
XY = (X)(Y) + (X)(Y)
In fact, you can derive the two arithmetic tricks for working with
percentage changes presented in chapter 2.
Just take the preceding expression for the product rule and divide
through by XY to get (XY)/XY = X/X + Y/Y, the first of the two
arithmetic tricks.
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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.
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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.
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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.
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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 1995. 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.
52
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.
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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.”
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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.
56
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.
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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.
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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. In this problem, we’re holding total taxes constant, so
disposable income does not change, but we are changing the
composition of taxes to give consumers an incentive to increase their
saving.
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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.
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