Chapter 2 Core Functions
2.1 CES Demand Core Functions
This is the example vignette for function: bfw_mp_func_demand from the PrjLabEquiBFW Package. This function generates a container map with key CES demand-side equations for a particular sub-nest.
2.1.1 Default Test
Default test
bl_verbose = true;
mp_func_demand = bfw_mp_func_demand(bl_verbose);
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_func Functions
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx functionString
____ ____ __________________________________________________________________________________________________________________________
fc_OMEGA "1" "1" "@(p1,p2,rho,beta_1,beta_2)p1.*fc_d1(p1,p2,1,1,rho,beta_1,beta_2)+p2.*fc_d2(p1,p2,1,1,rho,beta_1,beta_2)"
fc_d1 "2" "2" "@(p1,p2,Y,Z,rho,beta_1,beta_2)(Y/Z).*(beta_1+beta_2.*((p1./p2).*(beta_2./beta_1)).^(rho/(1-rho))).^(-1/rho)"
fc_d2 "3" "3" "@(p1,p2,Y,Z,rho,beta_1,beta_2)(Y/Z).*(beta_1.*((p2./p1).*(beta_1./beta_2)).^(rho/(1-rho))+beta_2).^(-1/rho)"
fc_lagrange_x1 "4" "4" "@(p1,rho,beta_1,beta_2,x_1,x_2)p1/(((beta_1*x_1^(rho)+beta_2*x_2^(rho))^((1/rho)-1))*(beta_1*x_1^(rho-1)))"
fc_lagrange_x2 "5" "5" "@(p2,rho,beta_1,beta_2,x_1,x_2)p2/(((beta_1*x_1^(rho)+beta_2*x_2^(rho))^((1/rho)-1))*(beta_2*x_2^(rho-1)))"
fc_output_nest "6" "6" "@(q1,q2,rho,beta_1,beta_2)((beta_1)*q1^(rho)+beta_2*q2^(rho))^(1/rho)"
fc_p1_foc "7" "7" "@(lagrangem,rho,beta_1,beta_2,x_1,x_2)lagrangem*(((beta_1*x_1^(rho)+beta_2*x_2^(rho))^((1/rho)-1))*(beta_1*x_1^(rho-1)))"
fc_p2_foc "8" "8" "@(lagrangem,rho,beta_1,beta_2,x_1,x_2)lagrangem*(((beta_1*x_1^(rho)+beta_2*x_2^(rho))^((1/rho)-1))*(beta_2*x_2^(rho-1)))"
fc_share_given_elas_foc "9" "9" "@(rho,p1,p2,x1,x2)fc_share_given_elas_foc_Q(rho,p1,p2,x1,x2)/(1+fc_share_given_elas_foc_Q(rho,p1,p2,x1,x2))"
fc_w1dw2 "10" "10" "@(x_1,x_2,rho,beta_1,beta_2)(x_2/x_1)^(1-rho)*(beta_1/beta_2)"
fc_yz_ratio "11" "11" "@(p1,p2,q1,q2,rho,beta_1,beta_2)fc_revenue(p1,p2,q1,q2)/fc_OMEGA(p1,p2,rho,beta_1,beta_2)" 2.2 Multinomial Logit Core Functions
This is the example vignette for function: bfw_mp_func_supply from the PrjLabEquiBFW Package. This function generates a container map with key multinomial logit supply-side equations.
2.2.1 Test BL_LOG_WAGE is false
Default test
bl_log_wage = false;
bl_verbose = true;
mp_func_supply = bfw_mp_func_supply(bl_log_wage, bl_verbose);
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_func Functions
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx functionString
___ ___ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
fc_ar_prob_wrk "1" "1" "@(arpsi0,psi1,mtwage,probdenom)fc_v_occ(reshape(arpsi0,[1,length(arpsi0)]),psi1,mtwage)./probdenom"
fc_log_pmdpo_occ "2" "2" "@(psi0,psi1,arwage,pie1,pie2,pie3,pie4,pie5,pie6,t,prbchd,prbmar,prbapp,prbjsy)(psi0+psi1.*arwage)-(pie1+pie2.*(t)+pie3.*prbchd+pie4.*prbmar+pie5.*prbapp+pie6.*prbjsy)"
fc_prob_denom "3" "3" "@(arpsi0,psi1,arpie,arwage1,arwage2,arwage3,t,prbchd,prbmar,prbapp,prbjsy)fc_v_occ(arpsi0(1),psi1,arwage1)+fc_v_occ(arpsi0(2),psi1,arwage2)+fc_v_occ(arpsi0(3),psi1,arwage3)+fc_v_lei(arpie(1),arpie(2),arpie(3),arpie(4),arpie(5),arpie(6),t,prbchd,prbmar,prbapp,prbjsy)"
