%RAMSEY_DYNAMICS.M %Compute analytically the Ramsey equilibrium conditions and its first derivatives, evaluate this functions at the Ramsey steady state, and compute matrices gx and hx defining a first-order approximation to the Ramsey equilbrium clear %Compute analytically the Ramsey equilibrium conditions and tis first derivatives [f, fx, fxp, fy, fyp, controlvar_cu, statevar_cu] = ramsey_eqm; disp('execution of RAMSEY_EQM.M completed') %Compute the Ramsey steady state [ALFA, ALFATIL, B, BETTA, CHI, CHITIL, DELTA, ETA, ETATIL, KAPA, NU, PHI1, PHI2, PHI3, PHI4, PSSI, THETA, GAMA1, GAMA2, TAUPROFITS, s_cu, stil_cu, assets_cu, k_cu, n_cu, g_cu, z_cu, qq_cu, hd_cu, output_cu, c_cu, la_cu, pai_cu, u_cu, f2_cu, x2_cu, r_cu, tauh_cu, tauk_cu, iv_cu, w_cu, xi1_cu, xi2_cu, xi3_cu, xi4_cu, xi5_cu, xi6_cu, xi7_cu, xi8_cu, xi9_cu, xi10_cu, xi11_cu, xi12_cu, xi13_cu, xi14_cu, xi15_cu, s_cup, stil_cup, assets_cup, k_cup, n_cup, g_cup, z_cup, qq_cup, hd_cup, output_cup, c_cup, la_cup, pai_cup, u_cup, f2_cup, x2_cup, r_cup, tauh_cup, tauk_cup, iv_cup, w_cup, xi1_cup, xi2_cup, xi3_cup, xi4_cup, xi5_cup, xi6_cup, xi7_cup, xi8_cup, xi9_cup, xi10_cup, xi11_cup, xi12_cup, xi13_cup, xi14_cup, xi15_cup, s_ba1, stil_ba1, assets_ba1, k_ba1, n_ba1, g_ba1, z_ba1, qq_ba1, hd_ba1, output_ba1, c_ba1, la_ba1, pai_ba1, u_ba1, f2_ba1, x2_ba1, r_ba1, tauh_ba1, tauk_ba1, iv_ba1, w_ba1, xi1_ba1, xi2_ba1, xi3_ba1, xi4_ba1, xi5_ba1, xi6_ba1, xi7_ba1, xi8_ba1, xi9_ba1, xi10_ba1, xi11_ba1, xi12_ba1, xi13_ba1, xi14_ba1, xi15_ba1, s_ba1p, stil_ba1p, assets_ba1p, k_ba1p, n_ba1p, g_ba1p, z_ba1p, qq_ba1p, hd_ba1p, output_ba1p, c_ba1p, la_ba1p, pai_ba1p, u_ba1p, f2_ba1p, x2_ba1p, r_ba1p, tauh_ba1p, tauk_ba1p, iv_ba1p, w_ba1p, xi1_ba1p, xi2_ba1p, xi3_ba1p, xi4_ba1p, xi5_ba1p, xi6_ba1p, xi7_ba1p, xi8_ba1p, xi9_ba1p, xi10_ba1p, xi11_ba1p, xi12_ba1p, xi13_ba1p, xi14_ba1p, xi15_ba1p, s_fu1, stil_fu1, assets_fu1, k_fu1, n_fu1, g_fu1, z_fu1, qq_fu1, hd_fu1, output_fu1, c_fu1, la_fu1, pai_fu1, u_fu1, f2_fu1, x2_fu1, r_fu1, tauh_fu1, tauk_fu1, iv_fu1, w_fu1, xi1_fu1, xi2_fu1, xi3_fu1, xi4_fu1, xi5_fu1, xi6_fu1, xi7_fu1, xi8_fu1, xi9_fu1, xi10_fu1, xi11_fu1, xi12_fu1, xi13_fu1, xi14_fu1, xi15_fu1, s_fu1p, stil_fu1p, assets_fu1p, k_fu1p, n_fu1p, g_fu1p, z_fu1p, qq_fu1p, hd_fu1p, output