$title General Equilibrium Model for Korea (KORCGE,SEQ=100) $onText This mini equilibrium model of Korea for the year 1963 is used to illustrate the basic use of CGE models. This version follows closely Chapter 11 of the reference. Lewis, J, and Robinson, S, Chapter 11. In Chenery, H B, Robinson, S, and Syrquin, S, Eds, Industrialization and Growth: A Comparative Study. Oxford University Press, London, 1986. Keywords: nonlinear programming, general equilibrium model, economic growth, industrialization, economic policy, Korean economy $offText Set i 'sectors' / agricult 'agriculture' industry 'industrial sectors' services 'infra. & services' / hh 'household type' / lab-hh 'labor households' cap-hh 'capitalist household' / lc 'labor categories' / labor1 'agricultural labor' labor2 'industrial labor' labor3 'service labor' / it(i) 'traded sectors' in(i) 'nontraded sectors'; Alias (i,j); Parameter delta(i) 'Armington function share parameter' ac(i) 'Armington function shift parameter' rhoc(i) 'Armington function exponent' rhot(i) 'cet function exponent' at(i) 'cet function shift parameter' gamma(i) 'cet function share parameter' ad(i) 'production function shift parameter' gles(i) 'government consumption shares' depr(i) 'depreciation rates' dstr(i) 'ratio of inventory investment to gross output' kio(i) 'shares of investment by sector of destination' te(i) 'export duty rates' itax(i) 'indirect tax rates' htax(hh) 'income tax rate by household type' pwm(i) 'world market price of imports (in dollars)' pwe(i) 'world market price of exports (in dollars)' tm(i) 'tariff rates on imports' pwts(i) 'cpi weights'; htax("lab-hh ") = 0.08910; htax("cap-hh ") = 0.08910; Table alphl(i,lc) 'labor share parameter in production function' labor1 labor2 labor3 agricult 0.38258 0.06740 0.00000 industry 0.00000 0.53476 0.00000 services 0.00000 0.16234 0.42326; Table io(i,j) 'input-output coefficients' agricult industry services agricult 0.12591 0.19834 0.01407 industry 0.10353 0.35524 0.18954 services 0.02358 0.11608 0.08390; Table imat(i,j) 'capital composition matrix' agricult industry services agricult 0.00000 0.00000 0.00000 industry 0.93076 0.93774 0.93080 services 0.06924 0.06226 0.06920; Table wdist(i,lc) 'wage proportionality factors' labor1 labor2 labor3 agricult 1.00000 0.52780 0.00000 industry 0.00000 1.21879 0.00000 services 0.00000 1.11541 1.00000; Table cles(i,hh) 'private consumption shares' lab-hh cap-hh agricult 0.47000 0.47000 industry 0.31999 0.31999 services 0.21001 0.21001; Table zz(*,i) 'miscellaneous parameters' agricult industry services depr 0.00000 0.00000 0.00000 itax 0.01000 0.03920 0.05000 gles 0.02000 0.07000 0.91000 kio 0.13000 0.29000 0.58000 dstr 0.00000 0.00000 0.00000 te 0.00000 0.00000 0.00000 tm 0.10000 0.22751 0.08084 ad 0.61447 1.60111 0.52019 pwts 0.33263 0.43486 0.23251 pwm 0.90909 0.81466 0.92521 pwe 1.00000 1.00000 1.00000 sigc 2.00000 0.66000 0.40000 delta 0.24820 0.05111 0.00001 ac 1.59539 1.34652 1.01839 sigt 2.00000 2.00000 2.00000 gamma 0.86628 0.84602 0.82436 at 3.85424 3.51886 