Download 2015 Spring - 421 Notes 03

Preliminaries
Business
Fluctuations
Business
Fluctuations
Notes 03
Notes 03
Preliminaries
Preliminaries
ECON 421: Business Fluctuations
Composition
of GDP
Demand for
Goods
Composition
of GDP
Demand for
Goods
Spring 2015
Tu 6:00PM–9:00PM
Section 102
Equilibrium
Output
Determination
Additional
Topics
Levels of Learning
Equilibrium
Output
Determination
1. Knowledge Level This is the ability to remember specific facts and
definitions.
2. Comprehension Level This is grasping the meaning of material and is often
demonstrated by translating from one medium to another. e.g.
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Additional
Topics
Problems
Created by
Problems
References
Richard Schwinn, Ph.D.
References
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from words to graphs
from words to calculations
3. Application Level This implies using learned material in new and concrete
situations.
4. Analysis Level This involves breaking down material into its component parts
so that its organizational structure may be understood.
Based on
Macroeconomics, Blanchard and Johnson [2011]
Your objective is to perform analyses involving language-based, graphical, and
mathematical macroeconomic relationships.
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
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Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Preliminaries
Business
Fluctuations
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Preliminaries
Functional Notation
Notes 03
Preliminaries
Preliminaries
Composition
of GDP
Composition
of GDP
Equilibrium
Output
Determination
Updated: March 10, 2015
Business
Fluctuations
Notes 03
Demand for
Goods
Business Fluctuations
Consider the equation y = 2x + 3.
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Demand for
Goods
Suppose you are told to find y when x = −1. You substitute for x and find
that y = 1.
Equilibrium
Output
Determination
Alternatively the equation could be expressed as
Additional
Topics
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When YD = 0 then C = c0 , i.e. autonomous consumption,
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Otherwise
C = c0 + c1 YD
Additional
Topics
f (x) = 2x + 3 or even y(x) = 2x + 3.
Problems
The functional relationship that we’re most concerned with in this chapter is
consumption (C) as a function of disposable income (YD ). C(YD )
Problems
References
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Since 0 < c1 < 1, we write
C(YD ).
References
+
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The LHSs are pronounced, ”f of x,” and, ”y of x.”
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While these equations have the same meaning, the second requires a bit of
caution due to the ambiguous roll of parentheses.
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
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The plus sign indicates that the two variables grow together.
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
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Composition of GDP
Demand for Goods
Business
Fluctuations
Business
Fluctuations
Notes 03
Notes 03
Preliminaries
Preliminaries
Composition
of GDP
Composition
of GDP
Demand for
Goods
On the expenditure side, GDP can be decomposed into
Equilibrium
Output
Determination
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consumption C (70.5% of GDP in 2010),
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government spending G (20.4% of GDP in 2010),
Additional
Topics
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fixed investment I (12% of GDP in 2010),
Problems
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and net exports X − IM (-3.5% of GDP in 2010).
Demand for
Goods
I
The terms Y, real GDP, output, national income and production are often
used interchangeably.
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The book briefly makes a distinction between the demand for goods (Z) and
actual production (Y ).
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Total demand appears to be identical to Y. The difference mathematically, is
that Z acknowledges the possibility of inventory investment (0.5% of GDP in
2010).
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When firms create goods that are not consumed in the period that they are
produced, these goods are recorded as inventory investment.
Consumption
(C)
Investment (I)
Equilibrium
Output
Determination
Additional
Topics
References
Problems
References
Z ≡ C + I + G + X − IM.
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Demand for Goods
Business
Fluctuations
Updated: March 10, 2015
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Consumption (C)
Demand for Goods
C
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Consumption (C)
Preliminaries
Composition
of GDP
Composition
of GDP
C(YD ) = c0 + c1 YD
Consumption is primarily determined by the level of disposable income, YD .
Consumption
(C)
Investment (I)
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Disposable income can be defined as YD = Y − tY Y or YD = Y − T when
taxes are lump sum.
Equilibrium
Output
Determination
Additional
Topics
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Note that taxes T refers to taxes minus government transfers.
Additional
Topics
Problems
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Additionally, autonomous consumption, c0 , represents how much consumption
would occur if disposable income were zero. How can consumption be positive
if income is zero?
References
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Dis-savings. It is assumed that the economy borrows to pay for c0 if needed.
