economysimple model of closed economy with ricardian equivalence

8/11/2019 EconomySimple Model of Closed Economy With Ricardian Equivalence

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SIMPLE MODEL OF CLOSED ECONOMY

WITH THE PRESENCE OF RICARDIANEQUIVALENCE

(Sticky Prices, Flexible Wages, Competitive Labor Market)

Prepared for Econ 296s Project

Tevy Chawwa

Aditya Rachmanto

DUKEUNIVERSITY

SPRING 2012


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Contents

I. INTRODUCTION ............................................................................................................................... 1II. MODEL ............................................................................................................................................ 2

A. GENERAL ASSUMPTIONS .............................................................................................................. 2

B. VARIABLES AND PARAMETERS ..................................................................................................... 2

C. BASIC EQUATIONS ....................................................................................................................... 3

III. SIMULATION RESULTS AND ANALYSIS .......................................................................................... 7

A. Policy: Increase in government expenditure ................................................................................. 7

B. Policy: Increase in income tax ...................................................................................................... 8

C. Policy: Increase in money supply .................................................................................................. 9

D. Policy: Increase in price ................................................................................................................ 9

E. Policy: Increase in Capital or Technology .................................................................................... 10

IV. CONCLUSION ............................................................................................................................. 11

APPENDIX 1 - Derivation of Differential Forms ....................................................................................... 12

APPENDIX 2Policy Matrices ................................................................................................................ 14


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I.

INTRODUCTION

This model aims to analyze the interaction between several economic variables in the

closed economy where the price is fixed, wage is flexible, and labor market is competitive. In

goods market, it is assumed that firms have market power so they can maximize profit by fixingthe price higher than the marginal cost. Therefore, at the flexible price equilibrium, firms are

better off if they can sell more at the prevailing price (Figure 1). As a result, a rise in demand

with rigid prices leads to higher output.

Firms demand of labor is determined by firms desire to meet the demand of goods.

The quantity of labor demanded depends on the amount of goods that firms are able to sell

(effective labor demand), as long as the real wage is not too high that it is unprofitable to meet

the full demand (Figure 2).1Real wage is determined by the intersection between effective labor

demand and labor supply curve. Capital is assumed to be determined from the past investment

and it is fixed (exogenous).

Figure 1 Supply Demand Curve Figure 2 Labor Market Curve

In this model, we also include the Ricardian Equivalence proposition that consumers

internalize the government's budget constraints. The proposition suggests that when

government tries to stimulate demand by increasing government spending through deficit, the

economic agents believe that they will have to pay higher tax in the future. Therefore they will

save a portion of their income for future tax paying. Savings can be done through buying the

bonds issued by the government, thus reducing their current consumption. We assume that

only some proportion of consumers (type A) pay attention to the Ricardian Equivalence. Thus,

their consumption will be a function of their after tax income and the government spending.

Meanwhile, the other consumers (type B) consumption are based only on their after tax

income.

1 Refer to Romer,David.Advanced Macroeconomics, 4th ed. New York: McGraw Hill, 2012.

P

Y

AD1

ADAS

LS

Effective Ld

L

w

L(Y L(Y1

E

E1


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With the aforementioned assumptions, we will develop a model that will analyze the

impact of government spending, tax, monetary policy and price increases on output,

consumption, investment, interest rate, wage, and rental rate. There will be 3 cases: (i) 100%

type A consumers (they pay attention to Ricardian Equivalence and have smaller marginal

propensity to consume (mpc)); (ii) 50% type A consumers and 50% type B consumers (they do

not care about Ricardian Equivalenceand have higher mpc); and (iii) 100% type B consumers.

In general, the result of this model conforms to the theory that the impacts of

government spending and changes in tax on all endogenous variables are smaller when more

consumers pay attention to Ricardian Equivalence and have less marginal propensity to

consume. One important difference between this model and the flexible price model is the

wage rate in this model does not depend on the marginal productivity of labor, but it depends

on the effective demand of labor. Thus, an increase in the demand of labor will increase the

wage rate. Moreover, since output is determined by demand of goods, an increase in capital or

technology will not have any impact on output. An increase in capital will only cause the

decrease in labor demand, real wage and rental rate. Meanwhile, an increase in technology willonly cause a decrease in labor demand and real wage.

II. MODEL

A. GENERAL ASSUMPTIONS

Fixed prices and fixed technological coefficient.

Labor is demand-constrained (endogenous). Labor supply is a function of real wage.

Capital is determined in the past (exogenous).

