Generated on 2023-07-10 01:36:14 by gEcon ver. 1.2.2 (2023-07-10) http://gecon.r-forge.r-project.org/ Model name: tc_rs_templ Index sets (1): COUNTRY = { 'F', 'H' } Variables selected for reduction: pi<'H'>[], pi<'F'>[], PI<'F'>[], PI<'H'>[], T<'H'>[], K_d<'H'>[], H_d<'H'>[], T<'F'>[], K_d<'F'>[], H_d<'F'>[], TR<'F'>[] Block: CONSUMER Definitions: u[] = (1 - eta)^-1 * (C[]^mu * (1 - H[])^(1 - mu))^(1 - eta) Controls: K[], C[], H[], I[] Objective: U[] = beta * E[][U[1]] + (1 - eta)^-1 * (C[]^mu * (1 - H[])^(1 - mu))^(1 - eta) Constraints: pi[] - C[] - I[] - T[] + TR[] + K[-1] * r[] + H[] * W[] - psi * K[-1] * (-delta + K[-1]^-1 * I[])^2 = 0 (lambda_c[]) I[] - K[] + K[-1] * (1 - delta) = 0 (lambda__CONSUMER_2[]) First order conditions: -lambda__CONSUMER_2[] + beta * ((1 - delta) * E[][lambda__CONSUMER_2[1]] + E[][lambda_c[1] * (r[1] - psi * (-delta + K[]^-1 * I[1])^2 + 2 * psi * K[]^-1 * I[1] * (-delta + K[]^-1 * I[1]))]) = 0 (K[]) -lambda_c[] + mu * C[]^(-1 + mu) * (1 - H[])^(1 - mu) * (C[]^mu * (1 - H[])^(1 - mu))^(-eta) = 0 (C[]) lambda_c[] * W[] + (-1 + mu) * C[]^mu * (1 - H[])^(-mu) * (C[]^mu * (1 - H[])^(1 - mu))^(-eta) = 0 (H[]) lambda__CONSUMER_2[] + lambda_c[] * (-1 - 2 * psi * (-delta + K[-1]^-1 * I[])) = 0 (I[]) Block: FIRM Controls: K_d[], H_d[], Y[], pi[] Objective: PI[] = pi[] Constraints: -Y[] + Z[] * H_d[]^(1 - alpha) * K_d[]^alpha = 0 (lambda__FIRM_1[]) -pi[] + Y[] - r[] * K_d[] - H_d[] * W[] = 0 (lambda__FIRM_2[]) First order conditions: -lambda__FIRM_2[] * r[] + alpha * lambda__FIRM_1[] * Z[] * H_d[]^(1 - alpha) * K_d[]^(-1 + alpha) = 0 (K_d[]) -lambda__FIRM_2[] * W[] + lambda__FIRM_1[] * Z[] * (1 - alpha) * H_d[]^(-alpha) * K_d[]^alpha = 0 (H_d[]) -lambda__FIRM_1[] + lambda__FIRM_2[] = 0 (Y[]) 1 - lambda__FIRM_2[] = 0 (pi[]) First order conditions after reduction: -r[] + alpha * Z[] * H_d[]^(1 - alpha) * K_d[]^(-1 + alpha) = 0 (K_d[]) -W[] + Z[] * (1 - alpha) * H_d[]^(-alpha) * K_d[]^alpha = 0 (H_d[]) Block: EQUILIBRIUM Identities: -SUM TR[] = 0 K[-1] - K_d[] = 0 H[] - H_d[] = 0 G_d[] - T[] = 0 lambda_c<'F'>[] - lambda_c<'H'>[] = 0 Block: EXOG Identities: epsilon_G[] - G_d[] + phi_G * G_d[-1] = 0 -Z[] + exp(epsilon_Z[] + phi_Z * log(Z[-1])) = 0 Variables (23): lambda_c<'F'>[], lambda_c<'H'>[], r<'F'>[], r<'H'>[], C<'F'>[], C<'H'>[], G_d<'F'>[], G_d<'H'>[], H<'F'>[], H<'H'>[], I<'F'>[], I<'H'>[], K<'F'>[], K<'H'>[], TR<'H'>[], U<'F'>[], U<'H'>[], W<'F'>[], W<'H'>[], Y<'F'>[], Y<'H'>[], Z<'F'>[], Z<'H'>[] Shocks (4): epsilon_Z<'F'>[], epsilon_Z<'H'>[], epsilon_G<'F'>[], epsilon_G<'H'>[] Parameters (13): beta, eta, mu, alpha<'F'>, alpha<'H'>, delta<'F'>, delta<'H'>, phi_G<'F'>, phi_G<'H'>, phi_Z<'F'>, phi_Z<'H'>, psi<'F'>, psi<'H'> Free parameters (13): beta, eta, mu, alpha<'F'>, alpha<'H'>, delta<'F'>, delta<'H'>, phi_G<'F'>, phi_G<'H'>, phi_Z<'F'>, phi_Z<'H'>, psi<'F'>, psi<'H'> Equations (23): (1) -lambda_c<'F'>[] + mu * C<'F'>[]^(-1 + mu) * (1 - H<'F'>[])^(1 - mu) * (C<'F'>[]^mu * (1 - H<'F'>[])^(1 - mu))^(-eta) = 0 (2) lambda_c<'F'>[] - lambda_c<'H'>[] = 0 (3) -lambda_c<'H'>[] + mu * C<'H'>[]^(-1 + mu) * (1 - H<'H'>[])^(1 - mu) * (C<'H'>[]^mu * (1 - H<'H'>[])^(1 - mu))^(-eta) = 0 (4) -r<'F'>[] + alpha<'F'> * Z<'F'>[] * K<'F'>[-1]^(-1 + alpha<'F'>) * H<'F'>[]^(1 - alpha<'F'>) = 0 (5) -r<'H'>[] + alpha<'H'> * Z<'H'>[] * K<'H'>[-1]^(-1 + alpha<'H'>) * H<'H'>[]^(1 - alpha<'H'>) = 0 (6) -W<'F'>[] + Z<'F'>[] * (1 - alpha<'F'>) * K<'F'>[-1]^alpha<'F'> * H<'F'>[]^(-alpha<'F'>) = 0 (7) -W<'H'>[] + Z<'H'>[] * (1 - alpha<'H'>) * K<'H'>[-1]^alpha<'H'> * H<'H'>[]^(-alpha<'H'>) = 0 (8) -Y<'F'>[] + Z<'F'>[] * K<'F'>[-1]^alpha<'F'> * H<'F'>[]^(1 - alpha<'F'>) = 0 (9) -Y<'H'>[] + Z<'H'>[] * K<'H'>[-1]^alpha<'H'> * H<'H'>[]^(1 - alpha<'H'>) = 0 (10) -Z<'F'>[] + exp(epsilon_Z<'F'>[] + phi_Z<'F'> * log(Z<'F'>[-1])) = 0 (11) -Z<'H'>[] + exp(epsilon_Z<'H'>[] + phi_Z<'H'> * log(Z<'H'>[-1])) = 0 (12) beta * (-(1 - delta<'F'>) * E[][lambda_c<'F'>[1] * (-1 - 2 * psi<'F'> * (-delta<'F'> + K<'F'>[]^-1 * I<'F'>[1]))] + E[][lambda_c<'F'>[1] * (r<'F'>[1] - psi<'F'> * (-delta<'F'> + K<'F'>[]^-1 * I<'F'>[1])^2 + 2 * psi<'F'> * K<'F'>[]^-1 * I<'F'>[1] * (-delta<'F'> + K<'F'>[]^-1 * I<'F'>[1]))]) + lambda_c<'F'>[] * (-1 - 2 * psi<'F'> * (-delta<'F'> + K<'F'>[-1]^-1 * I<'F'>[])) = 0 (13) beta * (-(1 - delta<'H'>) * E[][lambda_c<'H'>[1] * (-1 - 2 * psi<'H'> * (-delta<'H'> + K<'H'>[]^-1 * I<'H'>[1]))] + E[][lambda_c<'H'>[1] * (r<'H'>[1] - psi<'H'> * (-delta<'H'> + K<'H'>[]^-1 * I<'H'>[1])^2 + 2 * psi<'H'> * K<'H'>[]^-1 * I<'H'>[1] * (-delta<'H'> + K<'H'>[]^-1 * I<'H'>[1]))]) + lambda_c<'H'>[] * (-1 - 2 * psi<'H'> * (-delta<'H'> + K<'H'>[-1]^-1 * I<'H'>[])) = 0 (14) lambda_c<'F'>[] * W<'F'>[] + (-1 + mu) * C<'F'>[]^mu * (1 - H<'F'>[])^(-mu) * (C<'F'>[]^mu * (1 - H<'F'>[])^(1 - mu))^(-eta) = 0 (15) lambda_c<'H'>[] * W<'H'>[] + (-1 + mu) * C<'H'>[]^mu * (1 - H<'H'>[])^(-mu) * (C<'H'>[]^mu * (1 - H<'H'>[])^(1 - mu))^(-eta) = 0 (16) epsilon_G<'F'>[] - G_d<'F'>[] + phi_G<'F'> * G_d<'F'>[-1] = 0 (17) epsilon_G<'H'>[] - G_d<'H'>[] + phi_G<'H'> * G_d<'H'>[-1] = 0 (18) I<'F'>[] - K<'F'>[] + K<'F'>[-1] * (1 - delta<'F'>) = 0 (19) I<'H'>[] - K<'H'>[] + K<'H'>[-1] * (1 - delta<'H'>) = 0 (20) U<'F'>[] - beta * E[][U<'F'>[1]] - (1 - eta)^-1 * (C<'F'>[]^mu * (1 - H<'F'>[])^(1 - mu))^(1 - eta) = 0 (21) U<'H'>[] - beta * E[][U<'H'>[1]] - (1 - eta)^-1 * (C<'H'>[]^mu * (1 - H<'H'>[])^(1 - mu))^(1 - eta) = 0 (22) -C<'F'>[] - G_d<'F'>[] - I<'F'>[] - TR<'H'>[] + Y<'F'>[] - psi<'F'> * K<'F'>[-1] * (-delta<'F'> + K<'F'>[-1]^-1 * I<'F'>[])^2 = 0 (23) -C<'H'>[] - G_d<'H'>[] - I<'H'>[] + TR<'H'>[] + Y<'H'>[] - psi<'H'> * K<'H'>[-1] * (-delta<'H'> + K<'H'>[-1]^-1 * I<'H'>[])^2 = 0 Steady state equations (23): (1) -lambda_c<'F'>[ss] + mu * C<'F'>[ss]^(-1 + mu) * (1 - H<'F'>[ss])^(1 - mu) * (C<'F'>[ss]^mu * (1 - H<'F'>[ss])^(1 - mu))^(-eta) = 0 (2) lambda_c<'F'>[ss] - lambda_c<'H'>[ss] = 0 (3) -lambda_c<'H'>[ss] + mu * C<'H'>[ss]^(-1 + mu) * (1 - H<'H'>[ss])^(1 - mu) * (C<'H'>[ss]^mu * (1 - H<'H'>[ss])^(1 - mu))^(-eta) = 0 (4) -r<'F'>[ss] + alpha<'F'> * Z<'F'>[ss] * H<'F'>[ss]^(1 - alpha<'F'>) * K<'F'>[ss]^(-1 + alpha<'F'>) = 0 (5) -r<'H'>[ss] + alpha<'H'> * Z<'H'>[ss] * H<'H'>[ss]^(1 - alpha<'H'>) * K<'H'>[ss]^(-1 + alpha<'H'>) = 0 (6) -W<'F'>[ss] + Z<'F'>[ss] * (1 - alpha<'F'>) * H<'F'>[ss]^(-alpha<'F'>) * K<'F'>[ss]^alpha<'F'> = 0 (7) -W<'H'>[ss] + Z<'H'>[ss] * (1 - alpha<'H'>) * H<'H'>[ss]^(-alpha<'H'>) * K<'H'>[ss]^alpha<'H'> = 