SIMPLE MODEL OF CLOSED ECONOMY

Transcription

1 SIMPLE MODEL OF CLOSED ECONOMY WITH THE PRESENCE OF RICRDIN EQUIVLENCE (Sticky Pices, Flexible Wages, Competitive Labo Maket) Pepaed fo Econ 296s Poject Tevy Chawwa ditya Rachmanto DUKE UNIVERSITY SPRING 2012

2 Contents I. INTRODUCTION... 1 II. MODEL GENERL SSUMPTIONS VRILES ND PRMETERS... 2 C. SIC EQUTIONS... 3 III. SIMULTION RESULTS ND NLYSIS Policy: Incease in govenment expenditue Policy: Incease in income tax... 8 C. Policy: Incease in money supply... 9 D. Policy: Incease in pice... 9 E. Policy: Incease in Capital o Technology IV. CONCLUSION PPENDIX 1 - Deivation of Diffeential Foms PPENDIX 2 Policy Matices

3 I. INTRODUCTION This model aims to analyze the inteaction between seveal economic vaiables in the closed economy whee the pice is fixed, wage is flexible, and labo maket is competitive. In goods maket, it is assumed that fims have maket powe so they can maximize pofit by fixing the pice highe than the maginal cost. Theefoe, at the flexible pice equilibium, fims ae bette off if they can sell moe at the pevailing pice (Figue 1). s a esult, a ise in demand with igid pices leads to highe output. Fim s demand of labo is detemined by fim s desie to meet the demand of goods. The quantity of labo demanded depends on the amount of goods that fims ae able to sell (effective labo demand), as long as the eal wage is not too high that it is unpofitable to meet the full demand (Figue 2). 1 Real wage is detemined by the intesection between effective labo demand and labo supply cuve. Capital is assumed to be detemined fom the past investment and it is fixed (exogenous). w P D D 1 S Effective L d L S E 1 E Figue 1 Supply Demand Cuve Y L(Y L(Y 1 Figue 2 Labo Maket Cuve L In this model, we also include the Ricadian Equivalence poposition that consumes intenalize the govenment's budget constaints. The poposition suggests that when govenment ties to stimulate demand by inceasing govenment spending though deficit, the economic agents believe that they will have to pay highe tax in the futue. Theefoe they will save a potion of thei income fo futue tax paying. Savings can be done though buying the bonds issued by the govenment, thus educing thei cuent consumption. We assume that only some popotion of consumes (type ) pay attention to the Ricadian Equivalence. Thus, thei consumption will be a function of thei afte tax income and the govenment spending. Meanwhile, the othe consumes (type ) consumption ae based only on thei afte tax income. 1 Refe to Rome, David. dvanced Macoeconomics, 4th ed. New Yok: McGaw Hill,

4 With the afoementioned assumptions, we will develop a model that will analyze the impact of govenment spending, tax, monetay policy and pice inceases on output, consumption, investment, inteest ate, wage, and ental ate. Thee will be 3 cases: (i) 100% type consumes (they pay attention to Ricadian Equivalence and have smalle maginal popensity to consume (mpc)); (ii) 50% type consumes and 50% type consumes (they do not cae about Ricadian Equivalence and have highe mpc); and (iii) 100% type consumes. In geneal, the esult of this model confoms to the theoy that the impacts of govenment spending and changes in tax on all endogenous vaiables ae smalle when moe consumes pay attention to Ricadian Equivalence and have less maginal popensity to consume. One impotant diffeence between this model and the flexible pice model is the wage ate in this model does not depend on the maginal poductivity of labo, but it depends on the effective demand of labo. Thus, an incease in the demand of labo will incease the wage ate. Moeove, since output is detemined by demand of goods, an incease in capital o technology will not have any impact on output. n incease in capital will only cause the decease in labo demand, eal wage and ental ate. Meanwhile, an incease in technology will only cause a decease in labo demand and eal wage. II. MODEL. GENERL SSUMPTIONS Fixed pices and fixed technological coefficient. Labo is demand-constained (endogenous). Labo supply is a function of eal wage. Capital is detemined in the past (exogenous). Thee ae 2 types of consume: o Type : lowe mpc and pays attention to Ricadian Equivalence; and o Type : highe mpc and does not pay attention to Ricadian Equivalence. If a consume pays attention to Ricadian Equivalence, consumption is a function of mpc, income afte tax and govenment spending. Othewise, it is a function of mpc and income afte tax.. VRILES ND PRMETERS Vaiables and paametes used in the model ae descibed in Table 1 and Table 2. We use 9 endogenous vaiables, 6 exogenous vaiables and 11 paametes. 2

