********************************************************************* * Replication file 7/11 for "Are Sports Teams Multiproduct Firms?" * by K.G. Stewart and J.C.H. Jones (2010) Empirical Economics 39(2), * 487-514. * Estimation of MSGM factor demand systems for baseball player * characteristics, the model M0. We estimate the nonseparable model * both with and without concavity imposed. * This printout yields the Morishima elasticities of substitution * reported in Table 6, including their standard errors. * Morishima elasticities are computed from the demand elasticities * using the relationship Morishima(ij)=eji-eii ********************************************************************* * Sample consists of 26 teams x 6 seasons (1986-91) SAMPLE 1 156; * Read in team characteristics; documented in Team.doc read(Team.dat) season team league attend attlag ticprice & pmarkup gameswon gameslst wins salaries nplayers strkouts walks & slugavg nhitters npitchrs experhit experpit nstars roadatt & aleast alcentrl alwest nleast nlcentrl nlwest * Delete variables not used in this analysis delete season team league attlag ticprice pmarkup gameswon gameslst salaries nplayers * read in hedonic prices read(HedPrice1.dat) p1 p2 p3 p4 nobs * define team outputs * This scaling of road attendance requires fewest iterations to convergence GENR Y1=WINS GENR Y2=ROADatt/10000000 * conference dummies genr dum1=aleast genr dum2=alcentrl genr dum3=alwest genr dum4=nleast genr dum5=nlcentrl * define team factor inputs: experience, hitting, pitching, stars GENR q1=experhit+experpit GENR q2=nhitters*slugavg GENR q3=npitchrs*strkouts/walks GENR q4=nstars * DEFLATE HEDONIC PRICES TO 1991 DOLLARS SAMPLE 1 26 GENR p1=p1*135.0/109.6 GENR p2=p2*135.0/109.6 GENR p3=p3*135.0/109.6 GENR p4=p4*135.0/109.6 SAMPLE 27 52 GENR p1=p1*135.0/113.6 GENR p2=p2*135.0/113.6 GENR p3=p3*135.0/113.6 GENR p4=p4*135.0/113.6 SAMPLE 53 78 GENR p1=p1*135.0/118.3 GENR p2=p2*135.0/118.3 GENR p3=p3*135.0/118.3 GENR p4=p4*135.0/118.3 SAMPLE 79 104 GENR p1=p1*135.0/124.0 GENR p2=p2*135.0/124.0 GENR p3=p3*135.0/124.0 GENR p4=p4*135.0/124.0 SAMPLE 105 130 GENR p1=p1*135.0/130.7 GENR p2=p2*135.0/130.7 GENR p3=p3*135.0/130.7 GENR p4=p4*135.0/130.7 SAMPLE 1 156 * Generate cost identity and cost shares * (This synthetic (hedonic) cost series is used * only for descriptive purposes in calculating the implied cost shares, not * in estimation of cost function parameters. It can be compared with fitted * cost series predicted by estimated model.) genr cost=q1*p1+q2*p2+q3*p3+q4*p4 genr s1=q1*p1/cost genr s2=q2*p2/cost genr s3=q3*p3/cost genr s4=q4*p4/cost * Obtain mean factor inputs: * qm1=135.73077 * qm2=5.35117 * qm3=17.92278 * qm4=2.61538 stat q1 / mean=qm1 stat q2 / mean=qm2 stat q3 / mean=qm3 stat q4 / mean=qm4 GENR DENOM=qm1*p1+qm2*p2+qm3*p3+qm4*p4 gen1 theta1=qm1/2 gen1 theta2=qm2/2 gen1 theta3=qm3/2 gen1 theta4=qm4/2 * generate price constructs used in estimation GENR Pd1=p1/DENOM GENR Pd2=p2/DENOM GENR Pd3=p3/DENOM GENR Pd4=p4/DENOM GENR Pd11=pd1*pd1 GENR Pd12=pd1*pd2 GENR Pd13=pd1*pd3 GENR Pd14=pd1*pd4 GENR Pd21=pd2*pd1 GENR Pd22=pd2*pd2 GENR Pd23=pd2*pd3 GENR Pd24=pd2*pd4 GENR Pd31=pd3*pd1 GENR Pd32=pd3*pd2 GENR Pd33=pd3*pd3 GENR Pd34=pd3*pd4 GENR Pd41=pd4*pd1 GENR Pd42=pd4*pd2 GENR Pd43=pd4*pd3 GENR Pd44=pd4*pd4 GENR Pd11=Pd11-Pd14-(Pd41-Pd44) GENR Pd12=Pd12-Pd14-(Pd42-Pd44) GENR