Week 02, Lecture 03 Detailed Listing and Derivation of Accounting Equations

Transcription

1 Wee 02, Lecture 03 Detaled Lstng and Dervaton of Accountng Equatons In the GTAP Data Base all the equlbrum condtons hold. The pre-smulaton data base also represents the ntal or pre-smulaton equlbrum. The post-smulaton equlbrum wll also satsfy all the equlbrum condtons f the smulaton preserves the GE closure. Tradable maret clearng condton Endowment maret clearng condtons Zero pure proft condton Income - Expendture balance Savngs - Investment balance Summary of accountng relatonshps The possblty of relaxng any one of the equlbrum condtons results n the ntroducton of slac varables nto the equlbrum condtons or accountng relatonshps. Slac varables thus offer the flexblty of generatng certan types of partal equlbrum closures from the standard one regon GTAP model. The fve slac varables assocated wth the equlbrum condtons namely, TRADSLACK ENDWSLACK PROFITSLACK INCOMESLACK WALRASLACK are dscussed n the followng. Tradable Maret Clearng Condton - TRADSLACK The maret clearng condton for tradable commodty s gven by, _ COMM, PROD _ COMM QO = QF + QP + QG (1) The left hand sde of (1) represents supply of tradable commodty and the rght hand sde represents the varous sources of demand. (1) represents the maret clearng condton (supply = demand) when maret prce s allowed to adust to resolve any mbalance between supply and demand. The maret clearng equaton thus determnes the value for the endogenous varable, maret prce, PM. By ncludng a slac varable, TRADSLACK, (1) may be rewrtten as, _ COMM, PROD _ COMM QO = QF + QP + QG + TRADSLACK Where, TRADSLACK = 0, wll always hold n the data base. TRADSLACK thus represents the excess supply whch s the dfference, f any, between supply and demand. Totally dfferentatng (1.1) yelds, (1.1)

2 _ COMM, PROD _ COMM dqo = dqf + dqp + dqg + dtradslack Expressng (1.2) n lnearzed form 1, _ COMM, PROD _ COMM QO qo = QF qf + QP qp + QG qg + QO tradslac (1.1) s the levels representaton of the equlbrum condton, whle (1.3) s the lnearzed representaton of t 2. (1.2) (1.3) The equlbrum condton n the levels and lnearzed forms, so far represented n physcal quantty terms, can also be represented n value terms. The maret prce, PM, s used to convert the quantty equlbrum condton. VOM = VFM + VPM + VGM (1 ) VOM qo = VFM qf + VPM qp + VGM qg + VOM tradslac (1.3 ) In a smulaton whch preserves equlbrum n the maret for commodty by leavng maret prce, PM(), endogenous, tradslac() wll be zero snce TRADSLACK() = 0 n both the pre- and postsmulaton equlbra. A more ntutve representaton of (1.3') nvolves normalzng wth the ntal value of supply, VOM() and s wrtten as, qo = SHRFM qf + SHRPM qp + SHRGM qg + tradslac (1.4) The percentage change n supply of tradable s thus equal to the weghted sum of the percentage changes n the varous sources of demand and the percentage change n the excess supply, where the weghts are the shares of the ntal demands n the ntal supply. (1.4) s the equaton called MKTCLTRD n GTAPO.TAB. Moble Endowment Maret Clearng Condton - ENDWSLACK The development of the maret clearng condton for moble endowment s analogous to the maret equlbrum for tradable. ENDWM _ COMM, PROD _ COMM QO = QFE (2) 1 The lnearzed form of a varable, X, s the percentage change n X, and s denoted by, dx x = 100 X 2 The percentage change n excess supply s defned as a percentage of supply n the ntal equlbrum, QO(), to avod dvson by zero, dtradslack tradslac = QO 100

3 QO = QFE + ENDWSLACK (2.1) dqo = dqfe + dendwslack (2.2) QO qo = QFE qfe + QO enddwslac (2.3) VOM = VFM (2 ) VOM qo = VFM qfe + VOM endwslac (2.3 ) qo = SHRFM qfe + endwslac (2.4) The percentage change n supply of endowment s thus equal to the weghted sum of the percentage changes n the varous sources of demand and the percentage change n the excess supply, where the weghts are the shares of the ntal demands n the ntal supply. Note that n the standard model the endowments are n fxed supply resultng n the left hand sde beng zero. (2.4) s the equaton called MKTCLENDWM n GTAPO.TAB. Sluggsh Endowment Maret Clearng Condton - ENDWSLACK The maret equlbrum for sluggsh endowment s slghtly dfferent from the moble endowment case. Maret prce for sluggsh endowment s not determned by maret clearng condton. Instead, equlbrum s gven by, ENDWS _ COMM, PROD _ COMM QOES = QFE (2.5) Demand for endowment by frm n sector, QFE(,), s determned by the CES assumpton made on the frm's technology. Quantty suppled, QOES(,), merely equals quantty demanded, QFE(,). Supply prce, PMES(,), s determned by the CET assumpton made on the mperfect moblty of the endowment. PMES(,) thus adusts to resolve the mbalance, f any, between QOES(,) and QFE(,). Hence, the excess supply varable s ntroduced n the equaton for supply prce to denote the condton where maret equlbrum does not hold. Zero Pure Proft Condton - PROFITSLACK Zero profts equaton 3 for a frm n sector s gven by, ENDW _ COMM, _ COMM, PROD _ COMM VOA VFA = VFA + The left hand sde of (3) represents the value of output and the rght hand sde represents the sum of value of nputs, both endowment and tradable, used n producton. A frm facng exogenous nput and output prces uses a gven technology to choose output level. The zero (3 ) 3 Note that zero profts equaton s always wrtten n value terms and s evaluated at prces faced by the frm (agent's prces).

