national income: where it comes from and where it goes (in the long-run)

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Chapter 3 - The Long-run Model. National Income: Where it Comes From and Where it Goes (in the long-run). In this chapter, you will learn:. what determines the economy’s total output/income in the long-run. how the prices of the factors of production are determined - PowerPoint PPT Presentation

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Mankiw 6e PowerPoints© 2010 Worth Publishers, all rights reserved
S E V E N T H E D I T I O N
PowerPoint® Slides by Ron Cronovich
N. Gregory Mankiw
National Income:
Where it Comes From and Where it Goes (in the long-run)
Chapter 3 - The Long-run Model
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what determines the economy’s total output/income in the long-run.
how the prices of the factors of production are determined
how total income is distributed
what determines the demand for goods and services
how equilibrium in the goods market is achieved
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Supply side
determination of output/income
Equilibrium
L = labor:
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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.
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K units of capital and L units of labor
reflects the economy’s level of technology
exhibits constant returns to scale
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Scale all inputs by the same factor z:
K2 = zK1 and L2 = zL1
(e.g., if z = 1.2, then all inputs are increased by 20%)
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
What about:
Technology is fixed.
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Determining GDP – in the Long-run
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Who gets Y?
determined by factor prices,
the price a firms pay for a unit of the factor of production
wage rate (wage) = price of L
rental rate = price of K
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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.
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How factor prices are determined
Factor prices are determined by supply and demand in factor markets.
We assume supply of each factor is fixed.
What about demand? Its not fixed!
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Since the distribution of income depends on factor prices, we need to see how factor prices are determined.
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Basic idea:
if the cost does not exceed the benefit.
cost = real wage
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definition:
using an additional unit of labor
(holding other inputs fixed):
NOW YOU TRY:
Compute & graph MPL
value of L.
L on the horizontal axis.
L Y MPL
0 0 n.a.
L
labor
MPL
1
1
MPL
1
MPL
Slope of the production function equals MPL
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(Figure 3-3 on p.52)
It’s straightforward to see that the MPL = the prod function’s slope:
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its marginal product falls (other things equal).
Intuition:
machines per worker falls.
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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:
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NOW YOU TRY:
Identifying Diminishing Marginal Returns
Which of these production functions have diminishing marginal returns to labor?
Answers:
(a) does NOT have diminishing MPL; MPL = 15, regardless of the value of L.
(b) and (c) both feature diminishing MPL
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NOW YOU TRY:
Suppose W/P = 6.
If L = 3, should firm hire more or less labor? Why?
If L = 7, should firm hire more or less labor? Why?
NOW YOU TRY:
L Y MPL
0 0 n.a.
1 11 11
2 21 10
3 30 9
4 38 8
5 45 7
6 51 6
7 56 5
8 60 4
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.
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Each firm hires labor
Units of output
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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.
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labor demand with supply.
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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.
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The MPK curve is the firm’s demand curve
for renting capital.
such that MPK = R/P.
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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.
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The real rental rate adjusts to equate
demand for capital with supply.
Units of output
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states that each factor input is paid its marginal product
a good starting point for thinking about income distribution
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total labor income =
total capital income =
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CHAPTER 3 National Income
The ratio of labor income to total income in the U.S., 1960-2010
Labor’s share of total income
Labor’s share of income
is approximately constant over time.
(Thus, capital’s share is, too.)
Labor’s share of income
is approximately constant over time.
(Thus, capital’s share is, too.)
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This graph appears in the textbook as Figure 3-5 on p.59.
Source: www.bea.gov
The Cobb-Douglas production function is:
where A represents the level of technology.
= capital’s share of total income:
capital income = MPK x K = Y
labor income = MPL x L = (1 – )Y
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CHAPTER 3 National Income
The Cobb-Douglas Production Function
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U.S. data:
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The table shows the average annual rates of productivity and real wage growth in each time period.
Source: Economic Report of the President 2008
http://www.gpoaccess.gov/eop/tables08.html
http://www.bls.gov/news.release/prod2.t02.htm
Supply side
determination of output/income
Equilibrium
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I = demand for investment goods
G = government demand for g & s
(closed economy: no NX )
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Consumption, C
