A Dynamic Model of Aggregate Demand and Aggregate Supply

Transcription

1 A Dynamic Model of Aggregate Demand and Aggregate Supply

2 1 Introduction Theoritical Backround 2 3 4

3 I Introduction Theoritical Backround The model emphasizes the dynamic nature of economic fluctuations. The economy is continually exposured by various shocks. These shocks have on immediate impact on economy s short-run equilibrium. The model focuses attention on how output and inflation respond over time to exogenous changes in the economic environment. The model explicitly incorporates the response of monetary policy to economic conditions.

4 Output : The Demand for Goods and Services I Y t = Ȳ t α(r t ρ) + ɛ t Y t : the total ouput of goods and services Ȳ t : the economy s natural level of output r t : the real interest rate ɛ t : random demand shock α, ρ : parameters greater than zero the key feature : the negative relationship between the real interest rate (r t ) and the demand for goods and services (Y t ) the parameter α shows how sensitive demand is to changes in the real interest rate. Ȳ t is economy s natural level of output.

5 Output : The Demand for Goods and Services II ɛ t is random variable whose values are determined by chance. It is zero on average but fluctuates over time. Animal spirits are captured by ɛ t It also captures changes in fiscal policy. ρ is the real interest rate at which, in the absence of any shock ( ɛ t = 0 ) the demand for goods and services equals the natural level of output. We can call ρ the natural level of interest. ρ plays a key role in the setting of monetary policy.

6 The Real Interest Rate : The Fisher Equation r t = i t E t π t+1 E t π t+1 is the expectation of what the inflation rate will be in period t+1 based on information avaliable in period t.

7 Inflation : The Phillips Curve I π t = E t 1 π t + φ(y t Ȳt) + υ t E t 1 π t : previously expected inflation Y t Ȳt : the deviation of output from its natural level υ t : exogenous supply shock Inflation depends on expected inflation because some firms set prices in advance.

8 Inflation : The Phillips Curve II φ(φ > 0) shows how much inflation responds when output fluctuates around its natural level. φ reflects both how much marginal cost responds to the state of economic activity and how quickly firms adjust prices in response to changes in cost. υ t is supply shock. It is a random variable whose average value is zero.

9 Expected Inflation : Adaptive Expectations E t π t+1 = π t People form their expectations of inflation based on the inflation the have recently observed.

10 The Nominal Interest Rate : The Monetary-Policy Rule i t = π t + ρ + θ π (π t π T t ) + θ Y (Y t Ȳt) r t = i t π t = ρ + θ π (π t π T t ) + θ Y (Y t Ȳt) for the equilibrium : π t πt T we get r t = ρ and Y t Ȳ t

11 The Taylor Rule Introduction i t = π t (π t 2.0) + 0.5(Y t Ȳ t )

12 Equations Introduction Y t = Ȳt α(r t ρ) + ɛ t r t = i t E t π t+1 π t = E t 1 π t + φ(y t Ȳ t ) + υ t E t π t+1 = π t i t = π t + ρ + θ π (π t π T t ) + θ Y (Y t Ȳ t )

13 The Starting Point : The Long-Run Equilibrium The long-run equilibrium represents the normal state around which the economy fluctuates. It occurs when there are no shocks (ɛ t = υ t = 0) and inflation stabilized (π t = π t 1) Y t = Ȳt ; r t = ρ ; π t = π t t T ; E t π t+1 = πt T ; i t = ρ + πt T The long-run equilibrium of this model reflects two related principles : the classical dichotomy and monetary neutrality.

14 The Dynamic Aggregate Supply Curve π t = E t 1 π t + φ(y t Ȳ t ) + υ t

15 The Dynamic Aggregate Demand Curve I We begin with the demand for goods and services Y t = Ȳ t α(r t ρ) + ɛ t to eliminate the endogenous variable r t, we use Fisher equation Y t = Ȳt α(i t E t π t+1 ρ) + ɛ t to eliminate another endogenous variable i t, we put Taylor rule and adaptive expectations Y t = Ȳt α[π t + ρ + θ π (π t π T t ) + θ Y (Y t Ȳt) π t ρ] + ɛ t

16 The Dynamic Aggregate Demand Curve II equation simplifies to Y t = Ȳt α[θ π (π t πt T ) + θ Y (Y t Ȳt)] + ɛ t solving for Y t αθ π Y t = Ȳ t [ (1 + αθ Y ) ](π t πt T 1 ) [ (1 + αθ Y ) ]ɛ t

17 The Dynamic Aggregate Demand Curve III

18 The Short-Run Equilibrium I Dynamic Aggregate Demand αθ π Y t = Ȳ t [ (1 + αθ Y ) ](π t πt T 1 ) [ (1 + αθ Y ) ]ɛ t Dynamic Aggregate Supply π t = π t 1 + φ(y t Ȳ t ) + υ t

19 The Short-Run Equilibrium II

20 Long-Run Growth Introduction

21 A Shock to Aggregate Supply

22 A Shock to Aggregate Supply

23 A Shock to Aggregate Demand

24 A Shock to Aggregate Demand

25 A Shift in

26 A Shift in

27 The Tradeoff Between Output and Inflation αθ π Y t = Ȳt [ (1 + αθ Y ) ](π t πt T 1 ) [ (1 + αθ Y ) ]ɛ t

28 References Introduction Mankiw, Macroeconomics, 9th Edition - Chapter 15