Pd13=Pd13-Pd14-(Pd43-Pd44) GENR Pd21=Pd21-Pd24-(Pd41-Pd44) GENR Pd22=Pd22-Pd24-(Pd42-Pd44) GENR Pd23=Pd23-Pd24-(Pd43-Pd44) GENR Pd31=Pd31-Pd34-(Pd41-Pd44) GENR Pd32=Pd32-Pd34-(Pd42-Pd44) GENR Pd33=Pd33-Pd34-(Pd43-Pd44) GENR Pd12=2*Pd12 GENR Pd13=2*Pd13 GENR Pd23=2*Pd23 GENR Pd1=Pd1-Pd4 GENR Pd2=Pd2-Pd4 GENR Pd3=Pd3-Pd4 * Obtain parallel scalar means used in elasticities stat p1 / mean=m1 stat p2 / mean=m2 stat p3 / mean=m3 stat p4 / mean=m4 GEN1 mDENOM=qm1*m1+qm2*m2+qm3*m3+qm4*m4 GEN1 mdenom2=mdenom*mdenom GEN1 md1=m1/mDENOM GEN1 md2=m2/mDENOM GEN1 md3=m3/mDENOM GEN1 md4=m4/mDENOM GEN1 md11=md1*md1 GEN1 md12=md1*md2 GEN1 md13=md1*md3 GEN1 md14=md1*md4 GEN1 md21=md2*md1 GEN1 md22=md2*md2 GEN1 md23=md2*md3 GEN1 md24=md2*md4 GEN1 md31=md3*md1 GEN1 md32=md3*md2 GEN1 md33=md3*md3 GEN1 md34=md3*md4 GEN1 md41=md4*md1 GEN1 md42=md4*md2 GEN1 md43=md4*md3 GEN1 md44=md4*md4 GEN1 md11=md11-md14-(md41-md44) GEN1 md12=md12-md14-(md42-md44) GEN1 md13=md13-md14-(md43-md44) GEN1 md21=md21-md24-(md41-md44) GEN1 md22=md22-md24-(md42-md44) GEN1 md23=md23-md24-(md43-md44) GEN1 md31=md31-md34-(md41-md44) GEN1 md32=md32-md34-(md42-md44) GEN1 md33=md33-md34-(md43-md44) GEN1 md12=2*md12 GEN1 md13=2*md13 GEN1 md23=2*md23 gen1 md1=md1-md4 gen1 md2=md2-md4 gen1 md3=md3-md4 stat y1 / mean=ym1 stat y2 / mean=ym2 ** INITIAL PARAMETERIZATION ** * Shazam requires that the theta's (/2) appear numerically * Multiplicative factor 2 is included in parameter D1 nl 4 / ncoef=41 iter=999 Eq q1=(S11*Pd1+S12*Pd2+S13*Pd3 & -67.8654*(S11*Pd11+S12*Pd12+S13*Pd13 & +S22*Pd22+S23*Pd23 & +S33*Pd33))*(Y1+BETA*Y2) & +d11*dum1+d12*dum2+d13*dum3+d14*dum4+d15*dum5 & +B11*(Y1+BETA*Y2)+B1+LAMBDA1*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q2=(S12*Pd1+S22*Pd2+S23*Pd3 & -2.67558*(S11*Pd11+S12*Pd12+S13*Pd13 & +S22*Pd22+S23*Pd23 & +S33*Pd33))*(Y1+BETA*Y2) & +d21*dum1+d22*dum2+d23*dum3+d24*dum4+d25*dum5 & +B22*(Y1+BETA*Y2)+B2+LAMBDA2*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q3=(S13*Pd1+S23*Pd2+S33*Pd3 & -8.96111*(S11*Pd11+S12*Pd12+S13*Pd13 & +S22*Pd22+S23*Pd23 & +S33*Pd33))*(Y1+BETA*Y2) & +d31*dum1+d32*dum2+d33*dum3+d34*dum4+d35*dum5 & +B33*(Y1+BETA*Y2)+B3+LAMBDA3*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q4=-((S11+S12+S13)*Pd1+(S12+S22+S23)*Pd2+(S13+S23+S33)*Pd3 & +1.30769*(S11*Pd11+S12*Pd12+S13*Pd13 & +S22*Pd22+S23*Pd23 & +S33*Pd33))*(Y1+BETA*Y2) & +d41*dum1+d42*dum2+d43*dum3+d44*dum4+d45*dum5 & +B44*(Y1+BETA*Y2)+B4+LAMBDA4*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) end ** ALTERNATIVE (BUT EQUIVALENT) PARAMETERIZATION ** GENR Z11=Pd1-THETA1*Pd11 GENR Z12=Pd2-THETA1*Pd12 GENR Z13=Pd3-THETA1*Pd13 GENR Z14=-THETA1*Pd22 GENR Z15=-THETA1*Pd23 GENR Z16=-THETA1*Pd33 GENR Z21=-THETA2*Pd11 GENR Z22=Pd1-THETA2*Pd12 GENR Z23=-THETA2*Pd13 GENR Z24=Pd2-THETA2*Pd22 GENR Z25=Pd3-THETA2*Pd23 GENR Z26=-THETA2*Pd33 GENR Z31=-THETA3*Pd11 GENR Z32=-THETA3*Pd12 GENR Z33=Pd1-THETA3*Pd13 GENR Z34=-THETA3*Pd22 GENR Z35=Pd2-THETA3*Pd23 GENR Z36=Pd3-THETA3*Pd33 GENR Z41=-(Pd1+THETA4*Pd11) GENR Z42=-(Pd1+Pd2+THETA4*Pd12) GENR Z43=-(Pd1+Pd3+THETA4*Pd13) GENR Z44=-(Pd2+THETA4*Pd22) GENR Z45=-(Pd2+Pd3+THETA4*Pd23) GENR Z46=-(Pd3+THETA4*Pd33) * Multiplicative factor 2 is included in parameter D1 nl 4 / ncoef=41 iter=999 coef=s predict=qpred Eq q1=(Y1+BETA*Y2) & *(B11+S11*Z11+S12*Z12+S13*Z13+S22*Z14+S23*Z15+S33*Z16) & +d11*dum1+d12*dum2+d13*dum3+d14*dum4+d15*dum5 & +B1+LAMBDA1*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q2=(Y1+BETA*Y2) & *(B22+S11*Z21+S12*Z22+S13*Z23+S22*Z24+S23*Z25+S33*Z26) & +d21*dum1+d22*dum2+d23*dum3+d24*dum4+d25*dum5 & +B2+LAMBDA2*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q3=(Y1+BETA*Y2) & *(B33+S11*Z31+S12*Z32+S13*Z33+S22*Z34+S23*Z35+S33*Z36) & +d31*dum1+d32*dum2+d33*dum3+d34*dum4+d35*dum5 & +B3+LAMBDA3*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q4=(Y1+BETA*Y2) & *(B44+S11*Z41+S12*Z42+S13*Z43+S22*Z44+S23*Z45+S33*Z46) & +d41*dum1+d42*dum2+d43*dum3+d44*dum4+d45*dum5 & +B4+LAMBDA4*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) end * e(1,1) elasticity test ( s11 - qm1*(s11*md1+s12*md2+s13*md3)-qm1*(s11*md1+s12*md2+s13*md3) & + qm1*qm1*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm1) * M(1,2)=e21-e11 test ( s12 - qm1*(s12*md1+s22*md2+s23*md3)-qm2*(s11*md1+s12*md2+s13*md3) & + qm2*qm1*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm2) & - ( s11 - qm1*(s11*md1+s12*md2+s13*md3)-qm1*(s11*md1+s12*md2+s13*md3) & + qm1*qm1*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm1) * M(1,3)=e31-e11 test ( s13 - qm1*(s13*md1+s23*md2+s33*md3)-qm3*(s11*md1+s12*md2+s13*md3) & + qm3*qm1*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm3) & - ( s11 - qm1*(s11*md1+s12*md2+s13*md3)-qm1*(s11*md1+s12*md2+s13*md3) & + qm1*qm1*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm1) * M(1,4)=e41-e11 test ( -(s11+s12+s13) & - qm1*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & - qm4*(s11*md1+s12*md2+s13*md3) & + qm4*qm1*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm4) & - ( s11 - qm1*(s11*md1+s12*md2+s13*md3)-qm1*(s11*md1+s12*md2+s13*md3) & + qm1*qm1*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm1) * M(2,1)=e12-e22 test ( s12 - qm2*(s11*md1+s12*md2+s13*md3)-qm1*(s12*md1+s22*md2+s23*md3) & + qm1*qm2*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm1) & - ( s22 - qm2*(s12*md1+s22*md2+s23*md3)-qm2*(s12*md1+s22*md2+s23*md3) & + qm2*qm2*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm2) * e(2,2) elasticity test ( s22 - qm2*(s12*md1+s22*md2+s23*md3)-qm2*(s12*md1+s22*md2+s23*md3) & + qm2*qm2*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm2) * M(2,3)=e32-e22 test ( s23 - qm2*(s13*md1+s23*md2+s33*md3)-qm3*(s12*md1+s22*md2+s23*md3) & + qm3*qm2*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm3) & - ( s22 - qm2*(s12*md1+s22*md2+s23*md3)-qm2*(s12*md1+s22*md2+s23*md3) & + qm2*qm2*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm2) * M(2,4)=e42-e22 test ( -(s12+s22+s23) & - qm2*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & - qm4*(s12*md1+s22*md2+s23*md3) & + qm4*qm2*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm4) & - ( s22 - qm2*(s12*md1+s22*md2+s23*md3)-qm2*(s12*md1+s22*md2+s23*md3) & + qm2*qm2*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm2) * M(3,1)=e13-e33 test ( s13 - qm3*(s11*md1+s12*md2+s13*md3)-qm1*(s13*md1+s23*md2+s33*md3) & + qm1*qm3*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm1) & - ( s33 - qm3*(s13*md1+s23*md2+s33*md3)-qm3*(s13*md1+s23*md2+s33*md3) & + qm3*qm3*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm3) * M(3,2)=e23-e33 test ( s23 - qm3*(s12*md1+s22*md2+s23*md3)-qm2*(s13*md1+s23*md2+s33*md3) & + qm2*qm3*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm2) & - ( s33 - qm3*(s13*md1+s23*md2+s33*md3)-qm3*(s13*md1+s23*md2+s33*md3) & + qm3*qm3*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm3) * e(3,3) elasticity