_fu1p, c_fu1p, la_fu1p, pai_fu1p, u_fu1p, f2_fu1p, x2_fu1p, r_fu1p, tauh_fu1p, tauk_fu1p, iv_fu1p, w_fu1p, xi1_fu1p, xi2_fu1p, xi3_fu1p, xi4_fu1p, xi5_fu1p, xi6_fu1p, xi7_fu1p, xi8_fu1p, xi9_fu1p, xi10_fu1p, xi11_fu1p, xi12_fu1p, xi13_fu1p, xi14_fu1p, xi15_fu1p, s_ba2, stil_ba2, assets_ba2, k_ba2, n_ba2, g_ba2, z_ba2, qq_ba2, hd_ba2, output_ba2, c_ba2, la_ba2, pai_ba2, u_ba2, f2_ba2, x2_ba2, r_ba2, tauh_ba2, tauk_ba2, iv_ba2, w_ba2, xi1_ba2, xi2_ba2, xi3_ba2, xi4_ba2, xi5_ba2, xi6_ba2, xi7_ba2, xi8_ba2, xi9_ba2, xi10_ba2, xi11_ba2, xi12_ba2, xi13_ba2, xi14_ba2, xi15_ba2, s_ba2p, stil_ba2p, assets_ba2p, k_ba2p, n_ba2p, g_ba2p, z_ba2p, qq_ba2p, hd_ba2p, output_ba2p, c_ba2p, la_ba2p, pai_ba2p, u_ba2p, f2_ba2p, x2_ba2p, r_ba2p, tauh_ba2p, tauk_ba2p, iv_ba2p, w_ba2p, xi1_ba2p, xi2_ba2p, xi3_ba2p, xi4_ba2p, xi5_ba2p, xi6_ba2p, xi7_ba2p, xi8_ba2p, xi9_ba2p, xi10_ba2p, xi11_ba2p, xi12_ba2p, xi13_ba2p, xi14_ba2p, xi15_ba2p, MC, RK, N, G, RHOG, RHOZ, RHON, STD_EPSG, STD_EPSZ, STD_EPSN, dist, exitflag] = ramsey_ss; disp('first execution of RAMSEY_SS.M completed') %Convert to logs u_cu =log(u_cu); tauh_cu = -log(1-tauh_cu); tauk_cu = -log(1-tauk_cu);; z_cu = log(z_cu); qq_cu = log(qq_cu); r_cu = log(r_cu); s_cu = log(s_cu); hd_cu = log(hd_cu); stil_cu = log(stil_cu); k_cu = log(k_cu); iv_cu = log(iv_cu); w_cu = log(w_cu); output_cu = log(output_cu); g_cu = log(g_cu); n_cu = log(n_cu); assets_cu = log(assets_cu); c_cu = log(c_cu); la_cu = log(la_cu); pai_cu = log(pai_cu); f2_cu = log(f2_cu); x2_cu = log(x2_cu); xi1_cu = log(xi1_cu); xi2_cu = log(xi2_cu); xi3_cu = log(xi3_cu); xi4_cu = log(xi4_cu); xi5_cu = log(xi5_cu); xi6_cu = log(xi6_cu); xi7_cu = log(xi7_cu); xi8_cu = log(xi8_cu); xi9_cu = log(xi9_cu); xi10_cu = log(xi10_cu); xi11_cu = log(xi11_cu); xi12_cu = log(xi12_cu); xi13_cu = log(xi13_cu); xi14_cu = log(xi14_cu); xi15_cu = log(xi15_cu); u_cup =log(u_cup); tauh_cup = -log(1-tauh_cup); tauk_cup = -log(1-tauk_cup);; z_cup = log(z_cup); qq_cup = log(qq_cup); r_cup = log(r_cup); s_cup = log(s_cup); hd_cup = log(hd_cup); stil_cup = log(stil_cup); k_cup = log(k_cup); iv_cup = log(iv_cup); w_cup = log(w_cup); output_cup = log(output_cup); g_cup = log(g_cup); n_cup = log(n_cup); assets_cup = log(assets_cup); c_cup = log(c_cup); la_cup = log(la_cup); pai_cup = log(pai_cup); f2_cup = log(f2_cup); x2_cup = log(x2_cup); xi1_cup = log(xi1_cup); xi2_cup = log(xi2_cup); xi3_cup = log(xi3_cup); xi4_cup = log(xi4_cup); xi5_cup = log(xi5_cup); xi6_cup = log(xi6_cup); xi7_cup = log(xi7_cup); xi8_cup = log(xi8_cup); xi9_cup = log(xi9_cup); xi10_cup = log(xi10_cup); xi11_cup = log(xi11_cup); xi12_cup = log(xi12_cup); xi13_cup = log(xi13_cup); xi14_cup = log(xi14_cup); xi15_cup = log(xi15_cup); u_ba1 =log(u_ba1); tauh_ba1 = -log(1-tauh_ba1); tauk_ba1 = -log(1-tauk_ba1);; z_ba1 = log(z_ba1); qq_ba1 = log(qq_ba1); r_ba1 = log(r_ba1); s_ba1 = log(s_ba1); hd_ba1 = log(hd_ba1); stil_ba1 = log(stil_ba1); k_ba1 = log(k_ba1); iv_ba1 = log(iv_ba1); w_ba1 = log(w_ba1); output_ba1 = log(output_ba1); g_ba1 = log(g_ba1); n_ba1 = log(n_ba1); assets_ba1 = log(assets_ba1); c_ba1 = log(c_ba1); la_ba1 = log(la_ba1); pai_ba1 = log(pai_ba1); f2_ba1 = log(f2_ba1); x2_ba1 = log(x2_ba1); xi1_ba1 = log(xi1_ba1); xi2_ba1 = log(xi2_ba1); xi3_ba1 = log(xi3_ba1); xi4_ba1 = log(xi4_ba1); xi5_ba1 = log(xi5_ba1); xi6_ba1 = log(xi6_ba1); xi7_ba1 = log(xi7_ba1); xi8_ba1 = log(xi8_ba1); xi9_ba1 = log(xi9_ba1); xi10_ba1 = log(xi10_ba1); xi11_ba1 = log(xi11_ba1); xi12_ba1 = log(xi12_ba1); xi13_ba1 = log(xi13_ba1); xi14_ba1 = log(xi14_ba1); xi15_ba1 = log(xi15_ba1); u_ba1p =log(u_ba1p); tauh_ba1p = -log(1-tauh_ba1p); tauk_ba1p = -log(1-tauk_ba1p);; z_ba1p = log(z_ba1p); qq_ba1p = log(qq_ba1p); r_ba1p = log(r_ba1p); s_ba1p = log(s_ba1p); hd_ba1p = log(hd_ba1p); stil_ba1p = log(stil_ba1p); k_ba1p = log(k_ba1p); iv_ba1p = log(iv_ba1p); w_ba1p = log(w_ba1p); output_ba1p = log(output_ba1p); g_ba1p = log(g_ba1p); n_ba1p = log(n_ba1p); assets_ba1p = log(assets_ba1p); c_ba1p = log(c_ba1p); la_ba1p = log(la_ba1p); pai_ba1p = log(pai_ba1p); f2_ba1p = log(f2_ba1p); x2_ba1p = log(x2_ba1p); xi1_ba1p = log(xi1_ba1p); xi2_ba1p = log(xi2_ba1p); xi3_ba1p = log(xi3_ba1p); xi4_ba1p = log(xi4_ba1p); xi5_ba1p = log(xi5_ba1p); xi6_ba1p = log(xi6_ba1p); xi7_ba1p = log(xi7_ba1p); xi8_ba1p = log(xi8_ba1p); xi9_ba1p = log(xi9_ba1p); xi10_ba1p = log(xi10_ba1p); xi11_ba1p = log(xi11_ba1p); xi12_ba1p = log(xi12_ba1p); xi13_ba1p = log(xi13_ba1p); xi14_ba1p = log(xi14_ba1p); xi15_ba1p = log(xi15_ba1p); u_ba2 =log(u_ba2); tauh_ba2 = -log(1-tauh_ba2); tauk_ba2 = -log(1-tauk_ba2);; z_ba2 = log(z_ba2); qq_ba2 = log(qq_ba2); r_ba2 = log(r_ba2); s_ba2 = log(s_ba2); hd_ba2 = log(hd_ba2); stil_ba2 = log(stil_ba2); k_ba2 = log(k_ba2); iv_ba2 = log(iv_ba2); w_ba2 = log(w_ba2); output_ba2 = log(output_ba2); g_ba2 = log(g_ba2); n_ba2 = log(n_ba2); assets_ba2 = log(assets_ba2); c_ba2 = log(c_ba2); la_ba2 = log(la_ba2); pai_ba2 = log(pai_ba2); f2_ba2 = log(f2_ba2); x2_ba2 = log(x2_ba2); xi1_ba2 = log(xi1_ba2); xi2_ba2 = log(xi2_ba2); xi3_ba2 = log(xi3_ba2); xi4_ba2 = log(xi4_ba2); xi5_ba2 = log(xi5_ba2); xi6_ba2 = log(xi6_ba2); xi7_ba2 = log(xi7_ba2); xi8_ba2 = log(xi8_ba2); xi9_ba2 = log(xi9_ba2); xi10_ba2 = log(xi10_ba2); xi11_ba2 = log(xi11_ba2); xi12_ba2 = log(xi12_ba2); xi13_ba2 = log(xi13_ba2); xi14_ba2 = log(xi14_ba2); xi15_ba2 = log(xi15_ba2); u_ba2p =log(u_ba2p); tauh_ba2p = -log(1-tauh_ba2p); tauk_ba2p = -log(1-tauk_ba2p);; z_ba2p = log(z_ba2p); qq_ba2p = log(qq_ba2p); r_ba2p = log(r_ba2p); s_ba2p = log(s_ba2p); hd_ba2p = log(hd_ba2p); stil_ba2p = log(stil_ba2p); k_ba2p = log(k_ba2p); iv_ba2p = log(iv_ba2p); w_ba2p = log(w_ba2p); output_ba2p = log(output_ba2p); g_ba2p = log(g_ba2p); n_ba2p = log(n_ba2p); assets_ba2p = log(assets_ba2p); c_ba2p = log(c_ba2p); la_ba2p = log(la_ba2p); pai_ba2p = log(pai_ba2p); f2_ba2p = log(f2_ba2p); x2_ba2p = log(x2_ba2p); xi1_ba2p = log(xi1_ba2p); xi2_ba2p = log(xi2_ba2p); xi3_ba2p = log(xi3_ba2p); xi4_ba2p = log(xi4_ba2p); xi5_ba2p = log(xi5_ba2p); xi6_ba2p = log(xi6_ba2p); xi7_ba2p = log(xi7_ba2p); xi8_ba2p = log(xi8_ba2p); xi9_ba2p = log(xi9_ba2p); xi10_ba2p = log(xi10_ba2p); xi11_ba2p = log(xi11_ba2p); xi12_ba2p = log(xi12_ba2p); xi13_ba2p = log(xi13_ba2p); xi14_ba2p = log(xi14_ba2p); xi15_ba2p = log(xi15_ba2p); u_fu1 =log(u_fu1); tauh_fu1 = -log(1-tauh_fu1); tauk_fu1 = -log(1-tauk_fu1);; z_fu1 = log(z_fu1); qq_fu1 = log(qq_fu1); r_fu1 = log(r_fu1); s_fu1 = log(s_fu1); hd_fu1 = log(hd_fu1); stil_fu1 = log(stil_fu1); k_fu1 = log(k_fu1); iv_fu1 = log(iv_fu1); w_fu1 = log(w_fu1); output_fu1 = log(output_fu1); g_fu1 = log(g_fu1); n_fu1 = log(n_fu1); assets_fu1 = log(assets_fu1); c_fu1 = log(c_fu1); la_fu1 = log(la_fu1); pai_fu1 = log(pai_fu1); f2_fu1 = log(f2_fu1); x2_fu1 = log(x2_fu1); xi1_fu1 = log(xi1_fu1); xi2_fu1 = log(xi2_fu1); xi3_fu1 = log(xi3_fu1); xi4_fu1 = log(xi4_fu1); xi5_fu1 = log(xi5_fu1); xi6_fu1 = log(xi6_fu1); xi7_fu1 = log(xi7_fu1); xi8_fu1 = log(xi8_fu1); xi9_fu1 = log(xi9_fu1); xi10_fu1 = log(xi10_fu1); xi11_fu1 = log(xi11_fu1); xi12_fu1 = log(xi12_fu1); xi13_fu1 = log(xi13_fu1); xi14_fu1 = log(xi14_fu1); xi15_fu1 = log(xi15_fu1); u_fu1p =log(u_fu1p); tauh_fu1p = -log(1-tauh_fu1p); tauk_fu1p = -log(1-tauk_fu1p);; z_fu1p = log(z_fu1p); qq_fu1p = log(qq_fu1p); r_fu1p = log(r_fu1p); s_fu1p = log(s_fu1p); hd_fu1p = log(hd_fu1p); stil_fu1p = log(stil_fu1p); k_fu1p = log(k_fu1p); iv_fu1p = log(iv_fu1p); w_fu1p = log(w_fu1p); output_fu1p = log(output_fu1p); g_fu1p = log(g_fu1p); n_fu1p = log(n_fu1p); assets_fu1p = log(assets_fu1p); c_fu1p = log(c_fu1p); la_fu1p = log(la_fu1p); pai_fu1p = log(pai_fu1p); f2_fu1p = log(f2_fu1p); x2_fu1p = log(x2_fu1p); xi1_fu1p = log(xi1_fu1p); xi2_fu1p = log(xi2_fu1p); xi3_fu1p = log(xi3_fu1p); xi4_fu1p = log(xi4_fu1p); xi5_fu1p = log(xi5_fu1p); xi6_fu1p = log(xi6_fu1p); xi7_fu1p = log(xi7_fu1p); xi8_fu1p = log(xi8_fu1p); xi9_fu1p = log(xi9_fu1p); xi10_fu1p = log(xi10_fu1p); xi11_fu1p = log(xi11_fu1p); xi12_fu1p = log(xi12_fu1p); xi13_fu1p = log(xi13_fu1p); xi14_fu1p = log(xi14_fu1p); xi15_fu1p = log(xi15_fu1p); nf=eval(f); nfx =eval(fx); nfxp = eval(fxp); nfy = eval(fy); nfyp = eval(fyp); %compute matrices defining the first-order approximation to the equilibrium evolution of the sate vector (hx) and of the control vector (gx). [gx,hx] = gx_hx(nfy,nfx,nfyp,nfxp); disp('execution of GX_HX.M completed') %Evaluate variables in levels again [ALFA, ALFATIL, B, BETTA, CHI, CHITIL, DELTA, ETA, ETATIL, KAPA, NU, PHI1, PHI2, PHI3, PHI4, PSSI, THETA, GAMA1, GAMA2, TAUPROFITS, s_cu, stil_cu, assets_cu, k_cu, n_cu, g_cu, z_cu, qq_cu, hd_cu, output_cu, c_cu, la_cu, pai_cu, u_cu, f2_cu, x2_cu, r_cu, tauh_cu, tauk_cu, iv_cu, w_cu, xi1_cu, xi2_cu, xi3_cu, xi4_cu, xi5_cu, xi6_cu, xi7_cu, xi8_cu, xi9_cu, xi10_cu, xi11_cu, xi12_cu, xi13_cu, xi14_cu, xi15_cu, s_cup, stil_cup, assets_cup, k_cup, n_cup, g_cup, z_cup, qq_cup, hd_cup, output_cup, c_cup, la_cup, pai_cup, u_cup, f2_cup, x2_cup, r_cup, tauh_cup, tauk_cup, iv_cup, w_cup, xi1_cup, xi2_cup, xi3_cup, xi4_cup, xi5_cup, xi6_cup, xi7_cup, xi8_cup, xi9_cup, xi10_cup, xi11_cup, xi12_cup, xi13_cup, xi14_cup, xi15_cup, s_ba1, stil_ba1, assets_ba1, k_ba1, n_ba1, g_ba1, z_ba1, qq_ba1, hd_ba1, output_ba1, c_ba1, la_ba1, pai_ba1, u_ba1, f2_ba1, x2_ba1, r_ba1, tauh_ba1, tauk_ba1, iv_ba1, w_ba1, xi1_ba1, xi2_ba1, xi3_ba1, xi4_ba1, xi5_ba1, xi6_ba1, xi7_ba1, xi8_ba1, xi9_ba1, xi10_ba1, xi11_ba1, xi12_ba1, xi13_ba1, xi14_ba1, xi15_ba1, s_ba1p, stil_ba1p, assets_ba1p, k_ba1p, n_ba1p, g_ba1p, z_ba1p, qq_ba1p, hd_ba1p, output_ba1p, c_ba1p, la_ba1p, pai_ba1p, u_ba1p, f2_ba1p, x2_ba1p, r_ba1p, tauh_ba1p, tauk_ba1p, iv_ba1p, w_ba1p, xi1_ba1p, xi2_ba1p, xi3_ba1p, xi4_ba1p, xi5_ba1p, xi6_ba1p, xi7_ba1p, xi8_ba1p, xi9_ba1p, xi10_ba1p, xi11_ba1p, xi12_ba1p, xi13_ba1p, xi14_ba1p, xi15_ba1p, s_fu1, stil_fu1, assets_fu1, k_fu1, n_fu1, g_fu1, z_fu1, qq_fu1, hd_fu1, output_fu1, c_fu1, la_fu1, pai_fu1, u_fu1, f2_fu1, x2_fu1, r_fu1, tauh_fu1, tauk_fu1, iv_fu1, w_fu1, xi1_fu1, xi2_fu1, xi3_fu1, xi4_fu1, xi5_fu1, xi6_fu1, xi7_fu1, xi8_fu1, xi9_fu1, xi10_fu1, xi11_fu1, xi12_fu1, xi13_fu1, xi14_fu1, xi15_fu1, s_fu1p, stil_fu1p, assets_fu1p, k_fu1p, n_fu1p, g_fu1p, z_fu1p, qq_fu1p, hd_fu1p, output_fu1p, c_fu1p, la_fu1p, pai_fu1p, u_fu1p, f2_fu1p, x2_fu1p, r_fu1p, tauh_fu1p, tauk_fu1p, iv_fu1p, w_fu1p, xi1_fu1p, xi2_fu1p, xi3_fu1p, xi4_fu1p, xi5_fu1p, xi6_fu1p, xi7_fu1p, xi8_fu1p, xi9_fu1p, xi10_fu1p, xi11_fu1p, xi12_fu1p, xi13_fu1p, xi14_fu1p, xi15_fu1p, s_ba2, stil_ba2, assets_ba2, k_ba2, n_ba2, g_ba2, z_ba2, qq_ba2, hd_ba2, output_ba2, c_ba2, la_ba2, pai_ba2, u_ba2, f2_ba2, x2_ba2, r_ba2, tauh_ba2, tauk_ba2, iv_ba2, w_ba2, xi1_ba2, xi2_ba2, xi3_ba2, xi4_ba2, xi5_ba2, xi6_ba2, xi7_ba2, xi8_ba2, xi9_ba2, xi10_ba2, xi11_ba2, xi12_ba2, xi13_ba2, xi14_ba2, xi15_ba2, s_ba2p, stil_ba2p, assets_ba2p, k_ba2p, n_ba2p, g_ba2p, z_ba2p, qq_ba2p, hd_ba2p, output_ba2p, c_ba2p, la_ba2p, pai_ba2p, u_ba2p, f2_ba2p, x2_ba2p, r_ba2p, tauh_ba2p, tauk_ba2p, iv_ba2p, w_ba2p, xi1_ba2p, xi2_ba2p, xi3_ba2p, xi4_ba2p, xi5_ba2p, xi6_ba2p, xi7_ba2p, xi8_ba2p, xi9_ba2p, xi10_ba2p, xi11_ba2p, xi12_ba2p, xi13_ba2p, xi14_ba2p, xi15_ba2p, MC, RK, N, G, RHOG, RHOZ, RHON, STD_EPSG, STD_EPSZ, STD_EPSN, dist, exitflag] = ramsey_ss; disp('second execution of RAMSEY_SS.M completed') %evaluate vector of states and controls nstatevar = eval(statevar_cu(:)); ncontrolvar = eval(controlvar_cu(:));