There are 2 types of consumer:

o Type A: lower mpcand pays attention to Ricardian Equivalence; and

o Type B: higher mpcand does not pay attention to Ricardian Equivalence.

If a consumer pays attention to Ricardian Equivalence, consumption is a function of mpc,

income after tax and government spending. Otherwise, it is a function of mpcand income

after tax.

B. VARIABLES AND PARAMETERS

Variables and parameters used in the model are described in Table 1 and Table 2. We use 9

endogenous variables, 6 exogenous variables and 11 parameters.


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Table 1 Description of Variables

Table 2 Parameters

Parameters Definition Initial Value

Elasticity of output w.r.t. labor 0.7

ir Elasticity of investment w.r.t. interest rate 1

mpcA MPC for consumer type A 0.5

mpcB MPC for consumer type B 0.8

mr Elasticity of money demand w.r.t. interest rate 1

kr Elasticity of kapital w.r.t. interest rate 1

kv Elasticity of kapital w.r.t. real rate 1

A Proportion of consumer type ACase 1: 0Case 2: 0.5

Case 3 : 1

B Proportion of consumer type B

Case 1: 1

Case 2: 0.5

Case 3 : 0

y Initial output 100

lw Elasticity of labor supply to real wages 1

C. BASIC EQUATIONS2

We use 9 equations to define the relationship between the variables in the economy as

follows:

1. National Accounts

Aggregate demand for a closed economy is given bydy c i g where c is aggregate

consumption, iis aggregate capital investment,andgis government purchases of goods and

2Derivation of the equations can be seen in the Appendix

Variables Definition Unit Status

y real income widgets per year Endogenous

c real consumption widgets per year Endogenous

i real investment widgets per year Endogenous

g real gov. expenditure widgets per year Exogenousr interest rate proportion/year Endogenous

t real tax collection widgets per year Exogenous

P price level $/widget Exogenous

M money stock $ Exogenous

a Technological coefficient Unit Exogenous

w real wage widget per person year Endogenous

v real rental rate widgets per machine year Endogenous

W nominal wage $ per person year Endogenous

V nominal rental rate $ per machine year Endogenous

L Labor Workers Endogenous

K capital Machine Exogenous


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services or government spending.The economy is in equilibrium when domestic production

sy equals aggregate demand dy .

The national accounts equation can then be written as: y c i g .

The differential form of the national accounts equation is: y y dc di dg .

We need the initial value of y, which we assume to be 100.

2. Consumption Function

Consumption consists of two parts: autonomous consumption and induced consumption.

(i) Autonomous consumption is the consumption that would take place if current

years income was zero. We assume that autonomous consumption is zero.

(ii) Induced consumption is the fraction of disposable income yD (defined as income

minus net taxes or yt) that is used for consumption. The fraction is defined from

the parameter mpc.

The basic Keynesian consumption function can then be written as: ( )c mpc y t

We assume that there are two types of consumers, i.e., consumers who pay attention to

Ricardian Equivalence and have lower mpc (Type A); and consumers who do not pay

attention to Ricardian Equivalence and have higher mpc (Type B). Thus, we will split the

consumption function into two parts, and we can split the total real income into two, i.e.,

income for Type A consumer (A y ) and Type B consumer ( B y ). A denotes the

proportion of Type A consumer in the population, and B the proportion for Type B

consumer.

Furthermore, since we assume the presence of Ricardian Equivalence, and that only Type A

consumer is aware of this effect, then we can formulate the disposable income as follows:(i)

Type A consumer: according to the concept of Ricardian Equivalence, when the

government increases its spending, consumers will not increase their consumption,

since they are aware that the government is financing its spending from debt, and in

the future the government will have to pay the debt by increasing tax. Hence the

consumer will save a portion of its current income to pay the future tax. One of the

means of consumer savings in the concept of Ricardian Equivalence is by buying

government bonds, which means that the consumers are financing the government

spending. For this reason, the disposable income is the fraction of total income

minus net taxes minus government spending ( )A y t g .

(ii) Type B consumer: since we assume that Type B consumer are not aware of

Ricardian Equivalence, we can formulate the disposable income as the fraction of

total income minus tax ( )B y t .

Since each type of consumers has their own mpc, we will denote Ampc for Type A

consumer, and Bmpc for Type B consumer, where we assume Ampc < Bmpc .


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The consumption function can then be written as:

mpc ( ) mpc ( )A A B Bc y t g y t .