0 (8) -Y<'F'>[ss] + Z<'F'>[ss] * H<'F'>[ss]^(1 - alpha<'F'>) * K<'F'>[ss]^alpha<'F'> = 0 (9) -Y<'H'>[ss] + Z<'H'>[ss] * H<'H'>[ss]^(1 - alpha<'H'>) * K<'H'>[ss]^alpha<'H'> = 0 (10) -Z<'F'>[ss] + exp(phi_Z<'F'> * log(Z<'F'>[ss])) = 0 (11) -Z<'H'>[ss] + exp(phi_Z<'H'> * log(Z<'H'>[ss])) = 0 (12) beta * (lambda_c<'F'>[ss] * (r<'F'>[ss] - psi<'F'> * (-delta<'F'> + I<'F'>[ss] * K<'F'>[ss]^-1)^2 + 2 * psi<'F'> * I<'F'>[ss] * K<'F'>[ss]^-1 * (-delta<'F'> + I<'F'>[ss] * K<'F'>[ss]^-1)) - lambda_c<'F'>[ss] * (-1 - 2 * psi<'F'> * (-delta<'F'> + I<'F'>[ss] * K<'F'>[ss]^-1)) * (1 - delta<'F'>)) + lambda_c<'F'>[ss] * (-1 - 2 * psi<'F'> * (-delta<'F'> + I<'F'>[ss] * K<'F'>[ss]^-1)) = 0 (13) beta * (lambda_c<'H'>[ss] * (r<'H'>[ss] - psi<'H'> * (-delta<'H'> + I<'H'>[ss] * K<'H'>[ss]^-1)^2 + 2 * psi<'H'> * I<'H'>[ss] * K<'H'>[ss]^-1 * (-delta<'H'> + I<'H'>[ss] * K<'H'>[ss]^-1)) - lambda_c<'H'>[ss] * (-1 - 2 * psi<'H'> * (-delta<'H'> + I<'H'>[ss] * K<'H'>[ss]^-1)) * (1 - delta<'H'>)) + lambda_c<'H'>[ss] * (-1 - 2 * psi<'H'> * (-delta<'H'> + I<'H'>[ss] * K<'H'>[ss]^-1)) = 0 (14) lambda_c<'F'>[ss] * W<'F'>[ss] + (-1 + mu) * C<'F'>[ss]^mu * (1 - H<'F'>[ss])^(-mu) * (C<'F'>[ss]^mu * (1 - H<'F'>[ss])^(1 - mu))^(-eta) = 0 (15) lambda_c<'H'>[ss] * W<'H'>[ss] + (-1 + mu) * C<'H'>[ss]^mu * (1 - H<'H'>[ss])^(-mu) * (C<'H'>[ss]^mu * (1 - H<'H'>[ss])^(1 - mu))^(-eta) = 0 (16) -G_d<'F'>[ss] + phi_G<'F'> * G_d<'F'>[ss] = 0 (17) -G_d<'H'>[ss] + phi_G<'H'> * G_d<'H'>[ss] = 0 (18) I<'F'>[ss] - K<'F'>[ss] + K<'F'>[ss] * (1 - delta<'F'>) = 0 (19) I<'H'>[ss] - K<'H'>[ss] + K<'H'>[ss] * (1 - delta<'H'>) = 0 (20) U<'F'>[ss] - beta * U<'F'>[ss] - (1 - eta)^-1 * (C<'F'>[ss]^mu * (1 - H<'F'>[ss])^(1 - mu))^(1 - eta) = 0 (21) U<'H'>[ss] - beta * U<'H'>[ss] - (1 - eta)^-1 * (C<'H'>[ss]^mu * (1 - H<'H'>[ss])^(1 - mu))^(1 - eta) = 0 (22) -C<'F'>[ss] - G_d<'F'>[ss] - I<'F'>[ss] - TR<'H'>[ss] + Y<'F'>[ss] - psi<'F'> * K<'F'>[ss] * (-delta<'F'> + I<'F'>[ss] * K<'F'>[ss]^-1)^2 = 0 (23) -C<'H'>[ss] - G_d<'H'>[ss] - I<'H'>[ss] + TR<'H'>[ss] + Y<'H'>[ss] - psi<'H'> * K<'H'>[ss] * (-delta<'H'> + I<'H'>[ss] * K<'H'>[ss]^-1)^2 = 0