1
Equilibrium in Goods and Services Market
Supply and Demand – Equilibrium
The equilibrium output depends on how the demand and supply are determined
We will first focus on the demand side: What determines the demand?
Sources of Demand
We have considered three approaches to measure the GDP
Product approach
emphasizes the value-added of domestic producers
Expenditure approach
emphasizes spending on final goods and services produced domestically
Income approach
emphasizes income earned by factors operating in domestic markets
These numbers should approximately be the same, though they are not exactly identical
Since we are interested in the behavior of economic agents in determining their demand, we start with
the expenditure approach
Expenditure Approach to GDP
Captures spending on all final goods and services produced domestically
Divide spending into four groups
C: Personal consumption of households and non-profit organization
I: firms investment spending on capital goods and change in inventories
G: government expenditure (consumption and investment)
NX: net exports, NX=X-M
X=Exports of goods and services
M= imports of goods and services
Y=C+I+G+NX
Personal Consumption Expenditure
the largest component of expenditure: a little more than 2/3 of GDP
Three categories
Durable goods:
motor vehicles and parts
Furnishings and durable household equipment
Recreational goods and vehicles
other durable goods
Nondurable goods
Food and beverages purchased for off premise consumption
Clothing and footwear
Gasoline and other energy good
other nondurable goods
Services
Households: Housing and utilities, health care, transportation, recreation, food and
accommodation, financial, others
Non-profit institutions
2
Investment
Fixed Investment
Non residential:
Structures:
equipment: Information processing. industrial, transportation, others
Intellectual properties: software, R&D, entertainment & arts
Residential: new houses and new apartments
Inventory investment
the reason for a change in inventory does not matter
Government Expenditure:
consumption expenditure (employee salaries, etc) and investment expenditure (buildings) on
domestic or foreign goods and services produced in current period
Transfer payments (social security, medicare, unemployment insurance, welfare payments, etc) are
not payment on currently produced goods and services, and hence they are not included in the
government expenditure
Interest payments on government debts are excluded.
Federal government
National Defense: Consumption and gross investment
National Non-defense: Consumption and gross investment
State and Local Government
Consumption and gross investment
This approach identifies four groups of economic agents who demand domestically produced goods
HH: Households & nonprofit organization - C
Firms - I
Government - G
Foreign countries - EX
The first three groups' expenditure includes expenditures on imported goods
C=Cd+Cf,
I=Id+If,
G=Gd+Gf
Demand for domestically produced goods
Cd+Id+Gd+EX=(C-Cf ) + (I-If) + (G-Gf) + EX=C+I+G+(EX-Cf-If+Gf)=C+I+G+NX
Total demand for domestically produced goods and services is
Y=C+I+G+NX
3
Determinants of each component
Consumption expenditure – there are many factors, but the most important factor is the disposable
income: C=C(Y-T)
Properties of the consumption function
MPC (Marginal Propensity to Consume): additional amount of consumption as disposable
income rises by 1 dollar
MPC is usually less than one: 0<MPC<1
If MPC is a constant, the consumption function is a linear function: C=C0+MPC*(Y-T)
C0 is called the subsistence level consumption
Investment expenditure: I=I(r), r=real interest rate
An increase in interest rate reduces investment
Government expenditure: G
This includes employee salaries and investment in buildings, national defense, etc
It does not include transfer payment such as social securities, unemployment compensation, etc,
because this is not the expenditure on current output
Therefore, we can think of it as predetermined, unless there is a discrete fiscal policy changes such
as Obama's stimulus package
Net export: NX=NX() =real exchange rate
The nominal exchange rate is the amount of foreign currency (e.g., German Mark) that that you can
buy with one U.S. dollar (we will learn later the difference between the nominal and real
exchange rates)
An increase in exchange rate makes foreign good cheaper to U.S. buyers, and makes the U.S. good
more expensive to foreign buyers. Therefore, an increase in the exchange rate increases import
and reduces export. This means that the net export NX decreases as the exchange rate increases
Demand for Goods and Services
Sum of the demands of the four groups discussed above:
Yd=C(Y-T)+I(r)+G+NX()
Supply of Goods and Services
assume a perfectly elastic supply
That is, firms produce the amount of demand
Ys=Yd=Y
Equilibrium Output
Output/income Y that satisfies
Y=C(Y-T)+I(r)+G+NX()
Note: This assumes that firms distribute all proceeds of produced output to households. There is no
business taxes: only households pay income tax which is a lump sum tax (does not depend on
income level)
Endogenous and Exogenous variables
Endogenous variable: variable that depends on other variables in the system
Exogenous variable: variable that does not depend on other variables in the system
4
We start with a simplest system
Endogenous variables: Y, C,
Exogenous variables: r, , I, G, T, NX
For given exogenous variables I, G and NX, the equilibrium income Y is the value of Y that satisfies the
following equality
Y=C(Y-T)+I+G+NX
Graphical Analysis
A graph measuring Y on the horizontal axis
Draw a line that represents the supply (left hand side of the equation): It is a 45 degree line
Draw a line that represents the demand (right hand side of the equation): C+I+G+NX
The equilibrium income is where the two lines intersect each other
Note: Suppose the current output is below the equilibrium output Y*. Then, demand is higher than
supply and output rises.