The differential form of the consumption function is:

A A B Bdc mpc y y dt dg mpc y y dt .

We need the initial values forAmpc and Bmpc , which we will assume to be 0.5 and 0.8,

respectively. This is based on the assumption that Type A consumer favors investment more

than Type B consumer, hence they are aware of the Ricardian Equivalence.

We also need the initial values forA and B the proportion of Type A and Type B consumer

in the population. We will assume two cases of these shares:

Case 1: No Type A consumer in the population : A : 0% ; B : 100%.

Case 2: Equal proportion of Type A and B consumer : A : 50% ; B : 50%.

Case 3: No Type B consumer in the population : A : 100% ; B : 0%.

3.

Investment Function

The real investment, i,depends negatively on the interest rate, r. Investmentwilldecrease

as the present discounted return from any investment project falls with an increase in the

cost of borrowing, r.

The investment function can then be written as: ( ) ri ri i r e .

The differential form of the investment function is: .rdi i dr .

The parameter ir measures the elasticity of investment w.r.t. interest rate, and is assumed

to be 1. This means that investment is very dependent on interest rate. A 1 unit increase in r

will lead to 1 unit decrease in i.

4.

Money Demand

The money market is in equilibrium when the supply of money, MS, is equal to the demand

for money, MD. MS is a policy decision of the central bank. MD is assumed to reflect two

principal motives for holding money:

(i) the transactions motivefor holding money, meaning that MDincreases when output

y increases.

(ii)

The store of wealth motive for holding money, meaning that money shouldcompete with other assets as a store of wealth. Holding money has an opportunity

cost, i.e., the rate of return paid by other assets, r. Hence, MD decreases when r

increases.

We will use Cagan money demand function, which also depends on y and r. We assume that

the elasticity of money demand w.r.t output ( ym ) is 1.


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The money demand function can then be written as: ( , ) y rm m rM f y r y e

P

.

The differential form of the money demand is:

rM P y m dr

The parameter mr measures the elasticity of money demand w.r.t. interest rate, and isassumed to be 1. This means that money demand is very dependent on interest rate.

5.

Production Function

Production is assumed to be a Cobb-Douglas function with two factor inputs, capital and

labor, and a technological coefficient.

The production function can then be written as:1

y aK L .

The differential form of the production function is:

(1 )y a K L

The parameter measures the elasticity of output w.r.t. labor, and is assumed to be 0.7.

This means that elasticity of output w.r.t. capital is 0.3.

6. Labor Supply

Since labor is endogenous, then the amount of effective labor force is determined from the

intersection between labor supply (LS) curve and labor demand (LD) curve in the equilibrium.

LDis determined from the production function. LSis a function of the real wage. If real wage

increases, then labor supply will increase.

It is worth noting that the equilibrium real wage is not the marginal product of labor

anymore, since real wage is now a function of LS.

The labor supply function can then be written as: wlWL f f w w

P

.

The differential form of the labor supply is: wL l w .

The parameter lw measures the elasticity of labor force w.r.t. real wage, and is assumed to

be 1.

7. Nominal Wage

Nominal wage is the dollar value of real wage, which is defined as the product of real wage

and price.

The nominal wage function can then be written as: W w P . The differential form of the nominal wage is:

W w P .

8. Real Rental Rate

Real wage is defined as the marginal product of capital (MPK) from the Cobb-Douglas

production function.


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The real rental rate function can then be written as: (1 )y

v a K LK

.

The differential form of the real rental rate is:

( )v a K L .

9.

Nominal Rental RateNominal rental rate is the dollar value of real rental rate, which is defined as the product of

real rental rate and price.

The nominal rental rate function can then be written as: V v P .

The differential form of the nominal rental rate is:

V v P .

III.

SIMULATION RESULTS AND ANALYSIS

A.

Policy: Increase in government expenditure

The effect of 1 % increase in government expenditure for each case is presented in

Figure 3. In general, this policy will increase output, consumption, labor, real and nominal wage

rate, interest rate, real and nominal rental rate. Furthermore, the increase in interest rate will

decrease investment which popularly called as crowding out effect. In line with theory, the

effect of this policy on economy is smaller when more people pay attention to Ricardian

equivalence proposition.

Figure 3 Impact of Increase in Government Expenditure

Note: For graphs purposes, due to the high values of dc, it is calibrated so that dc = dc / y = dc / 100

Explanations:

Increase in government expenditure will increase the aggregate demand. Therefore, at fixed

price, firms will increase their output to meet the demand. To produce more output, firms need

more labor, then the demand of effective labor L^ increases. Since sensitivity of labor supply

with respect to real wage = 1, then the real wages (when labor demand meets labor supply)

increases. Since price is fixed, the nominal wage W increases.