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Thus C is modeled as a function of disposable income (YD ) and autonomous
consumption (c0 ).
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
C(YD ) = c0 + c1 YD
Demand for
Goods
The level of consumption spending depends on many factors.
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Equilibrium
Output
Determination
Updated: March 10, 2015
Notes 03
Preliminaries
Consumption
(C)
Investment (I)
Business Fluctuations
Business
Fluctuations
Notes 03
Demand for
Goods
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
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c1 is the marginal propensity to consume. This tells us how much of each
dollar is spent (c1 ) and how much is saved (1 − c1 ).
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Recall that since 0 < c1 < 1, we write C(YD ).
Problems
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This means that consumption increases when disposable income increases.
References
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Try to visualize C = c0 + c1 Y , where c0 > 0 and 0 < c1 < 1.
+
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
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Demand for Goods
Consumption (C)
Demand for Goods
Business
Fluctuations
Business
Fluctuations
Notes 03
Notes 03
Preliminaries
Preliminaries
Composition
of GDP
Composition
of GDP
Demand for
Goods
Demand for
Goods
Consumption
(C)
Investment (I)
Equilibrium
Output
Determination
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Additional
Topics
Consumption
(C)
Investment (I)
At YD = 0 There is a positive level
of C.
Equilibrium
Output
Determination
and an upward slowing line with a
slope less than 1.
Additional
Topics
Problems
Problems
References
References
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Demand for Goods
Business
Fluctuations
Updated: March 10, 2015
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Government Spending (G) and Taxes (T )
Preliminaries
Composition
of GDP
References
Demand for
Goods
Government spending is exogenous.
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Additional
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Problems
In biology exogenous means growing or originating from outside an organism.
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If a variable is not a function of any other variables in the model, then it is
exogenous.
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Notice that consumption is not exogenous since it is a function of Y . Such
variables are called endogenous.
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Is c0 exogenous or endogenous? What about c1 ?
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Investment (I)
X − IM
Notes 03
Composition
of GDP
Equilibrium
Output
Determination
I
Demand for Goods
Preliminaries
Consumption
(C)
Investment (I)
Assume that investment I is exogenous.
Investment (I)
Notes 03
Demand for
Goods
I and G
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business
Fluctuations
Investment (I)
I
Consumption
(C)
Investment (I)
Government spending includes the purchase of newly produced goods and
services.
Transfers, such as Social Security payments, veterans benefits, and interest on
the government debt are excluded.
The variable T is defined as taxes minus transfers and includes taxes minus
transfers at all levels of government.
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
Equilibrium
Output
Determination
Imports are subtracted from GDP on the expenditure side because the
domestic spending categories C, I, and G include spending on foreign goods
and services.
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To isolate spending on domestically produced goods and services, imports
must be subtracted.
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Likewise, exports are added because they represent foreign spending on
domestically produced goods and services.
Additional
Topics
Problems
References
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Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
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Equilibrium Output Determination
Equilibrium Output Determination
Business
Fluctuations
Business
Fluctuations
Notes 03
Notes 03
Preliminaries
Substituting the definition of consumption,
Composition
of GDP
Demand for
Goods
Preliminaries
Composition
of GDP
C(YD ) = c0 + c1 YD ,
into
Equilibrium
Output
Determination
Z ≡ C + I + G + X − IM,
we have
Using Algebra
Using a Graph
Using Words
Z ≡ c0 + c1 YD + I + G + X − IM.
Additional
Topics
Additional
Topics
Problems
References
Until the final third of the course, we will assume that X − IM = 0.
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Considering that X − IM was only -3.5% of GDP in 2010 for the US, this is
not an unforgivable assumption.
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Updated: March 10, 2015
References
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Three Paths to Comprehension
Preliminaries
Composition
of GDP
Problems
References
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If Y < Z then people are somehow spending more money than they’re earning
(borrowing) on average.
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Each alternative ultimately tends toward the equilibrium Y = Z over time, so
we put aside these complications so that income equals demand:
Business Fluctuations
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Using Algebra
Using Algebra
Notes 03
Composition
of GDP
Additional
Topics
If Y > Z, then firms have produced more goods than people demand, then
firms respond by accumulating inventories.
Equilibrium Output Determination
Preliminaries
Using Algebra
Using a Graph
Using Words
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Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business
Fluctuations
Notes 03
Equilibrium
Output
Determination
What if Y 6= Z?
