Generated on 2023-07-10 01:32:42 by gEcon ver. 1.2.2 (2023-07-10) http://gecon.r-forge.r-project.org/ Model name: cge_calibration_cd Index sets (2): HH = { '1', '2' } SEC = { 'A', 'B', 'C' } Block: CONSUMER Definitions: u = (SUM alpha * D^(omega^-1 * (-1 + omega)))^(omega * (-1 + omega)^-1) Controls: D Objective: U = (SUM alpha * D^(omega^-1 * (-1 + omega)))^(omega * (-1 + omega)^-1) Constraints: -INC - PI + SUM p * D = 0 (lambda__CONSUMER_1) Identities: -INC + L + p_k * K = 0 ks_data - K = 0 ls_data - L = 0 First order conditions: lambda__CONSUMER_1 * p + alpha * D^(-1 + omega^-1 * (-1 + omega)) * (SUM alpha * D^(omega^-1 * (-1 + omega)))^(-1 + omega * (-1 + omega)^-1) = 0 ( D) Block: FIRM Controls: Y, K, L, X Objective: pi = -L - p_k * K + p * Y - SUM p * X Constraints: -Y + gamma * K^beta_k * L^beta_l * (PROD X^beta_x) = 0 (lambda__FIRM_1) First order conditions: -lambda__FIRM_1 + p = 0 (Y) -p_k + beta_k * gamma * lambda__FIRM_1 * K^(-1 + beta_k) * L^beta_l * (PROD X^beta_x) = 0 (K) -1 + beta_l * gamma * lambda__FIRM_1 * K^beta_k * L^(-1 + beta_l) * (PROD X^beta_x) = 0 (L) -p + beta_x * gamma * lambda__FIRM_1 * X^-1 * K^beta_k * L^beta_l * (PROD X^beta_x) = 0 ( X) First order conditions after reduction: -p_k + beta_k * gamma * p * K^(-1 + beta_k) * L^beta_l * (PROD X^beta_x) = 0 (K) -1 + beta_l * gamma * p * K^beta_k * L^(-1 + beta_l) * (PROD X^beta_x) = 0 (L) -p + beta_x * gamma * p * X^-1 * K^beta_k * L^beta_l * (PROD X^beta_x) = 0 ( X) Block: EQUILIBRIUM Identities: -SUM K + SUM K = 0 1 - p = 0 -PI + pi_h * (SUM pi) = 0 Variables (43): p_k, lambda__CONSUMER_1<'1'>, lambda__CONSUMER_1<'2'>, p<'A'>, p<'B'>, p<'C'>, pi<'A'>, pi<'B'>, pi<'C'>, D<'A','1'>, D<'A','2'>, D<'B','1'>, D<'B','2'>, D<'C','1'>, D<'C','2'>, INC<'1'>, INC<'2'>, K<'1'>, K<'2'>, K<'A'>, K<'B'>, K<'C'>, L<'1'>, L<'2'>, L<'A'>, L<'B'>, L<'C'>, PI<'1'>, PI<'2'>, U<'1'>, U<'2'>, X<'A','A'>, X<'A','B'>, X<'A','C'>, X<'B','A'>, X<'B','B'>, X<'B','C'>, X<'C','A'>, X<'C','B'>, X<'C','C'>, Y<'A'>, Y<'B'>, Y<'C'> Parameters (50): omega, alpha<'A','1'>, alpha<'A','2'>, alpha<'B','1'>, alpha<'B','2'>, alpha<'C','1'>, alpha<'C','2'>, beta_k<'A'>, beta_k<'B'>, beta_k<'C'>, beta_l<'A'>, beta_l<'B'>, beta_l<'C'>, beta_x<'A','A'>, beta_x<'A','B'>, beta_x<'A','C'>, beta_x<'B','A'>, beta_x<'B','B'>, beta_x<'B','C'>, beta_x<'C','A'>, beta_x<'C','B'>, beta_x<'C','C'>, d_data<'B','1'>, d_data<'B','2'>, d_data<'C','1'>, d_data<'C','2'>, gamma<'A'>, gamma<'B'>, gamma<'C'>, ks_data<'1'>, ks_data<'2'>, l_data<'A'>, l_data<'B'>, l_data<'C'>, ls_data<'1'>, ls_data<'2'>, pi_h<'1'>, pi_h<'2'>, x_data<'A','A'>, x_data<'A','B'>, x_data<'A','C'>, x_data<'B','A'>, x_data<'B','B'>, x_data<'B','C'>, x_data<'C','A'>, x_data<'C','B'>, x_data<'C','C'>, y_data<'A'>, y_data<'B'>, y_data<'C'> Free parameters (25): omega, d_data<'B','1'>, d_data<'B','2'>, d_data<'C','1'>, d_data<'C','2'>, ks_data<'1'>, ks_data<'2'>, l_data<'A'>, l_data<'B'>, l_data<'C'>, ls_data<'1'>, ls_data<'2'>, pi_h<'2'>, x_data<'A','A'>, x_data<'A','B'>, x_data<'A','C'>, x_data<'B','A'>, x_data<'B','B'>, x_data<'B','C'>, x_data<'C','A'>, x_data<'C','B'>, x_data<'C','C'>, y_data<'A'>, y_data<'B'>, y_data<'C'> Calibrated parameters (25): alpha<'A','1'>, alpha<'A','2'>, alpha<'B','1'>, alpha<'B','2'>, alpha<'C','1'>, alpha<'C','2'>, beta_k<'A'>, beta_k<'B'>, beta_k<'C'>, beta_l<'A'>, beta_l<'B'>, beta_l<'C'>, beta_x<'A','A'>, beta_x<'A','B'>, beta_x<'A','C'>, beta_x<'B','A'>, beta_x<'B','B'>, beta_x<'B','C'>, beta_x<'C','A'>, beta_x<'C','B'>, beta_x<'C','C'>, gamma<'A'>, gamma<'B'>, gamma<'C'>, pi_h<'1'> Equations (43): (1) -1 + beta_l<'A'> * gamma<'A'> * p<'A'> * K<'A'>^beta_k<'A'> * L<'A'>^(-1 + beta_l<'A'>) * X<'A','A'>^beta_x<'A','A'> * X<'B','A'>^beta_x<'B','A'> * X<'C','A'>^beta_x<'C','A'> = 0 (2) -1 + beta_l<'B'> * gamma<'B'> * p<'B'> * K<'B'>^beta_k<'B'> * L<'B'>^(-1 + beta_l<'B'>) * X<'A','B'>^beta_x<'A','B'> * X<'B','B'>^beta_x<'B','B'> * X<'C','B'>^beta_x<'C','B'> = 0 (3) -1 + beta_l<'C'> * gamma<'C'> * p<'C'> * K<'C'>^beta_k<'C'> * L<'C'>^(-1 + beta_l<'C'>) * X<'A','C'>^beta_x<'A','C'> * X<'B','C'>^beta_x<'B','C'> * X<'C','C'>^beta_x<'C','C'> = 0 (4) 1 - p<'A'> = 0 (5) 1 - p<'B'> = 0 (6) 1 - p<'C'> = 0 (7) ks_data<'1'> - K<'1'> = 0 (8) ks_data<'2'> - K<'2'> = 0 (9) ls_data<'1'> - L<'1'> = 0 (10) ls_data<'2'> - L<'2'> = 0 (11) -p_k + beta_k<'A'> * gamma<'A'> * p<'A'> * K<'A'>^(-1 + beta_k<'A'>) * L<'A'>^beta_l<'A'> * X<'A','A'>^beta_x<'A','A'> * X<'B','A'>^beta_x<'B','A'> * X<'C','A'>^beta_x<'C','A'> = 0 (12) -p_k + beta_k<'B'> * gamma<'B'> * p<'B'> * K<'B'>^(-1 + beta_k<'B'>) * L<'B'>^beta_l<'B'> * X<'A','B'>^beta_x<'A','B'> * X<'B','B'>^beta_x<'B','B'> * X<'C','B'>^beta_x<'C','B'> = 0 (13) -p_k + beta_k<'C'> * gamma<'C'> * p<'C'> * K<'C'>^(-1 + beta_k<'C'>) * L<'C'>^beta_l<'C'> * X<'A','C'>^beta_x<'A','C'> * X<'B','C'>^beta_x<'B','C'> * X<'C','C'>^beta_x<'C','C'> = 0 (14) -p<'A'> + beta_x<'A','A'> * gamma<'A'> * p<'A'> * X<'A','A'>^-1 * K<'A'>^beta_k<'A'> * L<'A'>^beta_l<'A'> * X<'A','A'>^beta_x<'A','A'> * X<'B','A'>^beta_x<'B','A'> * X<'C','A'>^beta_x<'C','A'> = 0 (15) -p<'A'> + beta_x<'A','B'> * gamma<'B'> * p<'B'> * X<'A','B'>^-1 * K<'B'>^beta_k<'B'> * L<'B'>^beta_l<'B'> * X<'A','B'>^beta_x<'A','B'> * X<'B','B'>^beta_x<'B','B'> * X<'C','B'>^beta_x<'C','B'> = 0 (16) -p<'A'> + beta_x<'A','C'> * gamma<'C'> * p<'C'> * X<'A','C'>^-1 * K<'C'>^beta_k<'C'> * L<'C'>^beta_l<'C'> * X<'A','C'>^beta_x<'A','C'> * X<'B','C'>^beta_x<'B','C'> * X<'C','C'>^beta_x<'C','C'> = 0 (17) -p<'B'> + beta_x<'B','A'> * gamma<'A'> * p<'A'> * X<'B','A'>^-1 * K<'A'>^beta_k<'A'> * L<'A'>^beta_l<'A'> * X<'A','A'>^beta_x<'A','A'> * X<'B','A'>^beta_x<'B','A'> * X<'C','A'>^beta_x<'C','A'> = 0 (18) -p<'B'> + beta_x<'B','B'> * gamma<'B'> * p<'B'> * X<'B','B'>^-1 * K<'B'>^beta_k<'B'> * L<'B'>^beta_l<'B'> * X<'A','B'>^beta_x<'A','B'> * X<'B','B'>^beta_x<'B','B'> * X<'C','B'>^beta_x<'C','B'> = 0 (19) -p<'B'> + beta_x<'B','C'> * gamma<'C'> * p<'C'> * X<'B','C'>^-1 * K<'C'>^beta_k<'C'> * L<'C'>^beta_l<'C'> * X<'A','C'>^beta_x<'A','C'> * X<'B','C'>^beta_x<'B','C'> * X<'C','C'>^beta_x<'C','C'> = 0 (20) -p<'C'> + beta_x<'C','A'> * gamma<'A'> * p<'A'> * X<'C','A'>^-1 * K<'A'>^beta_k<'A'> * L<'A'>^beta_l<'A'> * X<'A','A'>^beta_x<'A','A'> * X<'B','A'>^beta_x<'B','A'> * X<'C','A'>^beta_x<'C','A'> = 0 (21) -p<'C'> + beta_x<'C','B'> * gamma<'B'> * p<'B'> * X<'C','B'>^-1 * K<'B'>^beta_k<'B'> * L<'B'>^beta_l<'B'> * X<'A','B'>^beta_x<'A','B'> * X<'B','B'>^beta_x<'B','B'> * X<'C','B'>^beta_x<'C','B'> = 0 (22) -p<'C'> + beta_x<'C','C'> * gamma<'C'> * p<'C'> * X<'C','C'>^-1 * K<'C'>^beta_k<'C'> * L<'C'>^beta_l<'C'> * X<'A','C'>^beta_x<'A','C'> * X<'B','C'>^beta_x<'B','C'> * X<'C','C'>^beta_x<'C','C'> = 0 (23) -PI<'1'> + pi_h<'1'> * (pi<'A'> + pi<'B'> + pi<'C'>) = 0 (24) -PI<'2'> + pi_h<'2'> * (pi<'A'> + pi<'B'> + pi<'C'>) = 0 (25) U<'1'> - (alpha<'A','1'> * D<'A','1'>^(omega^-1 * (-1 + omega)) + alpha<'B','1'> * D<'B','1'>^(omega^-1 * (-1 + omega)) + alpha<'C','1'> * D<'C','1'>^(omega^-1 * (-1 + omega)))^(omega * (-1 + omega)^-1) = 0 (26) U<'2'> - (alpha<'A','2'> * D<'A','2'>^(omega^-1 * (-1 + omega)) + alpha<'B','2'> * D<'B','2'>^(omega^-1 * (-1 + omega)) + alpha<'C','2'> * D<'C','2'>^(omega^-1 * (-1 + omega)))^(omega * (-1 + omega)^-1) = 0 (27) -Y<'A'> + gamma<'A'> * K<'A'>^beta_k<'A'> * L<'A'>^beta_l<'A'> * X<'A','A'>^beta_x<'A','A'> * X<'B','A'>^beta_x<'B','A'> * X<'C','A'>^beta_x<'C','A'> = 0 (28) -Y<'B'> + gamma<'B'> * K<'B'>^beta_k<'B'> * L<'B'>^beta_l<'B'> * X<'A','B'>^beta_x<'A','B'> * X<'B','B'>^beta_x<'B','B'> * X<'C','B'>^beta_x<'C','B'> = 0 (29) -Y<'C'> + gamma<'C'> * K<'C'>^beta_k<'C'> * L<'C'>^beta_l<'C'> * X<'A','C'>^beta_x<'A','C'> * X<'B','C'>^beta_x<'B','C'> * X<'C','C'>^beta_x<'C','C'> = 0 (30) lambda__CONSUMER_1<'1'> * p<'A'> + alpha<'A','1'> * D<'A','1'>^(-1 + omega^-1 * (-1 + omega)) * (alpha<'A','1'> * D<'A','1'>^(omega^-1 * (-1 + omega)) + alpha<'B','1'> * D<'B','1'>^(omega^-1 * (-1 + omega)) + alpha<'C','1'> * D<'C','1'>^(omega^-1 * (-1 + omega)))^(-1 + omega * (-1 + omega)^-1) = 0 (31) lambda__CONSUMER_1<'1'> * p<'B'> + alpha<'B','1'> * D<'B','1'>^(-1 + omega^-1 * (-1 + omega)) * (alpha<'A','1'> * D<'A','1'>^(omega^-1 * (-1 + omega)) + alpha<'B','1'> * D<'B','1'>^(omega^-1 * (-1 + omega)) + alpha<'C','1'> * D<'C','1'>^(omega^-1 * (-1 + omega)))^(-1 + omega * (-1 + omega)^-1) = 0 (32) lambda__CONSUMER_1<'1'> * p<'C'> + alpha<'C','1'> * D<'C','1'>^(-1 + omega^-1 * (-1 + omega)) * (alpha<'A','1'> * D<'A','1'>^(omega^-1 * (-1 + omega)) + alpha<'B','1'> * D<'B','1'>^(omega^-1 * (-1 + omega)) + alpha<'C','1'> * D<'C','1'>^(omega^-1 * (-1 + omega)))^(-1 + omega * (-1 + omega)^-1) = 0 (33) lambda__CONSUMER_1<'2'> * p<'A'> + alpha<'A','2'> * D<'A','2'>^(-1 + omega^-1 * (-1 + omega)) * (alpha<'A','2'> * D<'A','2'>^(omega^-1 * (-1 + omega)) + alpha<'B','2'> * D<'B','2'>^(omega^-1 * (-1 + omega)) + alpha<'C','2'> * D<'C','2'>^(omega^-1 * (-1 + omega)))^(-1 + omega * (-1 + omega)^-1) = 0 (34) lambda__CONSUMER_1<'2'> * p<'B'> + alpha<'B','2'> * D<'B','2'>^(-1 + omega^-1 * (-1 + omega)) * (alpha<'A','2'> * D<'A','2'>^(omega^-1 * (-1 + omega)) + alpha<'B','2'> * D<'B','2'>^(omega^-1 * (-1 + omega)) + alpha<'C','2'> * D<'C','2'>^(omega^-1 * (-1 + omega)))^(-1 + omega * (-1 + omega)^-1) = 0 (35) lambda__CONSUMER_1<'2'> * p<'C'> + alpha<'C','2'> * D<'C','2'>^(-1 + omega^-1 * (-1 + omega)) * (alpha<'A','2'> * D<'A','2'>^(omega^-1 * (-1 + omega)) + alpha<'B','2'> * D<'B','2'>^(omega^-1 * (-1 + omega)) + alpha<'C','2'> * D<'C','2'>^(omega^-1 * (-1 + omega)))^(-1 + omega * (-1 + omega)^-1) = 0 (36) -INC<'1'> + L<'1'> + p_k * K<'1'> = 0 (37) -INC<'2'> + L<'2'> + p_k * K<'2'> = 0 (38) -INC<'1'> - PI<'1'> + p<'A'> * D<'A','1'> + p<'B'> * D<'B','1'> + p<'C'> * D<'C','1'> = 0 (39) -INC<'2'> - PI<'2'> + p<'A'> * D<'A','2'> + p<'B'> * D<'B','2'> + p<'C'> * D<'C','2'> = 0 (40) -K<'1'> - K<'2'> + K<'A'> + K<'B'> + K<'C'> = 0 (41) pi<'A'> + L<'A'> + p_k * K<'A'> + p<'A'> * X<'A','A'> - p<'A'> * Y<'A'> + p<'B'> * X<'B','A'> + p<'C'> * X<'C','A'> = 0 (42) pi<'B'> + L<'B'> + p_k * K<'B'> + p<'A'> * X<'A','B'> + p<'B'> * X<'B','B'> - p<'B'> * Y<'B'> + p<'C'> * X<'C','B'> = 0 (43) pi<'C'> + L<'C'> + p_k * K<'C'> + p<'A'> * X<'A','C'> + p<'B'> * X<'B','C'> + p<'C'> * X<'C','C'> - p<'C'> * Y<'C'> = 0 Calibrating equations (25): (1) -d_data<'B','1'> + D<'B','1'> = 0 (2) -d_data<'B','2'> + D<'B','2'> = 0 (3) -d_data<'C','1'> + D<'C','1'> = 0 (4) -d_data<'C','2'> + D<'C','2'> = 0 (5) -l_data<'A'> + L<'A'> = 0 (6) -l_data<'B'> + L<'B'> = 0 (7) -l_data<'C'> + L<'C'> = 0 (8) -x_data<'A','A'> + X<'A','A'> = 0 (9) -x_data<'A','B'> + X<'A','B'> = 0 (10) -x_data<'A','C'> + X<'A','C'> = 0 (11) -x_data<'B','A'> + X<'B','A'> = 0 (12) -x_data<'B','B'> + X<'B','B'> = 0 (13) -x_data<'B','C'> + X<'B','C'> = 0 (14) -x_data<'C','A'> + X<'C','A'> = 0 (15) -x_data<'C','B'> + X<'C','B'> = 0 (16) -x_data<'C','C'> + X<'C','C'> = 0 (17) -y_data<'A'> + Y<'A'> = 0 (18) -y_data<'B'> + Y<'B'> = 0 (19) -y_data<'C'> + Y<'C'> = 0 (20) -1 + pi_h<'1'> + pi_h<'2'> = 0 (21) -1 + alpha<'A','1'>^omega + alpha<'B','1'>^omega + alpha<'C','1'>^omega = 0 (22) -1 + alpha<'A','2'>^omega + alpha<'B','2'>^omega + alpha<'C','2'>^omega = 0 (23) -1 + beta_k<'A'> + beta_l<'A'> + beta_x<'A','A'> + beta_x<'B','A'> + beta_x<'C','A'> = 0 (24) -1 + beta_k<'B'> + beta_l<'B'> + beta_x<'A','B'> + beta_x<'B','B'> + beta_x<'C','B'> = 0 (25) -1 + beta_k<'C'> + beta_l<'C'> + beta_x<'A','C'> + beta_x<'B','C'> + beta_x<'C','C'> = 0