3.23592; depr(i) = zz("depr",i); itax(i) = zz("itax",i); gles(i) = zz("gles",i); kio(i) = zz("kio",i); dstr(i) = zz("dstr",i); te(i) = zz("te",i); tm(i) = zz("tm",i); ad(i) = zz("ad",i); pwts(i) = zz("pwts",i); pwm(i) = zz("pwm",i); pwe(i) = zz("pwe",i); rhoc(i) = (1/zz("sigc",i)) - 1 ; delta(i) = zz("delta",i); ac(i) = zz("ac",i); rhot(i) = (1/zz("sigt",i)) + 1; gamma(i) = zz("gamma",i); at(i) = zz("at",i); $sTitle Model Definition Variable * prices block er 'real exchange rate (won per dollar)' pd(i) 'domestic prices' pm(i) 'domestic price of imports' pe(i) 'domestic price of exports' pk(i) 'rate of capital rent by sector' px(i) 'average output price by sector' p(i) 'price of composite goods' pva(i) 'value added price by sector' pr 'import premium' pindex 'general price level' * production block x(i) "composite goods supply ('68 bill won)" xd(i) "domestic output by sector ('68 bill won)" xxd(i) "domestic sales ('68 bill won)" e(i) "exports by sector ('68 bill won)" m(i) "imports ('68 bill won)" * factors block k(i) "capital stock by sector ('68 bill won)" wa(lc) "average wage rate by labor category (mill won pr person)" ls(lc) "labor supply by labor category (1000 persons)" l(i,lc) "employment by sector and labor category (1000 persons)" * demand block int(i) "intermediates uses ('68 bill won)" cd(i) "final demand for private consumption ('68 bill won)" gd(i) "final demand for government consumption ('68 bill won)" id(i) "final demand for productive investment ('68 bill won)" dst(i) "inventory investment by sector ('68 bill won)" y "private gdp (bill won)" gr "government revenue (bill won)" tariff "tariff revenue (bill won)" indtax "indirect tax revenue (bill won)" netsub "export duty revenue (bill won)" gdtot "total volume of government consumption ('68 bill won)" hhsav "total household savings (bill won)" govsav "government savings (bill won)" deprecia "total depreciation expenditure (bill won)" invest "total investment (bill won)" savings "total savings (bill won)" mps(hh) "marginal propensity to save by household type" fsav "foreign savings (bill dollars)" dk(i) "volume of investment by sector of destination ('68 bill won)" ypr "total premium income accruing to capitalists (bill won)" remit "net remittances from abroad (bill dollars)" fbor "net flow of foreign borrowing (bill dollars)" yh(hh) "total income by household type (bill won)" tothhtax "household tax revenue (bill won)" * welfare indicator for objective function omega "objective function variable ('68 bill won)"; er.l = 1.0000; pr.l = 0.0000; pindex.l = 1.0000; gr.l = 194.0449; tariff.l = 28.6572; indtax.l = 65.2754; netsub.l = 0.0000; gdtot.l = 141.1519; hhsav.l = 61.4089; govsav.l = 52.8930; deprecia.l = 0.0000; savings.l = 159.1419; invest.l = 159.1419; fsav.l = 39.1744; fbor.l = 58.7590; remit.l = 0.0000; tothhtax.l = 100.1122; y.l = 1123.5941; Table labres1(i,lc) 'summary matrix with sectoral employment results' labor1 labor2 labor3 agricult 2515.900 442.643 0.000 industry 0.000 767.776 0.000 services 0.000 355.568 948.100; Table labres2(*,lc) 'summary matrix with aggregate employment