张欣《可计算一般均衡模型的基本原理与编程》的课后习题答案.pdf 19页

'张欣《可计算一般均衡模型的基本原理与编程》的课后习题答案第2章投入产出表和投入产出模型1、将下面投入产出表填满：农业制造业中间投入合最终使用总产出计农业160210370380750制造业1403204606301090中间投入合300530计增加值4505601010总投入合计7501090计算过程：第一行，160+210=370，750-370=380。第二行，1090-630=460,460-140=320。第三行，160+140=300,210+320=530。第五行，总投入=总产出第四行，750-300=450,1090-530=560,450+560=10102.a行模型为：0.8180.0980.0848804808800.1590.2090.159153099015300.0910.0980.23410705901070Q139.062b.计算结果：Q2286.618Q41.3013程序 $titleinput-outputmodelsetac/sec1,sec2,sec3,labor,finaluse,fotal/;seti(ac)/sec1,sec2,sec3/;alias(i,j);tableIO(*,*)sec1sec2sec3finaluseTotalsec1160150100480880sec21403205309001530sec3801502505901070labor320350410capital180560150total88015301070;parameterint(i,j)use(i)lab(i)cap(i)a(i,j)Q0(i);int(i,j)=IO(i,j);use(i)=IO(i,"finaluse");lab(i)=IO("labor",i);cap(i)=IO("capital",i);Q0(i)=IO("total",i);a(i,j)=int(i,j)/Q0(j);displayint,use,lab,Q0,a;variableQ(i);equationcommodityequi(i);commodityequi(i)..sum(j,a(i,j)*Q(j))+use(i)=e=Q(i);Q.l(i)=Q0(i);modelIOmodel/all/;solveIOmodelusingmcp; displayQ.lparameteruse2(i)/sec10sec2200sec30/;displayuse2equationcommodityequi2(i);commodityequi2(i)..sum(j,a(i,j)*Q(j))+use2(i)=e=Q(i);modelsimiomodel/commodityequi2/solvesimiomodelusingmcp;display"Q.1,为求解的结果",Q.l第三章投入产出中的价格关系程序：setac/sec1,sec2,sec3,labor,capital,finaluse,total/;seti(ac)/sec1,sec2,sec3/;setg(ac)/labor,capital/;setj(ac)/sec1,sec2,sec3,finaluse,total/;sets(ac)/sec2,sec3/;alias(i,ii);alias(s,ss);tablei0(*,*)sec1sec2sec3finaluseTotalsec116015090480880sec21403201709001530sec3801502505901070labor320350410capital180560150total88015301070;parametera(i,ii)b(g,ii)*int(i,ii)p0(i) w0(g)use(i)lab(ii)cap(ii)q0(i);p0(i)=1;w0(g)=1;a(i,ii)=(p0(i)*i0(i,ii))/(p0(ii)*i0("total",ii));b(g,ii)=(w0(g)*i0(g,ii))/(p0(ii)*i0("total",ii));use(i)=i0(i,"finaluse")/p0(i);lab(ii)=i0("labor",ii)/w0("labor");cap(ii)=i0("capital",ii)/w0("capital");q0(i)=i0("total",i)/p0(i);variablep(i)w(g)q(i);displaya,b,p0,w0,use,lab,cap,q0;equationpriceequ(ii);priceequ(ii)..sum(i,a(i,ii)*p(i))+sum(g,b(g,ii)*w(g))=e=p(ii);p.l(i)=p0(i);w.fx(g)=w0(g);modeliopricemodel/all/;solveiopricemodelusingmcp;displayp.l,w.l;parameterwl1laborpricewk1capitalcost;wl1=1;wk1=1.1;displaywl1,wk1; equationsim1priceequ(ii);sim1priceequ(ii)..sum(i,a(i,ii)*p(i))+b("capital",ii)*wk1+b("labor",ii)*wl1=e=p(ii);p.l(i)=p0(i);modelsimpricemodel/sim1priceequ/;solvesimpricemodelusingmcp;parameterpincrease(ii)increaseinpriceinvarioussectors;pincrease(ii)=p.l(ii)-1displayp.l,pincrease;parameterp20(s)p2fx(ss)a2(s,ss)a22(ss)b2(g,ss);p20(s)=1;p2fx(ss)=1.15;a2(s,ss)=i0(s,ss)/i0("total",ss);a22(ss)=i0("sec1",ss)/i0("total",ss);b2(g,ss)=i0(g,ss)/i0("total",ss);displaya2,b2,p2fx;variablep2(s);equationsim2priceequ(ss);sim2priceequ(ss)..sum(s,a2(s,ss)*p2(s))+a22(ss)*p2fx(ss)+sum(g,b2(g,ss)*w(g))=e=p2(ss);p2.l(s)=p20(s);modelsim2pricemodel/sim2priceequ/;solvesim2pricemodelusingmcp;parameterpincrease2(ss)increaseinpriceinvarioussectors; pincrease2(ss)=p2.l(ss)-1displayp2.l,pincrease2;*end1.投入产出模型为：110.1820.1590.0910.205*1.10.0401ΔP(IA")Aw0.09810.2090.0980.366*1.10.055xx0.0840.19510.2340.140*1.10.0342.价格模型为PA"PAwAwttkk计算结果显示：制造业价格增加2.1%，服务业增加2.1%。第四章SAM表支出12345678储蓄—投活动商品要素居民企业政府国外汇总资账户市场销售居民自总产1活动产出产自销出市场销中间政府消总需2商品交易成本售的私投资出口投入费求人消费国外要要素3要素增值素收入收入居民之政府对国外对居民居民要素企业对居民4居民间转移居民转居民转总收收入转移支付支付移支付移支付入政府对国外对企业收企业要素企业的企业的5企业总收入收入转移支转移支入付付企业直接国外对生产销售税，要素税，直接政府税，企业向政府的6政府税增关税，出政府要素税，收总收政府缴纳盈转移支值税口税收入入税入余付储蓄—投居民储政府储国外净总储7企业储蓄资账蓄蓄储蓄蓄户对国外要企业向国外政府对外汇8国外进口素的支付支付盈余国外的支出 支付总投居民支政府支总投外汇收汇总总供应要素支出企业支出入出出资入注：表中标注黄色的为习题上要求归类的变量第五章SAM表平衡1.(a)最小二乘法平衡的结果是：1601509047014032017091080150250610Q3203604301705601501110880GAMS程序为：$title===leastsquarebalancemethod=====setac/sec1,sec2,sec3,lab,cap,hh,total/;seti(ac)/sec1,sec2,sec3,lab,cap,hh/;alias(ac,acp);alias(i,j);tablesam(*,*)sec1sec2sec3labcaphhtotalsec116015090540940sec21403201709101540sec3801502506101000lab3203604001080cap170550150870hh10508601910total8701530106010508602060;parametersQ0(i,j)initialvalue;Q0(i,j)=sam(i,j);variablesQ(i,j)z; positivevariablesQ(i,j);equationssumsquarebalance;sumsquare..z=e=sum((i,j)$sam(i,j),(Q(i,j)-sam(i,j))**2);balance(i)..sum(j,Q(i,j))=e=sum(j,Q(j,i));Q.l(i,j)=Q0(i,j);modelsambal/all/;solvesambalusingnlpminimizingz;displayQ.l;(b)假设居民消费不可靠，得到的结果为：160809054014032017091080150250610Q3203604301706301501110950在程序中加入限制条件，只需改equation步：equationssumsquarebalanceitem;sumsquare..z=e=sum((i,j)$sam(i,j),(Q(i,j)-sam(i,j))**2);balance(i)..sum(j,Q(i,j))=e=sum(j,Q(j,i));item(i)..Q(i,"hh")=e=Q0(i,"hh");Q.l(i,j)=Q0(i,j);(d)RAS法平衡的结果是：sec1sec2sec3labcaphhtotaltartotsec1105.09499.61899.163616.125920.000920.000sec292.554213.898188.5241045.0241540.0001540.000sec393.532177.318490.2991238.8512000.0002000.000lab472.334537.269990.3972000.0002000.000cap156.487511.896231.617900.000900.000hh2000.000900.0002900.0002900.000 