5 Table 1 Desciption of Vaiables Vaiables Definition Unit Status y eal income widgets pe yea Endogenous c eal consumption widgets pe yea Endogenous i eal investment widgets pe yea Endogenous g eal gov. expenditue widgets pe yea Exogenous inteest ate popotion/yea Endogenous t eal tax collection widgets pe yea Exogenous P pice level $/widget Exogenous M money stock $ Exogenous a Technological coefficient Unit Exogenous w eal wage widget pe peson yea Endogenous v eal ental ate widgets pe machine yea Endogenous W nominal wage $ pe peson yea Endogenous V nominal ental ate $ pe machine yea Endogenous L Labo Wokes Endogenous K capital Machine Exogenous Table 2 Paametes Paametes Definition Initial Value α Elasticity of output w..t. labo 0.7 i Elasticity of investment w..t. inteest ate 1 mpc MPC fo consume type 0.5 mpc MPC fo consume type 0.8 m Elasticity of money demand w..t. inteest ate 1 k Elasticity of kapital w..t. inteest ate 1 k v Elasticity of kapital w..t. eal ate 1 Case 1: 0 θ Popotion of consume type Case 2: 0.5 Case 3 : 1 Case 1: 1 θ Popotion of consume type Case 2: 0.5 Case 3 : 0 y Initial output 100 l w Elasticity of labo supply to eal wages 1 C. SIC EQUTIONS 2 follows: We use 9 equations to define the elationship between the vaiables in the economy as 1. National ccounts ggegate demand fo a closed economy is given by d y c i g whee c is aggegate consumption, i is aggegate capital investment, and g is govenment puchases of goods and 2 Deivation of the equations can be seen in the ppendix 3

6 sevices o govenment spending. The economy is in equilibium when domestic poduction s y equals aggegate demand d y. The national accounts equation can then be witten as: y c i g. The diffeential fom of the national accounts equation is: y yˆ dc di dg. We need the initial value of y, which we assume to be Consumption Function Consumption consists of two pats: autonomous consumption and induced consumption. (i) (ii) utonomous consumption is the consumption that would take place if cuent yea s income was zeo. We assume that autonomous consumption is zeo. Induced consumption is the faction of disposable income y D (defined as income minus net taxes o y t) that is used fo consumption. The faction is defined fom the paamete mpc. The basic Keynesian consumption function can then be witten as: c mpc( y t) We assume that thee ae two types of consumes, i.e., consumes who pay attention to Ricadian Equivalence and have lowe mpc (Type ); and consumes who do not pay attention to Ricadian Equivalence and have highe mpc (Type ). Thus, we will split the consumption function into two pats, and we can split the total eal income into two, i.e., income fo Type consume ( y ) and Type consume ( y ). denotes the popotion of Type consume in the population, and consume. the popotion fo Type Futhemoe, since we assume the pesence of Ricadian Equivalence, and that only Type consume is awae of this effect, then we can fomulate the disposable income as follows: (i) (ii) Type consume: accoding to the concept of Ricadian Equivalence, when the govenment inceases its spending, consumes will not incease thei consumption, since they ae awae that the govenment is financing its spending fom debt, and in the futue the govenment will have to pay the debt by inceasing tax. Hence the consume will save a potion of its cuent income to pay the futue tax. One of the means of consume savings in the concept of Ricadian Equivalence is by buying govenment bonds, which means that the consumes ae financing the govenment spending. Fo this eason, the disposable income is the faction of total income minus net taxes minus govenment spending ( y t g ). Type consume: since we assume that Type consume ae not awae of Ricadian Equivalence, we can fomulate the disposable income as the faction of total income minus tax ( y t ). Since each type of consumes has thei own mpc, we will denote consume, and mpc fo Type consume, whee we assume mpc < mpc fo Type mpc. 4