4 profts equaton thus determnes the level of output (quantty suppled). (3) may be rewrtten to nclude a slac varable as, ENDW _ COMM, TRA + D _ COMM, PROD _ COMM VOA = VFA + VFA PROFITSLACK + In the data base, frms mae zero profts, therefore, PROFITSLACK() always equals zero. Any smulaton that preserves the general equlbrum nature of the model wll have PROFITSLACK = 0 n the post-smulaton equlbrum. (3.1) may be rewrtten n prce-quantty 4 notaton as, PS QO = PFEQFE + PFQF + PROFITSLACK (3.2) Totally dfferentatng (3.2), we can elmnate the terms wth quantty changes usng the result that the prce-weghted output quantty change equals the sum of the prce-weghted nput quantty changes due to constant returns to scale and cost mnmzaton. Ths yelds the followng, where proftslac s evaluated relatve to VOA 5 : VOA ps = VFA pfe + VFA pf + VOA proftslac (3.3) If a smulaton results n proftslac() 0, then output level cannot be determned by ths equaton. (3.3) s equaton ZEROPROFITS n GTAPO.TAB. Income - Expendture Balance - INCOMESLACK The dervaton of INCOMESLACK n the REGINCOME equaton s analogous to PROFITSLACK. PRIVEXP s defned as total consumpton expendture by the prvate household. GOVEXP s the total consumpton expendture by the government. TOTAL EXPENDITURES s the sum of prvate and publc expendtures, and savngs. INCOME s the sum of factor ncome and net taxes, less deprecaton. _ COMM PRIVEXP = VPA GOVEXP = VGA EXPENDITURE = PRIVEXP + GOVEXP + SAVE = VPA + VGA + SAVE (4a ) ENDW _ COMM INCOME = VOA + NETAXES VDEP INCOME = PRIVEXP + GOVEXP + SAVE (4 ) Equaton (4 ) s the ncome-expendture (household budget) balance: total expendture equals net ncome. (3.1) (4b ) 4 Note that PROFITSLACK() s a value concept whch merely represents the excess of sales recepts over nput costs and has no prce-quantty representaton. 5 Note that the percentage change n PROFITSLACK() s defned as a percentage of ntal sales recepts to avod dvson by zero, dprofitslack proftslac = VOA 100

5 Savngs - Investment Balance, WALRASLACK Demand for savngs s SAVE and walras_dem s ts lnearzed form. Supply of net nvestment s NETINV and walras_sup s ts lnearzed form. Savng - nvestment balance s gven by, NETINV = SAVE (5) or, VOM (" cgds") VDEP = SAVE (5 ) Where, SAVE = PSAVE QSAVE NETINV = GROSSINV VDEP GROSSINV = VOA, CGDS _ COMM VOA(" cgds") = PS(" cgds") QO(" cgds") = PCGDS QCGDS The left hand sde of (5) s the supply of net nvestment goods and the rght hand sde s the demand for savngs. To reflect the excess of nvestment supply over savngs demand, a slac varable s ntroduced so that, NETINV = SAVE + WALRASLACK (5.1) Totally dfferentatng (5.1) and expressng t n percentage change form 6, NETINV. walras _ sup = SAVE. walras _ dem + NETINV. walraslac (5.2) Ths can be rewrtten as, walras _ sup = walras _ dem + walraslac (5.3) Where, walras _ dem = qsave GROSSINV walras _ sup = NETINV qcgds VDEP NETINV b 6 Agan the slac varable n the savngs - nvestment maret s defned as a percentage of the ntal supply of net nvestment, dwalraslack walraslac = 100 NETINV

6 Summary of Accountng Equatons (1') Maret Clearng for Tradables _ COMM, PROD _ COMM VOM = VFM + VPM + VGM (1 ) (2') Maret Clearng for (Moble) Endowment ENDW _ COMM, PROD _ COMM VOM = VFM (2 ) (3') Zero Proft Condton ENDW _ COMM, _ COMM, PROD _ COMM VOA VFA = VFA + (3 ) (4') Household Budget Balance INCOME = EXPENDITURE _ COMM EXPENDITURE = VPA + VGA + SAVE ENDW _ COMM INCOME = VOA + NETAXES VDEP (4 ) (5') Investment-Savngs Balance VOM cgds") VDEP = SAVE (" (5 )