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A Simple Macrodynamic Model Stephen Kinsella Dept. Economics, University of Limerick [email protected] March 10, 2008

Monetary Economics Guest Lecture

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Page 1: Monetary Economics Guest Lecture

A Simple Macrodynamic Model

Stephen Kinsella

Dept. Economics, University of [email protected]

March 10, 2008

Page 2: Monetary Economics Guest Lecture

Objectives

Introduction

The ModelThe Output MarketEquilibrium in the product and money markets

Examples

Aggregate supply

The Phillips curve

Dynamics of asset accumulationExpectations

I Lecture 1: Parts 1–3

I Lecture 2: Parts 3-6

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A Macro Model with Four Sectors

I The product market,

I The money market,

I The bond market,

I The labour market.

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Setup

GDP = C + I + G , (1)

GNP = C + I + G + (X −M). (2)

GDP = C + S + T . (3)

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The Output Market

Y = C + I + G (4)

(Caution)C = C (Y ). (5)

Y = C (Y ) + I + G . (6)

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Derivation

C = C (YD). (7)

C = C (YD,A, r). (8)

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A =M + PkB + PkK

P. (9)

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The Investment Function

I − I (r − π). (10)

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Put it all together

Y = C

(T − T , r − π,

M + B + PkK

P

)+ I (r − π) + G . (11)

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The IS Curve

Figure: The IS curve.

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Shifts in IS Curve

1. an increase the expected rate of inflation, or

2. a fall in the price of output, or

3. a rise in the stock of assets, or

4. an increase in the price of capital, or

5. a reduction in the level of taxes.

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Money Markets

MD

P= L

(Y ,−π, r − π, rk ,

M + B + PkK

P

)(12)

BD

P= J

(Y ,−π, r − π, rk ,

M + B + PkK

P

)(13)

PkK

P= N

(Y ,−π, r − π, rk ,

M + B + PkK

P

)(14)

MD + BD + PkKD

P=

M + B + PkK

P= A (15)

rk =P × R

(YK

)Pk

(16)

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Put this all together

M

P= L

[Y ,−π, r − π, rk ,

M + B

P+

RK

rk

](17)

B

PJ

[Y ,−π, r − π, rk ,

M + B

P+

RK

rk

](18)

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Edging towards LM

rk = r − π. (19)

M

P= L(Y , r ,A) (20)

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LM Curve

Figure: The LM Curve.

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Slot IS into LM to get

Y = Y (P;M,B,K , π, G ,T ). (21)

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Which looks like

Figure: Equilibrium in the IS-LM model

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[Bush’s fiscal stimulus]

Exercise

Consider a standard IS-LM model in equilibrium. Graphicallyanalyse the effects of a large increase in government expenditurefinanced through taxation on output/income and the interest rate,and briefly explain your reasoning.

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[The credit crunch]

Exercise

Consider a standard IS-LM model in equilibrium. Graphicallyanalyse the effects of a large decrease in the supply of money onoutput/income and the interest rate, and briefly explain yourreasoning.

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[Numerical example]

Exercise

Imagine a closed economy with equilibrium output given byY = C + I + G. Total supply is given by Y = 5, 000.Consumption is determined by C = 250 + 0.75(Y − T ).Investment is given by I = 1000− 50r . Initially, fix G and T atG = 1, 000,T = 1, 000. Suppose the government pursues anexpansionary policy, driving G from 1000 to 1250. What happensto national savings? Is there a deficit? How much of one? Will theinterest rate decrease or increase? By how much?

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Aggregate Supply

This aggregate production function relates the labour input L andthe level of the capital stock employed to the level of output in theeconomy.

Y = F (K , L). (22)

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Labour/Leisure Tradeoff

Σ = Pf (LD)− wL. (23)

W

P= θLD , (24)

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Household utility maximisers

max(Y , Le) (25)

subject toLe = Tot − LS , (26)

Y =W

PLS . (27)

LS = LD = L. (28)

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Household utility maximisers

W

P= θ(L) = φ(L). (29)

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[Lifetime earnings and the budget constraint]

Exercise

Jill earns 200 in period 1, and 50 in period two. Jill wants toconsume the same amount throughout her life. Without access toa credit market, Jill’s consumption stream is {200, 50}. With acredit market, Jill can consume 200+50/2 = 125 per period, soher consumption stream at {c1, c2}, which is {125, 125}. In reality,Jill would buy a bond or a treasury bill to achieve consumptionpatterns like this. What would her consumption set look like?

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The Phillips Curve

The Phillips curve relates changes in inflation to changes inunemployment.

p =P

P= α(Y − (Y )) + π (30)

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Govt. Budget Constraint; Growth theory

M + B = P[G − T ] + rB. (31)

K = I . (32)

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Expectations

π = γ(p − π). (33)

π = p. (34)

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Reading

1. Lecture notes

2. Readings on Jstor

3. Examples, etc, on www.stephenkinsella.net.