The increase in total output y^ makes the quantity of money demanded increases. Holding

M and P constant, interest rate must increases to compensate the excess demand of money.

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

0.080

y^ dc di L^ dr W^ w^ v^ V^

A= 0%; B= 100% A=50% ; B=5 0% A=100 %; B= 0%

A= 0%; B= 100% A=50%; B=50% A=100%; B= 0%

y^ 0.0476 0.0208 0.0098

dc 3.810 1.104 -0.010

di -0.048 -0.021 -0.010L^ 0.068 0.030 0.014

dr 0.048 0.021 0.010

W^ 0.068 0.030 0.014

w^ 0.068 0.030 0.014

v^ 0.048 0.021 0.010

V^ 0.048 0.021 0.010


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The increase in interest rate makes investment spending decrease. The decrease in investment

causes by the increase of government spending explains the crowding out effect.

Since real rental rate is defined as the marginal product of capital and capital is

constant, then increase in output makes real rental rate increases. Holding P constant, the

nominal rental rate must increase.

Increase in output can be seen as increase in income, therefore normally consumption

should be increase. However, since consumers type A believe of ricardian equivalence then they

will decrease their consumption. Aggregately when proportion of consumer type A increase,

then the impact of government spending on consumption will be less and could be negative

(case 3).

B. Policy: Increase in income tax

The effect of 1% increase in income tax is illustrated in Figure 4. In general, the effect of this

policy is contrary with the effect of government spending. Increase in income tax policy willdecrease output, consumption, labor, real and nominal wage rate, interest rate, real and

nominal rental rate. Decrease in interest rate will increase investment. The effect of this policy is

higher when more consumers that have higher marginal propensity to consume (case 1).

Remember that consumers type A have higher mpc than consumer type B.

Figure 4 Impact of Increase in Tax

Note: For graphs purposes, due to the high values of dc, it is calibrated so that dc = dc / y = dc / 100

Explanation

When the government increases income tax, consumers will decrease their consumption

therefore aggregate demand will decreases. Thus, the firms will decrease their production y^.Decline in production will make the firms reduce their labor, then the demand of effective labor

L^ decreases and this impact to the decrease in the real wages. Since price is fixed, the decrease

in real wage will make nominal wage W decreases.

The decrease in total income makes the quantity of money demanded falls. Holding M and P

constant, interest rate must to compensate the excess supply of money. The decrease in

interest rate makes firms investment spending increases.

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060


A= 0%; B= 100% A=50%; B=5 0% A=100 %; B= 0%

A= 0%; B= 100% A=50%; B=50% A=100%; B= 0%

y -0.038 -0.018 -0.010

dc -3.848 -1.824 -0.990

di 0.038 0.018 0.010

L^ -0.054 -0.026 -0.014dr -0.038 -0.018 -0.010

W^ -0.054 -0.026 -0.014

w^ -0.054 -0.026 -0.014

v^ -0.038 -0.018 -0.010

V^ -0.038 -0.018 -0.010


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Since capital is constant and output decrease, the marginal product of capital or real rental

rate will decreases. Holding P constant, the nominal rental rate must decreases.

C. Policy: Increase in money supply

The effect of 1 % in money supply is illustrated in Figure 5. In general, this policy will

increase output, consumption, investment, labor, real and nominal wage, real and nominal

rental rate. Furthermore, it will decrease interest rate. The impact of monetary policy on output

and consumption the effect of monetary policy is higher when more consumers have higher

marginal propensity to consume (case 1).

Figure 5 Impact of Increase in Money Supply

Note: For graphs purposes, due to the high values of dc, di and dr, it is calibrated so that dc=dc/100, di=di/10

and dr= dr/10

Explanation

1% increase in money supply will decrease the interest rate and increase aggregate

demand. The increase in aggregate demand will make the firms increase their production. The

decreases in interest rate make firms investment spending increases.

Increase in production will make the firms add more labor, then the demand of effective

labor increases and this impact to the increase in the real wages. Since price is fixed, the inrease

in real wage will make nominal wage W increases.

Since the capital is constant, then increase in the output will increase the marginal

product of capital or real rental rate. Holding P constant, the nominal rental rate must increase.

Increase in output can be seen as increase in income, therefore consumption will be

increase. When consumers type A (higher mpc) is more dominant, the effect of monetary policy

is higher.