fc_prob_lei "4" "4" "@(arpie,t,prbchd,prbmar,prbapp,prbjsy,probdenom)fc_v_lei(arpie(1),arpie(2),arpie(3),arpie(4),arpie(5),arpie(6),t,prbchd,prbmar,prbapp,prbjsy)./probdenom"
fc_s1 "5" "5" "@(p1,G_1,zeta_1_0,zeta_1_1)G_1./(1+(exp(-zeta_1_0-zeta_1_1.*p1)))"
fc_s2 "6" "6" "@(p2,G_2,zeta_2_0,zeta_2_1)G_2./(1+(exp(-zeta_2_0-zeta_2_1.*p2)))"
fc_supply "7" "7" "@(potlabor,prob)potlabor.*prob" 2.2.2 Test BL_LOG_WAGE is false
Default test
bl_log_wage = true;
mp_func_supply = bfw_mp_func_supply(bl_log_wage, bl_verbose);
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_func Functions
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx functionString
___ ___ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
fc_ar_prob_wrk "1" "1" "@(arpsi0,psi1,mtwage,probdenom)fc_v_occ(reshape(arpsi0,[1,length(arpsi0)]),psi1,mtwage)./probdenom"
fc_log_pmdpo_occ "2" "2" "@(psi0,psi1,arwage,pie1,pie2,pie3,pie4,pie5,pie6,t,prbchd,prbmar,prbapp,prbjsy)(psi0+psi1.*log(arwage))-(pie1+pie2.*(t)+pie3.*prbchd+pie4.*prbmar+pie5.*prbapp+pie6.*prbjsy)"
fc_prob_denom "3" "3" "@(arpsi0,psi1,arpie,arwage1,arwage2,arwage3,t,prbchd,prbmar,prbapp,prbjsy)fc_v_occ(arpsi0(1),psi1,arwage1)+fc_v_occ(arpsi0(2),psi1,arwage2)+fc_v_occ(arpsi0(3),psi1,arwage3)+fc_v_lei(arpie(1),arpie(2),arpie(3),arpie(4),arpie(5),arpie(6),t,prbchd,prbmar,prbapp,prbjsy)"
fc_prob_lei "4" "4" "@(arpie,t,prbchd,prbmar,prbapp,prbjsy,probdenom)fc_v_lei(arpie(1),arpie(2),arpie(3),arpie(4),arpie(5),arpie(6),t,prbchd,prbmar,prbapp,prbjsy)./probdenom"
fc_s1 "5" "5" "@(p1,G_1,zeta_1_0,zeta_1_1)G_1./(1+(exp(-zeta_1_0-zeta_1_1.*p1)))"
fc_s2 "6" "6" "@(p2,G_2,zeta_2_0,zeta_2_1)G_2./(1+(exp(-zeta_2_0-zeta_2_1.*p2)))"
fc_supply "7" "7" "@(potlabor,prob)potlabor.*prob" 2.3 Equilibrium Core Functions
This is the example vignette for function: bfw_mp_func_equi from the PrjLabEquiBFW Package.
2.3.1 Default Test
Default test
bl_verbose = true;
mp_func_demand = bfw_mp_func_equi(bl_verbose);
----------------------------------------
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
CONTAINER NAME: mp_func Functions
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
i idx functionString
___ ___ _________________________________________________________________________________________________________________________________________________________________________________
f_x_root "1" "1" "@(x,price_ratio,yfz_per_input,rho)(1-x)+(x).*(price_ratio.*(x./(1-x))).^((rho)./(1-rho))-(yfz_per_input).^rho"
fc_p1_of_p2 "2" "2" "@(p2,G_2,zeta_2_0,zeta_2_1,Y,Z,rho,beta_1,beta_2)((((((1+exp(-zeta_2_0-zeta_2_1.*p2))./(G_2)).*(Y/Z)).^rho).*(1/beta_1)-(beta_2/beta_1)).^((rho-1)/(rho))).*(beta_1/beta_2).*p2"
fc_p1_of_p2andSupply "3" "3" "@(p2,supplyQofP,Y,Z,rho,beta_1,beta_2)((((((Y/Z)./supplyQofP)).^rho).*(1/beta_1)-(beta_2/beta_1)).^((rho-1)/(rho))).*(beta_1/beta_2).*p2"
fc_p2_of_p1 "4" "4" "@(p1,G_1,zeta_1_0,zeta_1_1,Y,Z,rho,beta_1,beta_2)((((((1+exp(-zeta_1_0-zeta_1_1.*p1))./(G_1)).*(Y/Z)).^rho).*(1/beta_2)-(beta_1/beta_2)).^((rho-1)/(rho))).*(beta_2/beta_1).*p1"
fc_p2_of_p1andSupply "5" "5" "@(p1,supplyQofP,Y,Z,rho,beta_1,beta_2)((((((Y/Z)./supplyQofP)).^rho).*(1/beta_2)-(beta_1/beta_2)).^((rho-1)/(rho))).*(beta_2/beta_1).*p1"