total920.0001540.0002000.0002000.000900.0002900.000tartot920.0001540.0002000.0002000.000900.0002900.000相应的GAMS程序为：setac/sec1,sec2,sec3,lab,cap,hh,total,tartot/;seti(ac)/sec1,sec2,sec3,lab,cap,hh/;alias(ac,acp);alias(i,j);tablesam(*,*)thesocialaccountingmatrixsec1sec2sec3labcaphhtotalTARTOTsec116015090540940920sec214032017091015401540sec38015025061010002000lab32036040010802000cap170550150870900hh105086019102900total8701530106010508602060TARTOT9201540200020009002900;parameterrowdis(i)condis(i)maxdisiter;maxdis=0.1;iter=1;while(iter<5000andmaxdis>1e-10,sam("total",j)=sum(i,sam(i,j));sam(i,j)=sam(i,j)/sam("total",j)*sam("tartot",j);sam(i,"total")=sum(j,sam(i,j));sam(i,j)=sam(i,j)/sam(i,"total")*sam(i,"tartot");condis(i)=abs(sum(j,sam(j,i)))-sam("tartot",i);rowdis(i)=abs(sum(j,sam(i,j)))-sam(i,"tartot");maxdis=smax{i,max{condis(i),rowdis(i)}};iter=iter+1; );displaysam,maxdis,iter;*end(e)直接交叉熵平衡的结果为：SAMS程序为：setac/sec1,sec2,sec3,lab,cap,hh,total/;seti(ac)/sec1,sec2,sec3,lab,cap,hh/;alias(ac,acp);alias(i,j);tablesam(*,*)sec1sec2sec3labcaphhtotalsec116015090540940sec21403201709101540sec3801502506101000lab3203604001080cap170550150870hh10508601910total8701530106010508602060;parametersq0(i,j)h0;*assignmentforparametersq0(i,j)=sam(i,j);h0=sum((i,j),sam(i,j));displayh0,sam;variablesq(i,j) hhratioz*nonnegpositivevariableq(i,j);equationstotalsumdirectentropybalancehratiodef;totalsum..h=e=sum((i,j),q(i,j));hratiodef..hratio=e=h/h0;directentropy..z=e=sum((i,j)$sam(i,j),(1/h)*q(i,j)*log(q(i,j)/sam(i,j))-log(hratio));balance(i)..sum(j,q(i,j))=e=sum(j,q(j,i));q.l(i,j)=q0(i,j);h.l=h0;hratio.lo=0.5;hratio.up=2;modelsambal/all/;solvesambalusingnlpminimizingz;displayq.l,h.l,hratio.l;*end第六章一般均衡理论及其应用化1.消费者在预算约束条件下对效用最大化1maxuqls.t.lL1,qcL,ywlpq1u(cL)(1L)du*令0,得到LdL****假设价格p=1，则进一步解得：qc,p1,wc,yc2.超额需求函数可定义为 iiiZk(p)xk(p,pe)ekiIiI其中e为禀赋，x为需求，p是价格向量。ii消费约束为pxpeii从约束出发，取等号pxpennniikiipkxpkepk(xi(p,pe)ek)0k1k1k1nkii将上式对消费人数求和，有pk(xi(p,pe)ek)0iIk1nki由于求和的次序可以互换，有pk(xi(p,pe)0k1iInkii这等价于pk(xi(p,pe)ek)0k1IiIn由超额需求函数定义有pkZk(p)0k1即pZ(p)0证毕！第七章CES生产函数2.解：mincwxwxwx112233s.t.f(x1,x2,x3)A(xxx)/q112233使用拉格朗日乘数等式解得：11w11x2w33x2；；A(xxx)/q；wxwx112233221223即为要素需求函数的联立方程隐形表达。解该联立方程得：1c1i111x(w1,w2,w3,q)[www]q（i=1,2,3）iAw112233i成本函数为：31c(w1,w2,w3,q)wxc(w1,w2,w3,q)1[w1w1w1]1qii112233i1A按照商品价格等于边际成本的利润最大化原则求导，即得到商品供应函数，有1pc(w1,w2,w3,q)1[w1w1w1]1112233cA 3.