D. Policy: Increase in price

Suppose the firms want a higher profit and they increase price by 1%. The effect of this

action is illustrated in figure 6. In general, this policy will decrease output, consumption,

investment, labor, real wage and real rental rate. Furthermore, it will increase interest rate,

nominal wage and nominal rental rate of capital. The impact of price on output and

-0.150

-0.100

-0.050

0.000

0.050

0.100

0.150


A= 0%; B= 100% A=50%; B=5 0% A=100 %; B= 0%

A= 0%; B= 100% A=50%; B=50% A=100%; B= 0%

y 0.048 0.028 0.020

dc 3.810 1.806 0.980

di 0.952 0.972 0.980

L^ 0.068 0.040 0.028

dr -0.952 -0.972 -0.980W^ 0.068 0.040 0.028

w^ 0.068 0.040 0.028

v^ 0.048 0.028 0.020

V^ 0.048 0.028 0.020


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consumption is higher when more consumers have higher marginal propensity to consume (case

1)

Figure 6 Impact of Increase in Price

Note: For graphs purposes, due to the high values of dc, di, dr,W^ and V^ it is calibrated

so that dc=dc/100, di=di/10, dr= dr/10, W^=W^/10 and V^=V^/10

Explanation

Increase in price will decrease aggregate demand and increase the interest rate. The

decrease in aggregate demand will make the firms decrease their production. The increases in

interest rate make firms investment spending decreases. Decrease in output can be seen as

decrease of income, therefore consumption will decrease.

Lower production will make the firms reduce labor, then the demand of effective labor

decreases and this impact to the decrease in the real wages. Since price is increase higher than

the decrease in real wage, the nominal wage W will increases.

Since the capital is constant meanwhile output decrease, then the marginal product of

capital will decrease and real rental rate decreases.

E. Policy: Increase in Capital or Technology

Increase in capital or technology will not have impact to output, since output is demand-

constrained. Therefore, changes in those variable wouldnt impact consumption, investment

and interest rate. Increase in capital and technology will make the demand of labor decrease,

because number of output is constant. Therefore labor and real wage will decrease. On the

other side, increase in capital will decrease the rental rate. Since price is constant, then nominal

wage and nominal rental rate will decrease. The impact of 1% increase in capital and 1%

increase in technology can be seen in Figure 8.

-0.150

-0.100

-0.050

0.000

0.050

0.100

0.150


A= 0%; B= 100% A=50%; B=5 0% A=100 %; B= 0%

A= 0%; B= 100% A=50%; B=50% A=100%; B= 0%

y^ -0.048 -0.028 -0.020dc -3.810 -1.806 -0.980

di -0.952 -0.972 -0.980

L^ -0.068 -0.040 -0.028

dr 0.952 0.972 0.980

W^ 0.932 0.960 0.972

w^ -0.068 -0.040 -0.028

v^ -0.048 -0.028 -0.020

V^ 0.952 0.972 0.980


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Figure 7 Impact of Increase in Capital and Technology

IV. CONCLUSION

The economic model that we develop can successfully explain the interaction between

economic variables in a fixed price, flexible wage and competitive labor market. Several

important conclusions from the simulation results are as follows:

1. An increase in government spending will increase output, consumption, labor, real and

nominal wage rate, interest rate, real and nominal rental rate. Furthermore, the increase in

interest rate will decrease investment (the crowding out effect).

2.

The impact of government spending and tax on all endogenous variables are smaller when

more consumers pay attention to Ricardian Equivalenceand have less marginal propensity to

consume.

3. An increase in income tax policy will decrease output, consumption, labor, real and nominal

wage rate, interest rate, real and nominal rental rate. A decrease in interest rate will increase

investment.

4. An increase in money supply will increase output, consumption, investment, labor, real and

nominal wage, real and nominal rental rate. It will also decrease interest rate.

5. An increase in price will decrease output, consumption, investment, labor, real wage and real

rental rate. It will also increase interest rate, nominal wage and nominal rental rate of capital.

6. The impact of changes in tax, money supply and price on output is higher when consumers

with high mpc are dominant in the economy.

7.

Since output is determined by demand, an increase in capital or technology will not have any

impact on output. An increase in capital will only cause a decrease in labor demand, real

wage and rental rate. Meanwhile, an increase in technology will only cause a decrease in

labor demand and real wage.