C+I+G+NX
Ys
Yd
Y
Comparative Statics
Increase in T by T: This reduces the disposable income and shifts Yd curve downward and the
equilibrium income decreases
Increase in G by G: This shifts Yd curve upward and the equilibrium income increases
Increase in interest rate: This reduces I and shifts Yd curve downward and the equilibrium income
decreases
Increase in exchange rate : This reduces NX and shifts Yd curve downward and the equilibrium income
decreases
5
Algebraic solution
Assume a linear consumption function
Y=C0+MPC*(Y-T)+I+G+NX
𝑌=
𝐶0 −𝑀𝑃𝐶∗𝑇+𝐼+𝐺+𝑁𝑋
1−𝑀𝑃𝐶
Comparative Static Analysis
Increase in T by T: Y=-[MPC/(1-MPC)]T
Increase in G by G: Y=[1/(1-MPC)]G
Increase in I by I: Y=[1/(1-MPC)]I
Increase in NX by NX: Y=[1/(1-MPC)]NX
Government expenditure multiplier 1/(1-MPC)
Tax multiplier: -MPC/(1-MPC)
Balanced budget multiplier: [1-MPC]/(1-MPC)=1
Explanation of Government Expenditure Multiplier Effects
1st round: an increase in G increases the demand ⇒ output increases to meet the demand:
∆𝑌1 = ∆𝐺
Proceeds from additional output are distributed to HH as wages and dividends (no retained earnings,
no business taxes). That is, households' income rises by ∆𝑌1
2nd round: an increase in income of HH by ∆𝑌1 ⇒ HH consumes MPC*∆𝑌1 (and saves (1-MPC) ∆𝑌1 ) ⇒
demand increases by MPC* ∆𝑌1 ⇒ output increases to meet this additional demand:
∆𝑌2 = 𝑀𝑃𝐶 ∗ ∆𝑌1 = 𝑀𝑃𝐶 ∗ ∆𝐺
This increases HH's income by ∆𝑌2 .
3rd round: an increase in income of HH by ∆𝑌2 ⇒ HH consumes MPC*∆𝑌2 (and saves (1-MPC) ∆𝑌2 ) ⇒
demand increases by MPC* ∆𝑌2 ⇒ output increases to meet this additional demand:
∆𝑌3 = 𝑀𝑃𝐶 ∗ ∆𝑌2 = 𝑀𝑃𝐶 ∗ (𝑀𝑃𝐶 ∗ ∆𝐺) = 𝑀𝑃𝐶 2 ∗ ∆𝐺
This increases HH's income by ∆𝑌3 .
This process continues and total increase in output/income is
∆𝑌 = ∆𝑌1 + ∆𝑌2 + ∆𝑌3 + ∆𝑌4 + ⋯ = ∆𝐺 + 𝑀𝑃𝐶 ∗ ∆𝐺 + 𝑀𝑃𝐶 2 ∗ ∆𝐺 + +𝑀𝑃𝐶 3 ∗ ∆𝐺 + ⋯
Therefore,
∆𝑌 = (1 + 𝑀𝑃𝐶 + 𝑀𝑃𝐶 2 + 𝑀𝑃𝐶 3 + ⋯ ) ∗ ∆𝐺 =
1
∆𝐺
1−𝑀𝑃𝐶
And one dollar increase in government expenditure increases income by 1/(1-MPC)
Remark: If the proceeds from the first round increase in output is retained and not distributed to
households, the multiplier process stops there and total increase in income is just the initial increase
in demand ∆𝐺.
6
Explanation of Tax Multiplier Effects
1st round: an increase in T by ∆𝐺 decreases the deposable income by the same amount. Therefore, HH
consumption decreases by MPC*∆𝑇 ⇒ output decreases to meet the reduced demand:
∆𝑌1 = 𝑀𝑃𝐶 ∗ ∆𝑇
2nd round: a decrease in income of HH by ∆𝑌1 ⇒ HH reduces consumption by MPC*∆𝑌1 ⇒ demand
decreases by MPC* ∆𝑌1 ⇒ output decreases to meet this additional reduced demand:
∆𝑌2 = 𝑀𝑃𝐶 ∗ ∆𝑌1 = 𝑀𝑃𝐶 2 ∗ ∆𝑇
This decreases HH's income by ∆𝑌2 .