results' labor1 labor2 labor3 wa 0.074 0.140 0.152 ls 2515.900 1565.987 948.100; Table hhres(*,hh) 'summary matrix with household results' lab-hh cap-hh yh 548.7478 574.8463 mps 0.0600 0.0600; l.l(i,lc) = labres1(i,lc); ls.l(lc) = labres2("ls",lc); wa.l(lc) = labres2("wa",lc); mps.l(hh) = hhres("mps",hh); yh.l(hh) = hhres("yh",hh); Table sectres(*,i) 'summary matrix with sectoral results' agricult industry services pd 1.0000 1.0000 1.0000 pk 1.0000 1.0000 1.0000 pva 0.7370 0.2911 0.6625 x 711.6443 930.3509 497.4428 xd 657.3677 840.0500 515.4296 xxd 641.7037 812.2222 492.0307 e 15.6639 27.8278 23.3988 m 69.9406 118.1287 5.4120 k 657.5754 338.7076 1548.5192 int 256.6450 464.1656 156.2598 cd 452.1765 307.8561 202.0416 gd 2.8230 9.8806 128.4482 id 0.0000 148.4488 10.6931 dst 0.0000 0.0000 0.0000 dk 20.6884 46.1511 92.3023 pm 1.0000 1.0000 1.0000 pe 1.0000 1.0000 1.0000 px 1.0000 1.0000 1.0000 p 1.0000 1.0000 1.0000; pd.l(i) = sectres("pd",i); pm.l(i) = sectres("pm",i); pe.l(i) = sectres("pe",i); pk.l(i) = sectres("pk",i); px.l(i) = sectres("px",i); p.l(i) = sectres("p",i); pva.l(i) = sectres("pva",i); x.l(i) = sectres("x",i); xd.l(i) = sectres("xd",i); xxd.l(i) = sectres("xxd",i); e.l(i) = sectres("e",i); m.l(i) = sectres("m",i); k.l(i) = sectres("k",i); int.l(i) = sectres("int",i); cd.l(i) = sectres("cd",i); gd.l(i) = sectres("gd",i); id.l(i) = sectres("id",i); dst.l(i) = sectres("dst",i); dk.l(i) = sectres("dk",i); it(i) = yes$(e.l(i) or m.l(i)); in(i) = not it(i); k.fx(i) = k.l(i); m.fx(in) = 0; e.fx(in) = 0; l.fx(i,lc)$( l.l(i,lc) = 0) = 0; p.lo(i) = .01; pd.lo(i) = .01; pm.lo(it) = .01; pk.lo(i) = .01; px.lo(i) = .01; x.lo(i) = .01; xd.lo(i) = .01; m.lo(it) = .01; xxd.lo(it) = .01; wa.lo(lc) = .01; int.lo(i) = .01; y.lo = .01; e.lo(it) = .01; l.lo(i,lc)$(l.l(i,lc) <> 0) = .01; $sTitle Equation Definitions Equation * price block pmdef(i) 'definition of domestic import prices' pedef(i) 'definition of domestic export prices' absorption(i) 'value of domestic sales' sales(i) 'value of domestic output' actp(i) 'definition of activity prices' pkdef(i) 'definition of capital goods price' pindexdef 'definition of general price level' * output block activity(i) 'production function' profitmax(i,lc) 'first order condition for profit maximum' lmequil(lc) 'labor market equilibrium' cet(i) 'cet function' esupply(i) 'export supply' armington(i) 'composite good aggregation function' costmin(i) 'f.o.c. for cost minimization of composite good' xxdsn(i) 'domestic sales for nontraded sectors' xsn(i) 'composite good agg. for nontraded sectors' * demand block inteq(i) 'total intermediate uses' cdeq(i) 'private consumption behavior' dsteq(i) 'inventory investment' gdp 'private gdp' labory 'total income accruing to labor' capitaly 'total income accruing to capital' hhtaxdef 'total household taxes collected by govt.' gdeq 'government consumption shares' greq 'government revenue' tariffdef 'tariff revenue' premium 'total import premium income' indtaxdef 'indirect taxes on domestic production' netsubdef 'export duties' * savings-investment block