7 The consumption function can then be witten as: c mpc ( y t g) mpc ( y t). The diffeential fom of the consumption function is: ˆ ˆ dc mpc y y dt dg mpc y y dt. We need the initial values fo mpc and mpc, which we will assume to be 0.5 and 0.8, espectively. This is based on the assumption that Type consume favos investment moe than Type consume, hence they ae awae of the Ricadian Equivalence. We also need the initial values fo in the population. We will assume two cases of these shaes: and the popotion of Type and Type consume Case 1: No Type consume in the population : : 0% ; : 100%. Case 2: Equal popotion of Type and consume : : 50% ; : 50%. Case 3: No Type consume in the population : : 100% ; : 0%. 3. Investment Function The eal investment, i, depends negatively on the inteest ate,. Investment will decease as the pesent discounted etun fom any investment poject falls with an incease in the cost of boowing,. The investment function can then be witten as: i i() e i. The diffeential fom of the investment function is: di i. d. The paamete i measues the elasticity of investment w..t. inteest ate, and is assumed to be 1. This means that investment is vey dependent on inteest ate. 1 unit incease in will lead to 1 unit decease in i. 4. Money Demand The money maket is in equilibium when the supply of money, M S, is equal to the demand fo money, M D. M S is a policy decision of the cental bank. M D is assumed to eflect two pincipal motives fo holding money: (i) the tansactions motive fo holding money, meaning that M D inceases when output y inceases. (ii) The stoe of wealth motive fo holding money, meaning that money should compete with othe assets as a stoe of wealth. Holding money has an oppotunity cost, i.e., the ate of etun paid by othe assets,. Hence, M D deceases when inceases. We will use Cagan money demand function, which also depends on y and. We assume that the elasticity of money demand w..t output ( m ) is 1. y 5

8 M m The money demand function can then be witten as: f y m ( y, ) y e. P The diffeential fom of the money demand is: M ˆ P ˆ y ˆ m d The paamete m measues the elasticity of money demand w..t. inteest ate, and is assumed to be 1. This means that money demand is vey dependent on inteest ate. 5. Poduction Function Poduction is assumed to be a Cobb-Douglas function with two facto inputs, capital and labo, and a technological coefficient. The poduction function can then be witten as: 1 y ak L. The diffeential fom of the poduction function is: yˆ aˆ (1 ) Kˆ Lˆ The paamete α measues the elasticity of output w..t. labo, and is assumed to be 0.7. This means that elasticity of output w..t. capital is Labo Supply Since labo is endogenous, then the amount of effective labo foce is detemined fom the intesection between labo supply (L S ) cuve and labo demand (L D ) cuve in the equilibium. L D is detemined fom the poduction function. L S is a function of the eal wage. If eal wage inceases, then labo supply will incease. It is woth noting that the equilibium eal wage is not the maginal poduct of labo anymoe, since eal wage is now a function of L S. W L f f w w l P The labo supply function can then be witten as: w The diffeential fom of the labo supply is: L ˆ l wˆ. The paamete l w measues the elasticity of labo foce w..t. eal wage, and is assumed to be 1. w. 7. Nominal Wage Nominal wage is the dolla value of eal wage, which is defined as the poduct of eal wage and pice. The nominal wage function can then be witten as: W w P. The diffeential fom of the nominal wage is: Wˆ wˆ Pˆ. 8. Real Rental Rate Real wage is defined as the maginal poduct of capital (MPK) fom the Cobb-Douglas poduction function. 6

9 y The eal ental ate function can then be witten as: v a(1 ) K L. K The diffeential fom of the eal ental ate is: vˆ aˆ ( Kˆ Lˆ). 9. Nominal Rental Rate Nominal ental ate is the dolla value of eal ental ate, which is defined as the poduct of eal ental ate and pice. The nominal ental ate function can then be witten as: V v P. The diffeential fom of the nominal ental ate is: Vˆ vˆ Pˆ. III. SIMULTION RESULTS ND NLYSIS. Policy: Incease in govenment expenditue The effect of 1 % incease in govenment expenditue fo each case is pesented in Figue 3. In geneal, this policy will incease output, consumption, labo, eal and nominal wage ate, inteest ate, eal and nominal ental ate. Futhemoe, the incease in inteest ate will decease investment which populaly called as cowding out effect. In line with theoy, the effect of this policy on economy is smalle when moe people pay attention to Ricadian equivalence poposition y^ dc di L^ d W^ w^ v^ V^ = 0%; = 100% =50%; =50% =100%; = 0% = 0%; = 100% =50%; =50% =100%; = 0% y^ dc di L^ d W^ w^ v^ V^ Figue 3 Impact of Incease in Govenment Expenditue Note: Fo gaphs puposes, due to the high values of dc, it is calibated so that dc = dc / y = dc / 100 Explanations: Incease in govenment expenditue will incease the aggegate demand. Theefoe, at fixed pice, fims will incease thei output to meet the demand. To poduce moe output, fims need moe labo, then the demand of effective labo L^ inceases. Since sensitivity of labo supply with espect to eal wage = 1, then the eal wages (when labo demand meets labo supply) inceases. Since pice is fixed, the nominal wage W inceases. The incease in total output y^ makes the quantity of money demanded inceases. Holding M and P constant, inteest ate must inceases to compensate the excess demand of money. 7

