V. The 45 Degree Model, Lecture notes of Dynamics

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V. The 45 Degree Model

Introduction to Economics Niclas Frederic Poitiers Group A6 BAM Degree October 25, 2018

Outlook

1. The Paradox of Thrift
2. The 45 Degree Model
3. Dynamics in the Model
4. The Multiplier Effect

Introduction to Economics V. The 45 Degree Model

Outline

1. The Paradox of Thrift
2. The 45 Degree Model
3. Dynamics in the Model
4. The Multiplier Effect

Introduction to Economics V. The 45 Degree Model

The Paradox of Thrift

Consider the following case:

• (^) When families and businesses are worried about the economic prospects, they prepare by cutting their spending & saving more.
• This reduction in spending depresses the economy, and businesses react by laying off workers and decreasing wages.
• As a result, families and businesses end up worse off than if they would have not tried to cut their spending. This is called the paradox of thrift. An increase in (autonomous) savings (a decrease in autonomous consumption) leads to an decrease in economic output and in the end result to lower total savings.

Introduction to Economics V. The 45 Degree Model

The AS-AD Model

E

Y

P

GDP

Price-Level

AS AD

The classical version of the Keynesian model is the so called AS-AD Model. In this model, the interaction of aggregate supply (AS), defined by the production of the economy, and the aggregate demand (AD), defined by the aggregate expenditure of the economy, define the GDP and the price level of an economy.

Introduction to Economics V. The 45 Degree Model

The 45 Degree Model

E

Y

P

GDP

Price-Level

AD

In our lecture, we will use a simplified version of the AS-AD model, focusing on the aggregate demand side. For this, we abstract from the aggregate supply side and assume the price level to be exogenous.

The goal of this model is to show, how changes in investment and government expenditure affect the aggregate demand in the short term.

Introduction to Economics V. The 45 Degree Model

Basic Assumptions

We assume in the 45 degree model that in the short term

• prices and wages are fixed.
• (^) there are idle resources.
• there is a fixed money supply.
• (^) financial markets are stable.

Introduction to Economics V. The 45 Degree Model

Aggregate Demand & Aggregate Expenditure

We have as aggregate demand AD the aggregate expenditure AE from the expenditure approach of deriving GDP:

AD = AE = C + I + G + X − Q

In the macroeconomic equilibrium, income Y is equal to aggregate demand AD :

Y = AD = AE

Introduction to Economics V. The 45 Degree Model

Consumption

We now define consumption as a function of disposable income YD = Y − T + TR :

C = f ( Y ) = C 0 + cYD

where C 0 is autonomous consumption independent of YD and c = MPC , with MPC being the marginal propensity to consume. We get for c :

c = MPC =

∆ C

∆ YD

and

0 ≤ c ≤ 1

Introduction to Economics V. The 45 Degree Model

The Consumption Function

0 5 10 15

0

5

10

15

Income

Expenditure

C = C 0 + cYD

Graphically, the slope of the consumption function is equal to c , and the interception with the y-axis (the AE -axis) equal to C 0.

Introduction to Economics V. The 45 Degree Model

The Hunting-Gathering Economy – Equilibrium

The equilibrium in the hunting-gathering economy is defined by

Y = AE = C = C 0 + cY

We can reformulate this to get the equilibrium:

Y =

C 0

1 − c

Introduction to Economics V. The 45 Degree Model

The Saving Function

We now also define savings as a function of disposable income YD. We do this by using C = C 0 + cYD and YD = C + S. Combining the two leads us to:

YD = C + S YD = ( C 0 + cYD ) + S S = − C 0 + (1 − c ) YD

with s = MPS being the marginal propensity of saving MPS we get

s = MPS =

∆ S

∆ YD

= 1 − c

and

0 ≤ s ≤ 1 ∧ s + c = 1

Introduction to Economics V. The 45 Degree Model

The Private Economy

ES

E

0 5 10 15

0

5

10

15

Income

Expenditure

S = − C 0 + (1 − c ) Y I C = C 0 + cY AE = C + I = C 0 + cY + I

In the private economy , there is no government and no trade and thus AE = C + I and Y = YD. The equilibrium is defined by

Y = AE = C + I = C 0 + cY + I Introduction to Economics V. The 45 Degree Model

The Private Economy

The equilibrium in the private economy is defined by

Y = AE = C + I = C 0 + cY + I

We can reformulate this to get the equilibrium income:

Y =

C 0 + I

1 − c

Introduction to Economics V. The 45 Degree Model