hhsaveq 'household savings' gruse 'government savings' depreq 'depreciation expenditure' totsav 'total savings' prodinv(i) 'investment by sector of destination' ieq(i) 'investment by sector of origin' * balance of payments caeq 'current account balance (bill dollars)' * market clearing equil(i) 'goods market equilibrium' * objective function obj 'objective function'; * price block pmdef(it).. pm(it) =e= pwm(it)*er*(1 + tm(it) + pr); pedef(it).. pe(it) =e= pwe(it)*(1 + te(it))*er; absorption(i).. p(i)*x(i) =e= pd(i)*xxd(i) + (pm(i)*m(i))$it(i); sales(i).. px(i)*xd(i) =e= pd(i)*xxd(i) + (pe(i)*e(i))$it(i); actp(i).. px(i)*(1-itax(i)) =e= pva(i) + sum(j, io(j,i)*p(j)); pkdef(i).. pk(i) =e= sum(j, p(j)*imat(j,i)); pindexdef.. pindex =e= sum(i, pwts(i)*p(i)); * output and factors of production block activity(i).. xd(i) =e= ad(i)*prod(lc$wdist(i,lc), l(i,lc)**alphl(i,lc)) * k(i)**(1 - sum(lc, alphl(i,lc))); profitmax(i,lc)$wdist(i,lc).. wa(lc)*wdist(i,lc)*l(i,lc) =e= xd(i)*pva(i)*alphl(i,lc); lmequil(lc).. sum(i, l(i,lc)) =e= ls(lc); cet(it).. xd(it) =e= at(it)*(gamma(it)*e(it)**rhot(it) + (1 - gamma(it))*xxd(it)**rhot(it))**(1/rhot(it)); esupply(it).. e(it)/xxd(it) =e= (pe(it)/pd(it)*(1 - gamma(it))/gamma(it)) ** (1/(rhot(it) - 1)); armington(it).. x(it) =e= ac(it)*(delta(it)*m(it)**(-rhoc(it)) + (1 - delta(it))*xxd(it)**(-rhoc(it)))**(-1/rhoc(it)); costmin(it).. m(it)/xxd(it) =e= (pd(it)/pm(it)*delta(it)/(1 - delta(it))) ** (1/(1 + rhoc(it))); xxdsn(in).. xxd(in) =e= xd(in); xsn(in).. x(in) =e= xxd(in); * demand block inteq(i).. int(i) =e= sum(j, io(i,j)*xd(j)); dsteq(i).. dst(i) =e= dstr(i)*xd(i); cdeq(i).. p(i)*cd(i) =e= sum(hh, cles(i,hh)*(1 - mps(hh))*yh(hh)*(1 - htax(hh))); gdp.. y =e= sum(hh, yh(hh)); labory.. yh("lab-hh") =e= sum(lc, wa(lc)*ls(lc)) + remit*er; capitaly.. yh("cap-hh") =e= sum(i, pva(i)*xd(i)) - deprecia - sum(lc, wa(lc)*ls(lc)) + fbor*er + ypr; hhsaveq.. hhsav =e= sum(hh, mps(hh)*yh(hh)*(1 - htax(hh))); greq.. gr =e= tariff - netsub + indtax +tothhtax; gruse.. gr =e= sum(i, p(i)*gd(i)) + govsav; gdeq(i).. gd(i) =e= gles(i)*gdtot; tariffdef.. tariff =e= sum(it, tm(it)*m(it)*pwm(it))*er; indtaxdef.. indtax =e= sum(i, itax(i)*px(i)*xd(i)); netsubdef.. netsub =e= sum(it, te(it)*e(it)*pwe(it))*er; premium.. ypr =e= sum(it, pwm(it)*m(it))*er*pr; hhtaxdef.. tothhtax =e= sum(hh, htax(hh)*yh(hh)); depreq.. deprecia =e= sum(i, depr(i)*pk(i)*k(i)); totsav.. savings =e= hhsav + govsav + deprecia + fsav*er; prodinv(i).. pk(i)*dk(i) =e= kio(i)*invest - kio(i)*sum(j, dst(j)*p(j)); ieq(i).. id(i) =e= sum(j, imat(i,j)*dk(j)); * balance of payments caeq.. sum(it, pwm(it)*m(it)) =e= sum(it, pwe(it)*e(it)) + fsav + remit + fbor; * market clearing equil(i).. x(i) =e= int(i) + cd(i) + gd(i) + id(i) + dst(i); * objective function obj.. omega =e= prod(i$cles(i,"lab-hh"), cd(i)**cles(i,"lab-hh")); er.fx = er.l; fsav.fx = fsav.l; remit.fx = remit.l; fbor.fx = fbor.l; pindex.fx = pindex.l; mps.fx(hh) = mps.l(hh); gdtot.fx = gdtot.l; ls.fx(lc) = ls.l(lc); Model model1 'square base model' / all /; solve model1 maximizing omega using nlp;