test ( s33 - qm3*(s13*md1+s23*md2+s33*md3)-qm3*(s13*md1+s23*md2+s33*md3) & + qm3*qm3*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm3) * M(3,4)=e43-e33 test ( -(s13+s23+s33) & - qm3*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & - qm4*(s13*md1+s23*md2+s33*md3) & + qm4*qm3*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm4) & - ( s33 - qm3*(s13*md1+s23*md2+s33*md3)-qm3*(s13*md1+s23*md2+s33*md3) & + qm3*qm3*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm3) * M(4,1)=e14-e44 test ( -(s11+s12+s13) - qm4*(s11*md1+s12*md2+s13*md3) & - qm1*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & + qm1*qm4*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm1) & - ( (s11+s12+s13)+(s12+s22+s23)+(s13+s23+s33) & - 2*qm4*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & + qm4*qm4*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm4) * M(4,2)=e24-e44 test ( -(s12+s22+s23) - qm4*(s12*md1+s22*md2+s23*md3) & - qm2*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & + qm2*qm4*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm2) & - ( (s11+s12+s13)+(s12+s22+s23)+(s13+s23+s33) & - 2*qm4*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & + qm4*qm4*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm4) * M(4,3)=e34-e44 test ( -(s13+s23+s33) - qm4*(s13*md1+s23*md2+s33*md3) & - qm3*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & + qm3*qm4*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm3) & - ( (s11+s12+s13)+(s12+s22+s23)+(s13+s23+s33) & - 2*qm4*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & + qm4*qm4*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm4) * e(4,4) elasticity test ( (s11+s12+s13)+(s12+s22+s23)+(s13+s23+s33) & - 2*qm4*(-(s11+s12+s13)*md1-(s12+s22+s23)*md2-(s13+s23+s33)*md3) & + qm4*qm4*(S11*md11+S12*md12+S13*md13 & +S22*md22+S23*md23 & +S33*md33) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm4) ** CONCAVITY IMPOSED USING WILEY-SCHMIDT-BRAMBLE REPARAMETERIZATION ** * Multiplicative factor 2 is included in parameter D1: this turns out to be * critical to the quick convergence of the concavity-constrained system nl 4 / ncoef=41 iter=999 coef=g predict=qpred Eq q1=-(G11*G11*Z11+G11*G21*Z12+G11*G31*Z13+(G21*G21+G22*G22)*Z14 & +(G31*G21+G32*G22)*Z15+(G31*G31+G32*G32+G33*G33)*Z16-B11)*(Y1+BETA*Y2) & +d11*dum1+d12*dum2+d13*dum3+d14*dum4+d15*dum5 & +B1+LAMBDA1*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q2=-(G11*G11*Z21+G11*G21*Z22+G11*G31*Z23+(G21*G21+G22*G22)*Z24 & +(G31*G21+G32*G22)*Z25+(G31*G31+G32*G32+G33*G33)*Z26-B22)*(Y1+BETA*Y2) & +d21*dum1+d22*dum2+d23*dum3+d24*dum4+d25*dum5 & +B2+LAMBDA2*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q3=-(G11*G11*Z31+G11*G21*Z32+G11*G31*Z33+(G21*G21+G22*G22)*Z34 & +(G31*G21+G32*G22)*Z35+(G31*G31+G32*G32+G33*G33)*Z36-B33)*(Y1+BETA*Y2) & +d31*dum1+d32*dum2+d33*dum3+d34*dum4+d35*dum5 & +B3+LAMBDA3*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) Eq q4=-(G11*G11*Z41+G11*G21*Z42+G11*G31*Z43+(G21*G21+G22*G22)*Z44 & +(G31*G21+G32*G22)*Z45+(G31*G31+G32*G32+G33*G33)*Z46-B44)*(Y1+BETA*Y2) & +d41*dum1+d42*dum2+d43*dum3+d44*dum4+d45*dum5 & +B4+LAMBDA4*(Y1*Y1+D1*Y1*Y2+D2*Y2*Y2) end * e(1,1) elasticity test ( -g11*g11 - qm1*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & - qm1*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & + qm1*qm1*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm1) * M(1,2)=e21-e11 