结果：A=2.7330.2680.6030.129123程序$titleDeamonstration:ExerciseforaCESfunctionparameterelasrhodelta1delta2delta3scaleAx10x20x30q0w10w20w30p0;elas=0.5;w10=1;w20=1;w30=1;p0=1;x10=130;x20=195;x30=90;q0=415;rho=1-1/elas;delta1=w10*x10**(1-rho)/(w10*x10**(1-rho)+w20*x20**(1-rho)+w30*x30**(1-rho));delta2=w20*x20**(1-rho)/(w10*x10**(1-rho)+w20*x20**(1-rho)+w30*x30**(1-rho));delta3=w30*x30**(1-rho)/(w10*x10**(1-rho)+w20*x20**(1-rho)+w30*x30**(1-rho));scaleA=q0/(delta1*x10**rho+delta2*x20**rho+delta3*x30**rho)**(1/rho);displayrho,delta1,delta2,delta3,scaleA,x10,x20,x30,q0,w10,w20,w30,p0;variablex1x2x3 qw1w2w3p;equationQeqFOCeqFOCeq2PRICEeq;Qeq..q=e=scaleA*(delta1*x1**rho+delta2*x2**rho+delta3*x30**rho)**(1/rho);FOCeq..delta1/delta2=e=w1*x1**(1-rho)/(w2*x2**(1-rho));FOCeq2..delta2/delta3=e=w2*x2**(1-rho)/(w3*x3**(1-rho));PRICEeq..p*q=e=w1*x1+w2*x2+w3*x3;p.l=p0;x1.l=x10;x2.l=x20;x3.l=x30;q.fx=q0;w1.fx=w10;w2.fx=w20;w3.fx=w30;modelCES/all/;solveCESusingmcp;parameterrepbase;repbase("inputx1")=x1.l;repbase("inputx2")=x2.l;repbase("inputx3")=x3.l;repbase("qpricep0")=p.l;displayrepbase; 第八章函数嵌套的CGE模型2.要将书中的第一层换成列昂惕夫函数，改动的主要是黄色部分，改动部分的数学表达式如下：第一层列昂惕夫函数关系式：QAQVAQINTAaaaQVAQAaba(sam("lab",a)sam("cap",a))/sam("total",a)b具体程序如下：$title有CES嵌套函数的CGE模型setac/agri,manu,serv,lab,cap,hh,total/;seta(ac)/agri,manu,serv/;setf(ac)/lab,cap/;;alias(ac,acp),(a,ap),(f,fp);tablesam(ac,acp)agrimanuservlabcaphhtotalagri3302401858351560manu28538029010151970serv3753153554651510lab4504954501395cap150540230920hh13959201620total15601970151013959202315;parameterrhoq(a)/agri=0.2,manu=0.3,serv=0.1/rhova(a)/agri=0.25,manu=0.5,serv=0.8/parametersscaleaq(a)deltaq(a)scaleava(a)deltava(a)ia(a,ap)deltab(a)shrh(a)pa0(a)qa0(a)pva0(a)qva0(a) pinta0(a)qinta0(a)qint0(a,ap)qld0(a)qkd0(a)qls0qks0wl0wk0yh0qh0(a);pa0(a)=1;pva0(a)=1;pinta0(a)=1;wk0=1;wl0=1;qa0(a)=sam("total",a)/pa0(a);qva0(a)=SUM(f,sam(f,a));qint0(a,ap)=sam(a,ap)/pa0(a);qinta0(a)=sum(ap,qint0(ap,a));ia(a,ap)=qint0(a,ap)/qinta0(ap);deltab(a)=qva0(a)/sam("total",a);qls0=sum(a,sam("lab",a))/wl0;qks0=sum(a,sam("cap",a))/wk0;Qld0(a)=sam("lab",a)/wl0;qkd0(a)=sam("cap",a)/wk0;deltaq(a)=pva0(a)*qva0(a)**(1-rhoq(a))/(pva0(a)*qva0(a)**(1-rhoq(a))+pinta0(a)*qinta0(a)**(1-rhoq(a)));scaleaq(a)=qa0(a)/(deltaq(a)*qva0(a)**rhoq(a)+(1-deltaq(a))*qinta0(a)**rhoq(a))**(1/rhoq(a));deltava(a)=wl0*qld0(a)**(1-rhova(a))/(wl0*qld0(a)**(1-rhova(a))+wk0*qkd0(a)**(1-rhova(a)));scaleava(a)=qva0(a)/(deltava(a)*qld0