Y = c0 + c1 YD + I + G
Equilibrium Output Determination
Demand for
Goods
Y = Z.
Problems
I
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business
Fluctuations
The equilibrium condition is
Demand for
Goods
Equilibrium
Output
Determination
Using Algebra
Using a Graph
Using Words
The Equilibrium Condition
Recall that the second level of learning is comprehension. There are three paths
to understanding this material.
1. via algebra,
Y = c0 + c1 Y − c1 T + I + G.
Demand for
Goods
Equilibrium
Output
Determination
Using Algebra
Using a Graph
Using Words
2. via language, or
Let disposable income YD = Y − T so that Y = c0 + c1 YD + I + G becomes
Now solve for Y by adding −c1 Y to both sides then distribute out the Y .
−c1 Y + Y = c0 + c1 Y − c1 T + I + G + (−c1 Y )
Additional
Topics
3. via graphs.
You will find that by employing all three techniques/mediums, you can solidify your
comprehension.
(1 − c1 )Y = c0 − c1 T + I + G
Problems
References
Now divide both sides by (1 − c1 ) to isolate Y:
Y =
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
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Notes 03 (Loyola-Chicago Spring 2015, Section 101)
c0 − c1 T + I + G
.
1 − c1
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Equilibrium Output Determination
Using Algebra
Equilibrium Output Determination
Business
Fluctuations
Business
Fluctuations
Notes 03
Notes 03
Preliminaries
Preliminaries
Composition
of GDP
Composition
of GDP
Y =
Demand for
Goods
Equilibrium
Output
Determination
Using Algebra
Using a Graph
Using Words
1
c0 − c1 T + I + G
=
[c0 − c1 T + I + G]
1 − c1
1 − c1
While this may not yet appear easy to interpret, you will find that it can be used to
quickly generate many different macroeconomic insights.
1. What is the effect of taxes have on output?
Equilibrium income is the product of
two factors:
Equilibrium
Output
Determination
autonomous spending (the term in
brackets)
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1
).
and the multiplier ( 1−c
1
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Demand depends on autonomous
spending and on income, via its
effect on consumption.
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The relation between demand and
income is drawn as ZZ in the
graph.
Using Algebra
Using a Graph
Using Words
Additional
Topics
Problems
3. If the government expands, is consumption unchanged?
Problems
References
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Equilibrium Output Determination
Updated: March 10, 2015
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Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Using a Graph
Business
Fluctuations
1
Y =
1 − c1
c0 − c1 T + I + G
Autonomous Spending
M ultiplier
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Demand for
Goods
I
Using Algebra
Using a Graph
Using Words
I
Additional
Topics
Problems
References
I
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
18 / 28
Using Words
Using Words
Notes 03
Composition
of GDP
Equilibrium
Output
Determination
Business Fluctuations
Equilibrium Output Determination
Business
Fluctuations
Preliminaries
c0 − c1 T + I + G
Autonomous Spending
M ultiplier
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2. What happens to Y if people increase their savings?
Notes 03
Demand for
Goods
Additional
Topics
References
1
Y =
1 − c1
Using a Graph
The intercept with the vertical axis
is the value of demand when
income is equal to zero.
The intercept is thus autonomous
spending.
When income increases by 1,
demand increases by c1 . Since
0 < c1 < 1, the line is upward
sloping but has a slope of less than
1.
In equilibrium, production equals
demand.
Updated: March 10, 2015
19 / 28
Preliminaries
Composition
of GDP
Demand for
Goods
Equilibrium
Output
Determination
Using Algebra
Using a Graph
Using Words
Using words to explain the equilibrium is less effective than the other modes:
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Production depends on demand,
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which depends on income,
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which is itself equal to production.
Discussing a change in the equilibrium seems more effective:
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An increase in demand, such as an increase in government spending, leads to
an increase in production and
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a corresponding increase in income.
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This increase in income leads to a further increase in demand, which leads to a
further increase in production, and so on.
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The end result is an increase in output that is larger than the initial shift in
demand, by a factor equal to the multiplier.
Additional
Topics
Problems
References
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
20 / 28
Additional Topics
Business
Fluctuations
How Long Does It Take for Output to Adjust?
