# bài giảng

Macroeconomics for Public Policy
Lecture 3: Long-run Models

Tran Lam Anh Duong
7-9 February 2018
1

Review of the Supply and Demand
１．Demand:
• Demand: indicate the
quantity of goods or services
purchased at a given price.
• Demand curve:
– If other conditions are the
same, the figure show the
volume of goods that a person
wants to buy under price 𝑝𝑝.
– The curve is right downward.

• Which factor makes a

demand curve shift?

Price(𝑝𝑝)

D
Quantity(𝑞𝑞)

2

Review of the Supply and Demand
2．Supply:
• Supply: indicate that the
quantity of goods or services
sold by the seller at a given
price.
• Supply Curve:

Price(𝑝𝑝)

S

– If other conditions are the
same, the figure show the
volume of goods that an agent
wants to sell under price 𝑝𝑝.
– The curve is right upward.

• Which factor makes a supply
curve shift?

Quantity(𝑞𝑞)

3

Review of the Supply and Demand
3. Market equilibrium:
• Intersection of demand
curve and supply curve.

• At that time, the demand
and supply are identical
and unambiguously
determine the price.
• We call the price
equilibrium price (𝑝𝑝∗ ), the
quantity equilibrium
quantity (𝑞𝑞 ∗ ).

Price(𝑝𝑝)

𝑝𝑝∗

S

𝐸𝐸

Market equilibrium
D

𝑞𝑞 ∗

Quantity(𝑞𝑞)
4

Review of the Supply and Demand
４．Excess supply: In the
market if the supply
exceeds the demand, then
the excessive part is
excess supply.
⇒The price will go down
in the market.

Price(𝑝𝑝)

𝑝𝑝′

S

Excess supply

D
Quantity(𝑞𝑞)
Demand

Supply
5

Reviews of the Supply and Demand
５． Excess demand: In the
market if the demand
exceeds the supply, then
the excessive part is
excess demand.
⇒ The price will go up
in the market.

Price(𝑝𝑝)

𝑝𝑝′

S

Excess demand

D
Quantity(𝑞𝑞)

Demand

Supply
6

Long-run vs Short-run
• Macroeconomics theory distinguishes “Long-run
• Long-run models: They focus on how the average
trend of the economy is determined in a long
period such as 10 or 20 years.
• Short-run models: They focus on changes of the
economy in a short period such as 1 or 2 months,
or one year.
7

Assumptions for simplification
• The following assumptions are suitable for both long-run and short-run
models ：
1. There is only one kind of goods.
2. Housing investment and inventory investment are not under
consideration. Investment here refers to equipment investment of a
firm.
3. Government purchases are only for government consumption: 𝐺𝐺 = 𝐺𝐺𝐶𝐶
4. Real variables are measured in units of goods.
5. Nominal variables:

Nominal GDP=𝑃𝑃 × 𝑌𝑌

Nominal consumption=𝑃𝑃 × 𝐶𝐶

Nominal investment=𝑃𝑃 × 𝐼𝐼

Nominal government purchases=𝑃𝑃 × 𝐺𝐺
※Price level 𝑃𝑃 : price per unit of goods which is measured in an unit of
currency.

8

Characteristics of long-run models
• A point of long-run models: price elasticity
• Price elasticity: It shows the rises and falls of
price in order to make the supply and demand
equal under economic mechanism.
• Long-run: The time is long enough so that all
9

Long-run equilibrium of firms
• Long-run equilibrium: In long-run models, the
equilibrium is that the demand and supply are
always equal.
１．Equilibrium of goods market
２．Equilibrium of labor market
３．Equilibrium of money market

10

Goods market

11

Equilibrium of goods market
Aggregate supply (𝑌𝑌 𝑆𝑆 )

Determined by firms

Capital stocks
Labor

Goods market

𝑌𝑌 𝑆𝑆 = 𝑌𝑌 𝐷𝐷 = 𝑌𝑌 ∗

Aggregate demand （𝑌𝑌 𝐷𝐷 ）

𝑌𝑌 𝐷𝐷 = 𝐶𝐶𝑌𝑌𝐷𝐷𝑆𝑆 += 𝐼𝐼𝑌𝑌𝐷𝐷𝐷𝐷+=𝐺𝐺𝑌𝑌𝐷𝐷∗ + 𝑁𝑁𝑁𝑁 𝐷𝐷

Equilibrium GDP

12

Supply side: Production function of firms
• Production factors: Necessary factors for production
– Capital stocks (equipment): 𝐾𝐾
– Labor: 𝐿𝐿

• Production function: It determines how much
output is produced from given amounts of capital
and labor.
𝑌𝑌 = 𝐹𝐹(𝐾𝐾, 𝐿𝐿)
• Characteristics of production function: 𝑌𝑌 is the
increasing function of 𝐾𝐾 and increasing function of
𝐿𝐿.

13

Production function of firms
• Example:
– Country A’s production function: 𝑌𝑌 = 𝐾𝐾 𝐿𝐿
– Country B’s production function: 𝑌𝑌 = 2 𝐾𝐾 𝐿𝐿

⇒If the value of 𝐾𝐾 and 𝐿𝐿 are the same for two countries,
then the production of B is twice than that of A.

• Total Factor Productivity （TFP - production
technology）: a factor which accounts for
total outputs that the firm produces with a
given input amount of labor and capital.