(a)**rhova(a)+(1-deltava(a))*qkd0(a)**rhova(a))**(1/rhova(a));yh0=wl0*qls0+wk0*qks0;qh0(a)=sam(a,"hh")/pa0(a);shrh(a)=(pa0(a)*qh0(a))/sum(ap,sam(ap,"hh"));variablepa(a),pva(a),pinta(a),wl,wk,qa(a),qva(a),qinta(a),qint(a,ap),qld(a),qkd(a),qls,qks,yh,qh(a);*pa(a),pva(a),pinta(a),wl,wk,qa(a),qva(a),qinta(a),qint(a,ap),qld(a),qkd(a),qls,qks,yh,qh(a);equationqafn(a)QAFOCeq(a)paeq(a)qvafn(a) qvafoc(a)pvaeq(a)qintfn(a,ap)pintaeq(ap)yheqqheq(a)comequi(a)leqkeq;qafn(a)..qa(a)=e=QVA(a)+QINTA(a);QAFOCeq(a)..QVA(a)=e=deltab(a)*QA(a);paeq(a)..PA(a)*QA(a)=e=PVA(a)*QVA(a)+PINTA(a)*QINTA(a);qvafn(a)..qva(a)=e=scaleava(a)*(deltava(a)*qld(a)**rhova(a)+(1-deltava(a))*qkd(a)**rhova(a))**(1/rhova(a));qvafoc(a)..wl/wk=e=(deltava(a)/(1-deltava(a)))*(qkd(a)/qld(a))**(1-rhova(a));pvaeq(a)..pva(a)*qva(a)=e=wl*qld(a)+wk*qkd(a);qintfn(a,ap)..qint(a,ap)=e=ia(a,ap)*qinta(ap);pintaeq(ap)..pinta(ap)=e=sum(a,ia(a,ap)*pa(a));yheq..yh=e=wl*qls+wk*qks;qheq(a)..pa(a)*qh(a)=e=shrh(a)*yh;comequi(a)..qa(a)=e=sum(ap,qint(a,ap))+qh(a);leq..sum(a,qld(a))=e=qls;keq..sum(a,qkd(a))=e=qks;pa.l(a)=pa0(a);pva.l(a)=pva0(a);pinta.l(a)=pinta0(a); qa.l(a)=qa0(a);qva.l(a)=qva0(a);qinta.l(a)=qinta0(a);qint.l(a,ap)=qint0(a,ap);qld.l(a)=qld0(a);qkd.l(a)=qkd0(a);wk.l=1;wl.l=1;qls.fx=qls0;qks.fx=qks0;yh.l=yh0;qh.l(a)=qh0(a);modelcge/all/;solvecgeusingmcp;qks.fx=qks0*1.1;modelsim1/all/;solvesim1usingmcp;*end第九章效用函数和居民的商品需求3.计算结果：0.3330.130平均预算份额：s0.367；边际预算份额：0.4300.3000.440519.544复制检验顺利通过。居民收入增加10%，新的需求为Q614.495。515.961GAMS程序：$title例9.LES需求函数的参数校调、函数赋复制检验和模拟*生产部门和商品包括农业制造业服务seta/agri,manu,serv/;setinst/hh/;alias(a,ap);tablesam(a,inst)hhagri500manu550serv450 ;parameterleselas(a)/agri0.4,manu1.2,serv1.5/frisch/-2/;parameterspa0(a)qh0(a)eh0bgtshr(a)bgtshrchklesbeta(a)lesbetachklessub(a);pa0(a)=1;qh0(a)=sam(a,"hh")/pa0(a);eh0=sum(a,qh0(a)*pa0(a));bgtshr(a)=sam(a,"hh")/eh0;bgtshrchk=sum(a,bgtshr(a));*以下是LES函数lesbeta(a)=leselas(a)*bgtshr(a)/(sum(ap,leselas(ap)*bgtshr(ap)));lesbetachk=sum(a,lesbeta(a));lessub(a)=sam(a,"hh")+(lesbeta(a)/pa0(a))/(eh0/frisch);displayfrisch,pa0,qh0,eh0,bgtshr,bgtshrchk,lesbeta,lesbetachk,lessub,leselas;variablepa(a),qh(a),eh;equationqheq(a);qheq(a)..pa(a)*qh(a)=e=pa(a)*lessub(a)+lesbeta(a)*(eh-sum(ap,pa(ap)*lessub(ap)));pa.fx(a)=pa0(a);qh.l(a)=qh0(a);eh.fx=eh0;modelcge/all/;solvecgeusingmcp;displaypa.l,qh.l,eh.l;eh.fx=eh0*1.1;modelsim1/all/;solvesim1usingmcp;displaypa.l,qh.l,eh.l;'