test ( - g11*g21 & - qm1*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & - qm2*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & + qm2*qm1*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm2) & - ( -g11*g11 - qm1*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & - qm1*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & + qm1*qm1*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm1) * M(1,3)=e31-e11 test ( - g11*g31 & - qm1*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & - qm3*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & + qm3*qm1*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm3) & - ( -g11*g11 - qm1*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & - qm1*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & + qm1*qm1*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm1) * M(1,4)=e41-e11 test ( g11*g11+g11*g21+g11*g31 & - qm1*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & - qm4*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & + qm4*qm1*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm4) & - ( -g11*g11 - qm1*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & - qm1*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & + qm1*qm1*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m1/(mdenom*qm1) * M(2,1)=e12-e22 test ( -g11*g21 - qm2*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & - qm1*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & + qm1*qm2*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm1) & - ( - (g21*g21+g22*g22) & - qm2*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & - qm2*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & + qm2*qm2*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm2) * e(2,2) elasticity test ( - (g21*g21+g22*g22) & - qm2*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & - qm2*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & + qm2*qm2*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm2) * M(2,3)=e32-e22 test ( - (g21*g31+g22*g32) & - qm2*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & - qm3*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & + qm3*qm2*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm3) & - ( - (g21*g21+g22*g22) & - qm2*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & - qm2*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & + qm2*qm2*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm2) * M(2,4)=e42-e22 test ( g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32) & - qm2*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & - qm4*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & + qm4*qm2*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm4) & - ( - (g21*g21+g22*g22) & - qm2*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & - qm2*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & + qm2*qm2*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m2/(mdenom*qm2) * M(3,1)=e13-e33 test ( -g11*g31 - qm3*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & - qm1*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & + qm1*qm3*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm1) & - ( - (g31*g31+g32*g32+g33*g33) & - qm3*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & - qm3*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & + qm3*qm3*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm3) * M(3,2)=e23-e33 