10 The incease in inteest ate makes investment spending decease. The decease in investment causes by the incease of govenment spending explains the cowding out effect. Since eal ental ate is defined as the maginal poduct of capital and capital is constant, then incease in output makes eal ental ate inceases. Holding P constant, the nominal ental ate must incease. Incease in output can be seen as incease in income, theefoe nomally consumption should be incease. Howeve, since consumes type believe of icadian equivalence then they will decease thei consumption. ggegately when popotion of consume type incease, then the impact of govenment spending on consumption will be less and could be negative (case 3).. Policy: Incease in income tax The effect of 1% incease in income tax is illustated in Figue 4. In geneal, the effect of this policy is contay with the effect of govenment spending. Incease in income tax policy will decease output, consumption, labo, eal and nominal wage ate, inteest ate, eal and nominal ental ate. Decease in inteest ate will incease investment. The effect of this policy is highe when moe consumes that have highe maginal popensity to consume (case 1). Remembe that consumes type have highe mpc than consume type y^ dc di L^ d W^ w^ v^ V^ = 0%; = 100% =50%; =50% =100%; = 0% = 0%; = 100% =50%; =50% =100%; = 0% y^ dc di L^ d W^ w^ v^ V^ Figue 4 Impact of Incease in Tax Note: Fo gaphs puposes, due to the high values of dc, it is calibated so that dc = dc / y = dc / 100 Explanation When the govenment inceases income tax, consumes will decease thei consumption theefoe aggegate demand will deceases. Thus, the fims will decease thei poduction y^. Decline in poduction will make the fims educe thei labo, then the demand of effective labo L^ deceases and this impact to the decease in the eal wages. Since pice is fixed, the decease in eal wage will make nominal wage W deceases. The decease in total income makes the quantity of money demanded falls. Holding M and P constant, inteest ate must to compensate the excess supply of money. The decease in inteest ate makes fims investment spending inceases. 8

11 Since capital is constant and output decease, the maginal poduct of capital o eal ental ate will deceases. Holding P constant, the nominal ental ate must deceases. C. Policy: Incease in money supply The effect of 1 % in money supply is illustated in Figue 5. In geneal, this policy will incease output, consumption, investment, labo, eal and nominal wage, eal and nominal ental ate. Futhemoe, it will decease inteest ate. The impact of monetay policy on output and consumption the effect of monetay policy is highe when moe consumes have highe maginal popensity to consume (case 1) y^ dc di L^ d W^ w^ v^ V^ = 0%; = 100% =50%; =50% =100%; = 0% = 0%; = 100% =50%; =50% =100%; = 0% y^ dc di L^ d W^ w^ v^ V^ Figue 5 Impact of Incease in Money Supply Note: Fo gaphs puposes, due to the high values of dc, di and d, it is calibated so that dc=dc/100, di=di/10 and d= d/10 Explanation 1% incease in money supply will decease the inteest ate and incease aggegate demand. The incease in aggegate demand will make the fims incease thei poduction. The deceases in inteest ate make fims investment spending inceases. Incease in poduction will make the fims add moe labo, then the demand of effective labo inceases and this impact to the incease in the eal wages. Since pice is fixed, the inease in eal wage will make nominal wage W inceases. Since the capital is constant, then incease in the output will incease the maginal poduct of capital o eal ental ate. Holding P constant, the nominal ental ate must incease. Incease in output can be seen as incease in income, theefoe consumption will be incease. When consumes type (highe mpc) is moe dominant, the effect of monetay policy is highe. D. Policy: Incease in pice Suppose the fims want a highe pofit and they incease pice by 1%. The effect of this action is illustated in figue 6. In geneal, this policy will decease output, consumption, investment, labo, eal wage and eal ental ate. Futhemoe, it will incease inteest ate, nominal wage and nominal ental ate of capital. The impact of pice on output and 9