Additional Topics
Business
Fluctuations
How Long Does It Take for Output to Adjust?
Notes 03
Notes 03
Preliminaries
Preliminaries
Composition
of GDP
Composition
of GDP
Demand for
Goods
Equilibrium
Output
Determination
Additional
Topics
How Long Does
It Take for
Output to
Adjust?
Investment
Equals Saving
Problems
Demand for
Goods
The answer for what we have developed is immediately.
Our simple model is unsuitable for answering the question of how long it takes to
adjust.
Equilibrium
Output
Determination
Additional
Topics
Recall from principles, the definitions of private, public, and national savings:
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Private savings: Sprv = Y − T − C
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Public savings: Spub = T − G
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National savings: S = Sprv + Spub = Y − C − G
Next notice that if we subtract C and G from both sides of the national income
equation (Y = C + I + G), then
How Long Does
It Take for
Output to
Adjust?
Investment
Equals Saving
In reality, the response to an increase in autonomous spending is not an
instantaneous jump to a new equilibrium. It increases more gradually over time.
Y − (C + G) = C + I + G − (C + G)
Y −C −G=S =I
Problems
References
References
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
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Thus savings exactly equals investment!
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Problems
Business
Fluctuations
Notes 03
Notes 03
Composition
of GDP
Demand for
Goods
Equilibrium
Output
Determination
Preliminaries
Suppose that the economy is
characterized by the following
behavioral equations:
Composition
of GDP
Additional
Topics
YD = Y − T
Problems
I = 150
Equilibrium
Output
Determination
1. Equilibrium GDP (Y )
2. Disposable income (YD )
Additional
Topics
3. Consumption spending (C)
Problems
References
References
G = 150
T = 100
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
Suppose the economy is
characterized by the following
behavioral equations:
Demand for
Goods
Solve for the following variables:
C = 160 + 0.6YD
Business Fluctuations
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Problems
Business
Fluctuations
Preliminaries
Investment Equals Saving
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C = c0 + c1 YD
YD = Y − T
I = b0 + b1 Y
and government spending and
taxes are constant. Note that
investment now increases with
output.
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
1. Solve for equilibrium output.
2. What is the value of the multiplier?
3. How does the relation between investment
and output affect the value of the multiplier?
4. For the multiplier to be positive, what
condition must (c1 + b1 ) satisfy?
5. Suppose that the parameter b0 , sometimes
called business confidence, increases. How
will equilibrium output be affected?
6. Will investment change by more or less than
the change in b0 ? Why? What will happen
to national saving?
Business Fluctuations
Updated: March 10, 2015
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Problems
Problems
Business
Fluctuations
Business
Fluctuations
Notes 03
Notes 03
Preliminaries
Composition
of GDP
If C = 2000 + .9YD , what decrease in taxes must occur for equilibrium output to
increase by 1000? (The 2000 is irrelevant so it is replaced with c0 )
Demand for
Goods
Y = c0 + 0.9(Y − T ) + I + G
Equilibrium
Output
Determination
(1)
(1 − 0.9)Y = c0 − 0.9T + I + G
c0 + I + G 0.9
−
T
Y =
0.1
0.1
c0 + I + G
Y =
− 9T
0.1
Additional
Topics
Problems
References
Preliminaries
Composition
of GDP
Demand for
Goods
(2)
Equilibrium
Output
Determination
(3)
Additional
Topics
Comments, questions, or errors detected?
Problems
(4)
References
Thus ∆T = −111 yields an increase of $1000 in GDP.
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
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Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Problems
Business
Fluctuations
Updated: March 10, 2015
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Problems
Business
Fluctuations
References
Notes 03
Uncopyright
Notes 03
Preliminaries
Preliminaries
Composition
of GDP
Composition
of GDP
Demand for
Goods
Demand for
Goods
Equilibrium
Output
Determination
Equilibrium
Output
Determination
Additional
Topics
Business Fluctuations
Olivier Jean Blanchard and David Johnson. Macroeconomics. Prentice Hall, 6th
edition, 2011. ISBN 9780133061635.
Additional
Topics
Problems
Problems
References
References
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This means I’ve put them in the public domain and released my copyright. Use this
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Attribution is greatly appreciated but not required.
Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
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Notes 03 (Loyola-Chicago Spring 2015, Section 101)
Business Fluctuations
Updated: March 10, 2015
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