test ( - (g21*g31+g22*g32) & - qm3*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & - qm2*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & + qm2*qm3*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm2) & - ( - (g31*g31+g32*g32+g33*g33) & - qm3*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & - qm3*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & + qm3*qm3*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm3) * e(3,3) elasticity test ( - (g31*g31+g32*g32+g33*g33) & - qm3*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & - qm3*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & + qm3*qm3*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm3) * M(3,4)=e43-e33 test ( g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33) & - qm3*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & - qm4*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & + qm4*qm3*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm4) & - ( - (g31*g31+g32*g32+g33*g33) & - qm3*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & - qm3*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & + qm3*qm3*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m3/(mdenom*qm3) * M(4,1)=e14-e44 test ( g11*g11+g11*g21+g11*g31 & - qm4*(-g11*g11*md1-g11*g21*md2-g11*g31*md3) & - qm1*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & + qm1*qm4*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm1) & - ( -(g11*g11+g11*g21+g11*g31) & -(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32)) & -(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33)) & - 2*qm4*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & + qm4*qm4*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm4) * M(4,2)=e24-e44 test ( g11*g21+g21*g21+g22*g22+g21*g31+g22*g32 & - qm4*(-g11*g21*md1-(g21*g21+g22*g22)*md2-(g21*g31+g22*g32)*md3) & - qm2*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & + qm2*qm4*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm2) & - ( -(g11*g11+g11*g21+g11*g31) & -(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32)) & -(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33)) & - 2*qm4*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & + qm4*qm4*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm4) * M(4,3)=e34-e44 test ( g11*g31+g21*g31+g22*g32+g31*g31+g32*g32+g33*g33 & - qm4*(-g11*g31*md1-(g21*g31+g22*g32)*md2-(g31*g31+g32*g32+g33*g33)*md3) & - qm3*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & + qm3*qm4*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm3) & - ( -(g11*g11+g11*g21+g11*g31) & -(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32)) & -(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33)) & - 2*qm4*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & + qm4*qm4*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm4) * e(4,4) elasticity test ( -(g11*g11+g11*g21+g11*g31) & -(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32)) & -(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33)) & - 2*qm4*((g11*g11+g11*g21+g11*g31)*md1 & +(g11*g21+(g21*g21+g22*g22)+(g21*g31+g22*g32))*md2 & +(g11*g31+(g21*g31+g22*g32)+(g31*g31+g32*g32+g33*g33))*md3) & + qm4*qm4*( -g11*g11*md11-g11*g21*md12-g11*g31*md13 & -(g21*g21+g22*g22)*md22-(g21*g31+g22*g32)*md23 & -(g31*g31+g32*g32+g33*g33)*md33 ) )*(Ym1+BETA*Ym2)*m4/(mdenom*qm4) stop