3rd round: a decrease in income of HH by ∆𝑌2 ⇒ HH reduces consumption MPC*∆𝑌2 ⇒ demand
decreases by MPC* ∆𝑌2 ⇒ output decreases to meet this additional reduced demand:
∆𝑌3 = 𝑀𝑃𝐶 ∗ ∆𝑌2 = 𝑀𝑃𝐶 ∗ (𝑀𝑃𝐶 2 ∗ ∆𝑇) = 𝑀𝑃𝐶 3 ∗ ∆𝑇
This decreases HH's income by ∆𝑌3 .
This process continues and total decrease in output/income is
∆𝑌 = ∆𝑌1 + ∆𝑌2 + ∆𝑌3 + ∆𝑌4 + ⋯ = 𝑀𝑃𝐶 ∗ ∆𝑇 + 𝑀𝑃𝐶 2 ∗ ∆𝑇 + +𝑀𝑃𝐶 3 ∗ ∆𝑇 + ⋯
Therefore,
𝑀𝑃𝐶
∆𝑌 = (𝑀𝑃𝐶 + 𝑀𝑃𝐶 2 + 𝑀𝑃𝐶 3 + ⋯ ) ∗ ∆𝑇 = 1−𝑀𝑃𝐶 ∆𝑇
And one dollar increase in lump sum tax collection decreases income by MPC/(1-MPC)
7
Alternative expression for the equilibrium condition
We will consider a closed economy first, that is, NX=0
The equilibrium condition is
Y=C(Y-T)+I+G
National Savings
S=Y-C-G
Note: National saving S can be decomposed into private saving (Y-T-C) and public saving (T-G):
Y-C-G = (Y-T-C) + (T-G).
The equilibrium condition can now be written as S=I
The national saving S is the supply of Loanable Funds and investment is the demand for loanable funds.
Interest rate is the price of loanable funds
If interest rate is flexible (endogenous) as we will learn later, then it adjusts until supply equals
demand (saving equals investment).
Graphical analysis of equilibrium condition S=I in loanable fund market in a closed economy
S=Y-C-G=Y-C(Y-T)-G=Y-[C0+MPC(Y-T)]-G = -(C0+G-MPC*T) + (1-MPC)*Y
In a graph with Y on the horizontal axis, the savings function is a line intercept -(C0+G-MPC*T) and
slope (1-MPC) which is the marginal propensity to save (MPS).
Investment is assumed I=I(r), which does not depend on Y. Therefore, for a given r, the line that
represents the investment is a horizontal line (i.e., stays the same as Y changes)
The equilibrium income is where the two lines intersect each other
S
I
Y
Comparative static analysis
An increase in G or a decrease in T reduces the national savings for any given Y (i.e., the intercept term
becomes a larger negative number). This shifts the S curve downward. Therefore, the equilibrium
income rises
An increase in investment (say, due to a decrease in r) shifts I curve upward, and hence the equilibrium
income rises.
An increase in G and T by the same amount shifts the S curve downward, which increases the
equilibrium income.
8
IS Curve: Goods and service market equilibrium
We showed that an increase in interest rate r reduces investment, which in turn reduces the equilibrium
income, given G and T. Therefore, there is a negative relationship between Y and r that keeps the
G&S market at equilibrium
Consider a graph that measures Y on the horizontal axis and r on the vertical axis. The line that shows
the relationship between Y and r for the equilibrium in the goods and service market is called the IS
curve. The name is from I=S equilibrium condition.
Algebraic derivation
Suppose the consumption and investment functions are linear
C=C0+MPC*(Y-T)
I=I0-d*r
where d is a constant slope of the investment function. It captures the effect of a change in r on I: an
increase in r by 1% reduces investment by $d
From the equilibrium condition Y=C(Y-T)+I(r)+G, or I(r)=S=Y-C(Y-T)-G, we write
Y=C(Y-T)+I(r)+G=C0+MPC*Y-MPC*T+I0-d*r+G
Solving for Y, we have
Y 
C0  MPC * T  I 0  G
d

r
1  MPC
1  MPC
or solving for r
r
C0  MPC * T  I 0  G 1  MPC

Y
d
d
This explicitly shows the negative relationship between Y and r.
r
An increase in C0, I0 and G shifts the IS curve upward
An increase in MPC shifts the IS curve down and makes it steeper
An increase in d shifts the IS curve down and makes it flatter
IS
Y