-1.600

-1.400

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000


Impact of Techonology Impact of Kapital

a^ K^

y 0.000 0.000

dc 0.000 0.000

di 0.000 0.000

L^ -1.429 -0.429

dr 0.000 0.000

W^ -1.429 -0.429w^ -1.429 -0.429

v^ 0.000 -1.000

V^ 0.000 -1.000


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APPENDIX 1 - Derivation of Differential Forms

1. National Accounts

.

y c i g

y y y ydy dc di dg y c i g

y y dc di dg

2. Consumption function

mpc ( ) mpc ( )

A A B B

A A

B B

A A

B B

A A

B B

c y t g y t

c c cdc mpc dy dt dg y t g

c cmpc dy dt

y t

mpc dy dt dg

mpc dy dt

dc mpc y y dt dg

mpc y y dt

3. Investment function

.

r

r

r

i r

i r

r

i r

r

i i r e

idi dr

r

i e dr di

i e

di i dr

4. Money demand

1

( , )

Let : equals 1, then

y r

y r

y y yr r r

y r

m m r

m m r

m m mm r m r m r

y r

m m r

y r

y

r

Mf y r y e

P

M Py e

M M MdM dP dy dr

P y r

y e dP m Py e dy m Py e drdM

M Py e

dP dym m dr P y

m

M P y m dr

5.

Production function

1

1

1 1

(1 )

(1 )

(1 )

y aK L

y y ydy da dK dL

a K L

K L da a K L dK

a K L dL

dy da dK dL

y a K L

y a K L

6.

Labor Supply

1

1

w

w

w

w

l

l

w

l

w

l

w

WL f f w w

P

dL l w dw

l w dwdL

L w

L l w


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7. Nominal wage

W w P

W WdW dw dP

w P

dW dw dP

W w P

W w P

8. Real rental rate

1

1

(1 )

(1 ) (1 )

(1 )

( )

yv a K L

K

v v vdv da dK dLa K L

K L da a K L dK

a K L dL

dv da dK dL

v a K L

v a K L

9.

Nominal rental rate

V v PV V

dV dv dP v P

dV dv dP

V w P

V v P


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APPENDIX 2 Policy Matrices

Proportion of consumer type A = 0%, B=100%

dg dt M^ P^ a^ K^

y^ 0.048 -0.038 0.048 -0.048 0.000 0.000

dc 3.810 -3.848 3.810 -3.810 0.000 0.000

di -0.048 0.038 0.952 -0.952 0.000 0.000

L^ 0.068 -0.054 0.068 -0.068 -1.429 -0.429

dr 0.048 -0.038 -0.952 0.952 0.000 0.000

W^ 0.068 -0.054 0.068 0.932 -1.429 -0.429

w^ 0.068 -0.054 0.068 -0.068 -1.429 -0.429

v^ 0.048 -0.038 0.048 -0.048 0.000 -1.000

V^ 0.048 -0.038 0.048 0.952 0.000 -1.000

Proportion of consumer type A = 50%, B=50%dg dt M^ P^ a^ K^

y^ 0.021 -0.018 0.028 -0.028 0.000 0.000

dc 1.104 -1.824 1.806 -1.806 0.000 0.000

di -0.021 0.018 0.972 -0.972 0.000 0.000

L^ 0.030 -0.026 0.040 -0.040 -1.429 -0.429

dr 0.021 -0.018 -0.972 0.972 0.000 0.000

W^ 0.030 -0.026 0.040 0.960 -1.429 -0.429

w^ 0.030 -0.026 0.040 -0.040 -1.429 -0.429

v^ 0.021 -0.018 0.028 -0.028 0.000 -1.000

V^ 0.021 -0.018 0.028 0.972 0.000 -1.000

Proportion of consumer type A = 100%, B=0%

dg dt M^ P^ a^ K^

y^ 0.0098 -0.010 0.020 -0.020 0.000 0.000

dc -0.010 -0.990 0.980 -0.980 0.000 0.000

di -0.010 0.010 0.980 -0.980 0.000 0.000

L^ 0.014 -0.014 0.028 -0.028 -1.429 -0.429

dr 0.010 -0.010 -0.980 0.980 0.000 0.000

W^ 0.014 -0.014 0.028 0.972 -1.429 -0.429

w^ 0.014 -0.014 0.028 -0.028 -1.429 -0.429

v^ 0.010 -0.010 0.020 -0.020 0.000 -1.000

V^ 0.010 -0.010 0.020 0.980 0.000 -1.000

economysimple model of closed economy with ricardian equivalence

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