14

Production function of firms
• The supply of capital stocks and the number of labor in
the whole economy are considered to be constant during
a certain period. The reasons are as follows:

– Supply of capital stocks: depends on long time accumulation
� (constant)
results ⇒ 𝐾𝐾 = 𝐾𝐾
– The number of labor: depends on the change in population of
the country ⇒ 𝐿𝐿 = 𝐿𝐿� (constant)

• An assumption: all of capital stocks and labor supplied in
the economy are used for production by firms.
• Long-run production function:
� 𝐿𝐿� ): constant
𝑌𝑌� = 𝐹𝐹(𝐾𝐾,
15

Aggregate supply
• The total amount of production＝Aggregate
supply（𝑌𝑌 𝑆𝑆 ）
𝑌𝑌 𝑆𝑆 = 𝑌𝑌� = 𝐹𝐹(𝐾𝐾, 𝐿𝐿)

⇒The value of aggregate supply is constant regardless
of various variables such as price.

• The important conclusion toward aggregate
supply：The long-run aggregate supply of the
economy depends only on the production
capacity of the economy, that is, the production
technology of the firms (TFP) and the volume of
production factors.

16

Determinants of GDP
• Equilibrium conditions for goods market:
𝑌𝑌 𝑆𝑆 = 𝑌𝑌 𝐷𝐷 = 𝑌𝑌 ∗
⟺ 𝑌𝑌 𝑆𝑆 = 𝑌𝑌 ∗ and 𝑌𝑌 𝐷𝐷 = 𝑌𝑌 ∗

• Determinant conditions of aggregate supply: 𝑌𝑌 𝑆𝑆 = 𝑌𝑌� =
� 𝐿𝐿� )
𝐹𝐹(𝐾𝐾,
• By this,

𝑌𝑌 ∗ = 𝑌𝑌�

 The equilibrium GDP becomes constant.
 The equilibrium GDP is determined by aggregate supply.
17

The equilibrium GDP
• The most important conclusion of models in
long run:
The equilibrium GDP is only determined by the total supply
conditions (the production technology and production
factors of firms). It is not influenced by the total demand
conditions.

18

Aggregate demand
• Total demand is the sum of consumption
demand（𝐶𝐶 𝐷𝐷 ）, investment demand（𝐼𝐼 𝐷𝐷 ）,
government purchases demand（𝐺𝐺 𝐷𝐷 ）, and net
exports demand（𝑁𝑁𝑁𝑁 𝐷𝐷 ）.
𝑌𝑌 𝐷𝐷 = 𝐶𝐶 𝐷𝐷 +𝐼𝐼 𝐷𝐷 +𝐺𝐺 𝐷𝐷 +𝑁𝑁𝑁𝑁 𝐷𝐷
19

Consumption demand
• What is the most important factor for determining the
amount of goods that households want to consume?
• Review of principles of equivalence of three approaches:
gross income is equal to gross product ⇒ gross product
affects consumption demand.
• We assume that the government imposes taxes 𝑇𝑇 to
households.

• Disposable income: gross product minus taxes ⇒ 𝑌𝑌 − 𝑇𝑇
20

Consumption function

Consumption function: Consumption
Consumption demand（𝐶𝐶 𝐷𝐷 ）
demand is an increasing function of
disposable income
𝐶𝐶 𝐷𝐷 = 𝑐𝑐 𝑌𝑌 − 𝑇𝑇 + 𝐶𝐶̅
Marginal propensity to consume (𝑐𝑐)：It
evaluates how many units of consumption
demand by households will increase if one
unit of disposable income increases.
An assumption of consumption function:
marginal propensity to consume is greater
𝑐𝑐
̅
𝐶𝐶
than 0 and smaller than 1
0 < 𝑐𝑐 < 1.
Consumption smoothing motivation:
people’s desire to have a stable
Disposable income
consumption across time.
𝑌𝑌 − 𝑇𝑇
̅
̅
𝐶𝐶: subsistence levels of consumption, 𝐶𝐶 ≥
0
21

Investment demand
• Interest rate: The issued interest on one
borrowed unit
Rate of return; Interest rate（％）
• Example:
10

A

7

B

5
4

C

2
100

100

100

Investment Demand
22

Investment function
• The interest rate
determines the cost of
investment.
• Investment function:
shows the relationship
that investment demand
is a decreasing function
of the interest rate.
𝐼𝐼 𝐷𝐷 = −𝑏𝑏𝑏𝑏 + 𝐼𝐼 ̅
where 𝑏𝑏 > 0 and 𝐼𝐼 ̅ > 0

Interest rate(𝑟𝑟)

Investment demand(𝐼𝐼 𝐷𝐷 )

23

Government purchases demand and tax
• Government purchases is the expenditure which is
determined by the government.
𝐺𝐺 𝐷𝐷 = 𝐺𝐺̅
̅
※𝐺𝐺：The
exogenous variable determined by the government
• We also assume that tax is also an exogenous variable
whose value is determined by the government.
𝑇𝑇 = 𝑇𝑇�

• Fiscal policy: The determinants of values of government
purchases and tax.
24

Net export demand
• The net export demand is constant:
𝑁𝑁𝑁𝑁 𝐷𝐷 = 𝑁𝑁𝑁𝑁

𝑁𝑁𝑁𝑁 generally describes all factors that affect
exports and imports.

25

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