70 lines
2.0 KiB
R
70 lines
2.0 KiB
R
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# Transition dynamics
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k1 <- function(t){
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numerator = c1_forward_shooting*exp((δ-r_1)*t)
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denom1 = ((q*w_2)/(1-q))^(ρ/(1-ρ))
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denom2=exp((γ_1*ρ/(1-ρ))*t)
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denomexponent = ((1-η)/ρ)-1
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denominator = q*((q+denom1*denom2*(1-q))^denomexponent)
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result_k1 = (numerator/denominator)^(-1/η)
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return(result_k1)
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}
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k1_prime <- function(t){
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numerator = c1_forward_shooting * exp((δ-r_1)*t)
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denominator_part1 = ((q*w_2)/(1-q))^(ρ/(1-ρ))
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denominator_part2 = exp( ( (γ_1*ρ)/(1-ρ) )*t )*(1-q)*denominator_part1
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denominator_part3 = (q+denominator_part2)
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denominator_part4 = denominator_part3^( ( (1-η)/ ρ ) - 1)
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denominator_part5 = q*denominator_part4
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denominator = denominator_part5
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exponent_total = (-1/η)
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result_k1 = (numerator/denominator)^exponent_total
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return(result_k1)
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}
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k2 <- function(t){
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constant1_k2 = (w_2 * λ_2 * δ_2)/(δ-r_2)
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constant2_k2 = ((1-λ_2)/λ_2)^(δ_2*(1-λ_2))
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constant_exponent = (1/(1-δ_2))
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constant_term_k2 = (constant1_k2*constant2_k2)^constant_exponent
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exponential_growth_term_k2 = (γ_2+γ_1*δ_2*λ_2)/(1-δ_2) + γ_1
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exponential_term_k2 = exp(exponential_growth_term_k2*t)
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result_k2 = constant_term_k2*exponential_term_k2
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return(result_k2)
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}
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l1 <- function(t, k1_t, L_t){
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constant_term_l1 = ((q*w_2)/(1-q))^(1/(ρ-1))
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exponential_term_l1 = exp((γ_1/(ρ-1))*t)
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result_l1 = (constant_term_l1*exponential_term_l1*k1_t)/L_t
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return(result_l1)
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}
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l2 <- function(t, k2_t, L_t){
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constant_term_l2 = (1-λ_2)/(w_2*λ_2)
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exponential_term_l2 = exp(γ_1*t)
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result_l2 = (constant_term_l2*k2_t) / (exponential_term_l2*L_t)
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return(result_l2)
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}
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dL <- function(t,k2_t,L_t,l2_t){
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dynamical_term_dL= ((k2_t^λ_2)*((L_t*l2_t)^(1-λ_2)))^(δ_2)
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result_dL = r_2*L_t + β_2*exp(γ_2*t)*dynamical_term_dL
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return(result_dL)
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}
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wagesPaidOrEarned <- function(L_t, t, l1_t, l2_t){
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result_wages = L_t*w_2*exp(γ_1*t)*(1-l1_t-l2_t)
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return(result_wages)
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}
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dK <- function(t,K_t,k1_t,k2_t,L_t,l1_t,l2_t){
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result_dK = r_1*K_t - k1_t - k2_t + L_t*w_2*exp(γ_1*t)*(1-l1_t-l2_t)
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return(result_dK)
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}
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