def: Disposable income is total income minus total taxes: Y – T.
Consumption function: C = C (Y – T )
Shows that (Y – T ) C
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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.”
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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
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G excludes transfer payments
(e.g., social security benefits,
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Aggregate demand:
Aggregate supply:
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In the equation for the equilibrium condition, note that the real interest rate is the only variable that doesn’t have a “bar” over it – it’s the only endogenous variable in the equation, and it adjusts to equate the demand and supply in the goods market.
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One asset: “loanable funds”
demand for funds: investment
supply of funds: saving
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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,
(cost of borrowing).
CHAPTER 3 National Income
Loanable funds demand curve
The investment curve is also the demand curve for loanable funds.
r
I
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
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public saving = T – G
= Y – C – G
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why private saving is part of the supply of loanable funds:
.
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For any variable X, X = “the change in X ”
is the Greek (uppercase) letter Delta
Examples:
More generally, if K = 0, then
(YT ) = Y T , so
C = MPC (Y T )
= MPC Y MPC T
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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
XY = (X)(Y) + (X)(Y)
In fact, you can derive the two arithmetic tricks for working with percentage changes presented in chapter 2.
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NOW YOU TRY:
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
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= public saving.
and public saving is negative.
If T = G , “balanced budget,” public saving = 0.
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U.S. Federal Government Surplus/Deficit, 1940-2007, as a percent of GDP
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. That could change due to the expensive stimulus package and bailouts enacted in 2008-2009.
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U.S. Federal Government Debt, 1940-2007
Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt.
(In 2007, it was about 10 cents)
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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).
The current financial crisis / recession will surely boost the debt ratio, as revenues have fallen while outlays (the stimulus package, bailouts) have sharply increased. The data shown end in 2007, and we are just beginning to see a rise in the debt ratio that will surely accelerate through 2010 and perhaps beyond.
The “pop-up” box highlights perhaps the most obvious cost of a large federal debt: interest payments. Students are often shocked to learn 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.
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so the supply curve is vertical.
r
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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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The special role of r
r adjusts to equilibrate the goods market and the loanable funds market simultaneously:
If L.F. market in equilibrium, then
Y – C – G = I
Thus,
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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
c. all the things that can shift the curve
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Things that shift the saving curve
public saving
private saving
401(k)
IRA
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increases in defense spending: G > 0
big tax cuts: T < 0
Both policies reduce national saving:
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I2
1. The increase in the deficit reduces saving…
r
variable 1970s 1980s
S 19.6 17.4
r 1.1 6.3
I 19.9 19.4
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:
Draw the diagram for the loanable funds model.
Suppose the tax laws are altered to provide more incentives for work, such that L ↑
(Assume that total tax revenue T does not change and G does not change)
What happens to the interest rate and investment?
Students may be confused because we are (somehow) changing taxes, but assuming T is unchanged. Taxes have different effects. The total amount of taxes (T ) affects disposable income. But even if we hold total taxes constant, a change in the structure or composition of taxes can have effects. Here, by holding total taxes constant, we ensure that neither disposable income nor public saving change, yet the composition of taxes changes to give consumers an incentive to increase their saving.
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some technological innovations
firms must buy new investment goods
tax laws that affect investment
e.g., investment tax credit
An increase
But the equilibrium level of investment cannot increase because the
supply of loanable
funds is fixed.
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?
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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.
Reasons why saving might depend on r:
An increase in r makes saving more attractive , increases the reward for postponing consumption
Many consumers finance their spending on big-ticket items like cars and furniture, and an increase in r makes such borrowing more expensive.
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An increase in investment demand when saving depends on r
r1
which induces an increase in the quantity of saving,
which allows I
Chapter Summary
the level of technology
Competitive firms hire each factor until its marginal product equals its price.
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Chapter Summary
consumption
investment
the demand for and supply of:
goods and services
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.
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(,)

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