12 consumption is highe when moe consumes have highe maginal popensity to consume (case 1) y^ dc di L^ d W^ w^ v^ V^ = 0%; = 100% =50%; =50% =100%; = 0% = 0%; = 100% =50%; =50% =100%; = 0% y^ dc di L^ d W^ w^ v^ V^ Figue 6 Impact of Incease in Pice Note: Fo gaphs puposes, due to the high values of dc, di, d,w^ and V^ it is calibated so that dc=dc/100, di=di/10, d= d/10, W^=W^/10 and V^=V^/10 Explanation Incease in pice will decease aggegate demand and incease the inteest ate. The decease in aggegate demand will make the fims decease thei poduction. The inceases in inteest ate make fims investment spending deceases. Decease in output can be seen as decease of income, theefoe consumption will decease. Lowe poduction will make the fims educe labo, then the demand of effective labo deceases and this impact to the decease in the eal wages. Since pice is incease highe than the decease in eal wage, the nominal wage W will inceases. Since the capital is constant meanwhile output decease, then the maginal poduct of capital will decease and eal ental ate deceases. E. Policy: Incease in Capital o Technology Incease in capital o technology will not have impact to output, since output is demandconstained. Theefoe, changes in those vaiable wouldn t impact consumption, investment and inteest ate. Incease in capital and technology will make the demand of labo decease, because numbe of output is constant. Theefoe labo and eal wage will decease. On the othe side, incease in capital will decease the ental ate. Since pice is constant, then nominal wage and nominal ental ate will decease. The impact of 1% incease in capital and 1% incease in technology can be seen in Figue 8. 10

13 y^ dc di L^ d W^ w^ v^ V^ Impact of Techonology Impact of Kapital a^ K^ y^ dc di L^ d W^ w^ v^ V^ Figue 7 Impact of Incease in Capital and Technology IV. CONCLUSION The economic model that we develop can successfully explain the inteaction between economic vaiables in a fixed pice, flexible wage and competitive labo maket. Seveal impotant conclusions fom the simulation esults ae as follows: 1. n incease in govenment spending will incease output, consumption, labo, eal and nominal wage ate, inteest ate, eal and nominal ental ate. Futhemoe, the incease in inteest ate will decease investment (the cowding out effect). 2. The impact of govenment spending and tax on all endogenous vaiables ae smalle when moe consumes pay attention to Ricadian Equivalence and have less maginal popensity to consume. 3. n incease in income tax policy will decease output, consumption, labo, eal and nominal wage ate, inteest ate, eal and nominal ental ate. decease in inteest ate will incease investment. 4. n incease in money supply will incease output, consumption, investment, labo, eal and nominal wage, eal and nominal ental ate. It will also decease inteest ate. 5. n incease in pice will decease output, consumption, investment, labo, eal wage and eal ental ate. It will also incease inteest ate, nominal wage and nominal ental ate of capital. 6. The impact of changes in tax, money supply and pice on output is highe when consumes with high mpc ae dominant in the economy. 7. Since output is detemined by demand, an incease in capital o technology will not have any impact on output. n incease in capital will only cause a decease in labo demand, eal wage and ental ate. Meanwhile, an incease in technology will only cause a decease in labo demand and eal wage. 11

14 PPENDIX 1 - Deivation of Diffeential Foms 1. National ccounts y c i g y y y y dy dc di dg y c i g y. yˆ dc di dg 2. Consumption function c mpc ( y t g) mpc ( y t) c c c dc mpc dy dt dg y t g c c mpc dy dt y t mpc dy dt dg mpc dy dt dc mpc y yˆ dt dg mpc y yˆ dt 3. Investment function i i e i i di d i di ie d i i e di i. d 4. Money demand M my f ( y, ) y e P Let : m my M Py e m my m y 1 m m m y m y my m y equals 1, then Mˆ Pˆ yˆ m d m M M M dm dp dy d P y dm y e dp m Py e dy m Py e d M Py e dp dy my md P y 5. Poduction function 1 y ak L y y y dy da dk dl a K L 1 K L da a(1 ) K L dk 1 1 a K L dl dy da (1 ) dk dl y a K L yˆ aˆ (1 ) Kˆ Lˆ 6. Labo Supply W L f f w w P lw 1 dl lww dw lw 1 dl lww dw lw L w Lˆ l wˆ w lw 12

15 7. Nominal wage W wp W W dw dw dp w P dw dw dp W w P Wˆ wˆ Pˆ 8. Real ental ate y v a(1 ) K L K v v v dv da dk dl a K L (1 ) (1 ) 1 K L da a K L dk 1 a(1 ) K L dl dv da dk dl v a K L vˆ aˆ ( Kˆ Lˆ) 9. Nominal ental ate V v P V V dv dv dp v P dv dv dp V w P Vˆ vˆ Pˆ 13

16 PPENDIX 2 Policy Matices Popotion of consume type = 0%, =100% dg dt M^ P^ a^ K^ y^ dc di L^ d W^ w^ v^ V^ Popotion of consume type = 50%, =50% dg dt M^ P^ a^ K^ y^ dc di L^ d W^ w^ v^ V^ Popotion of consume type = 100%, =0% dg dt M^ P^ a^ K^ y^ dc di L^ d W^ w^ v^ V^