# Multiple equations, derivatives in gather environment

I'm so frustrated with using latex to input mathematical equations. Now I have been noticed that the error"! LaTeX Error: Bad math environment delimiter." and the error with\gather.

 \documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
\begin{gather}
\intertext{The Household Problem:}
V(k_e,k_s;s,z,q)=\max_{c_t,l_t,h_t,k_e^(t+1),k_s^(t+1)}\{U(c_t,l_t)+\beta
E$V(k_e^(t+1),k_s^(t+1;s^(t+1),z^(t+1),q^(t+1))$ \\
\shortintertext{subject to}
\begin{split}
c+k_e^(t+1)/q+k_s^(t+1)&=(1-\tau_k)[R_e(\lambda)hk_e+R_S(\lambda)k_s]\\
&+(1-\tau_l)W(\lambda)l+(1-\delta_e(h))k_e/q+(1-\delta_s)k_s+T_(\lambda)\\
& -A_s(k_s^(t+1),k_s)-A_e(k_e^(t+1)/q,k_e/q;\eta),
\end{split}
\intertext{and s^(t+1)=S(\delta)}
\intertext{Form a period t+1 value Lagrangian:}
\begin{split}
\mathcal{L} & =E_0\sum\limits_{t=0}^\infty \beta^t U(c_t,l_t)+\Lambda_t\{(1-
\tau_k^t)(r_e^t h k_e^t +r_s^tk_s^t) \\
& +(1-\tau_l^t)W(\lambda)l+(1-\delta_e(h))k_e/q+(1-
\delta_s)k_s+T_(\lambda)\\
& -A_s(k_s^(t+1),k_s)-A_e(k_e^(t+1)/q,k_e/q;\eta)-c_t -k_e^(t+1)/q -
k_s^(t+1)\}\\
\end{split}
\intertext{First Order Conditions Of Household:}
\frac{\partial\mathcal{L}_(t+1)}{c_t} = \beta\theta\frac{1}{c_t}=\Lambda_t\\
\frac{\partial\mathcal{L}_(t+1)}{l_t} =\frac{\beta(1-\theta)}{l_t-
1}=\Lambda_t
\tau_l^tw_t(\lambda)\\
\frac{\partial\mathcal{L}_(t+1)}{k_s^(t+1)} =2\phi_s k_s^t+1-2(k_s^t)^2-
k_s^t=0\\
\frac{\partial\mathcal{L}_(t+1)}{k_e^(t+1)} =2e^\eta\phi_tk_e^t+1-2\kappa_e
k_e^t-k_e^tq=0\\
\frac{\partial\mathcal{L}_(t+1)}{h_t} =\r_e^t=\frac{1}{q(1-\tau_k^t)}
bh^\omega-1\\
\intertext{Dynamic Budget Constraints:}
\begin{split}
c_t &= k_e^{(t+1)}\frac{1}{q}+k_s^{(t+1)}+(1-\tau_k^t)(r_ehk_e+r_sk_s)+(1-
\tau_l)wl \\
\end{split}
\intertext{First Order Conditions Of Firms:}
\shortintertext{F.O.C with respect to k_e:}r_e=\alpha_e z h^{(\alpha_e-1)}
k_e^{(\alpha_e-1)}k_s^{\alpha_s}l^{(1-\alpha_e-\alpha_s)}\\
\shortintertext{F.O.C with respect to k_s:}r_s=\alpha_s z h^{(\alpha_e)}
k_e^{\alpha_e} k_s^{(\alpha_s-1)}l^{(1-\alpha_e-\alpha_s)}\\
\shortintertext{F.O.C with respect to l:}w=(1-\alpha_e-\alpha_s)z
h^{\alpha_e}k_e^{\alpha_e}k_s^{\alpha_s}\\
\shortintertext{F.O.C with respect to h:}r_e\widetilde{k_e}=\alpha_e z
h^{(\alpha_e-1)}k_e^{\alpha_e} k_s^{\alpha_s} l^{(1-\alpha_e-\alpha_s)}\\
\ln{z_{(t+1)}}=(1
\rho_a)\ln{\overline{z}}+\rho_a\ln{z_t}+\varepsilon_{(a,t)}\\
\intertext{Government:}
\tau=\tau_k(r_e h k_e +r_s k_s)+\tau_e wl
\end{gather}
\end{document}


I spent about one hour but still could't figure out so come to here to ask questions. I sincerely appreciate your help!

• In your code there are many errors: for example it is k_s^{t+1} instead of k_s^(t+1). Apr 1, 2018 at 22:05
• the main error is you have \] which is end pf equation instruction on the second line of the mathematics Apr 1, 2018 at 22:08
• I corrected them but still can't run. It is my second time to use \latex, however, I have to master it ASAP. Thank you!!!
– E.K
Apr 1, 2018 at 22:13
• @E.K, mastering latex is far from being easy, it requires years to only relatively well use a small portion of it. Start small, then try to expand your knowledge step by step. Apr 1, 2018 at 22:49
• Yes, I also want to learn through that way but the seminar requires everyone use Latex, which I first heard about. Thank you so much for your comments.
– E.K
Apr 2, 2018 at 23:10

How are you entering these codes? there were tex errors on more or less every line, spurious \] mis-matched } and missing  around nested math expressions in text. It is hard to debug a big alignment like gather or align as the errors are reported at the end, but if you add the expressions one line at a time and fix each error as it is reported you would not get into such a position.  \documentclass{article} \usepackage{amsmath} \usepackage{mathtools} \begin{document} \begin{gather} \intertext{The Household Problem:} V(k_e,k_s;s,z,q)=\max_{c_t,l_t,h_t,k_e^{t+1},k_s^{t+1}} U(c_t,l_t)+\beta E[V(k_e^{t+1},k_s^(t+1;s^{t+1},z^{t+1},q^{t+1})]\\ \shortintertext{subject to} \begin{split} c+k_e^{t+1}/q+k_s^{t+1}&=(1-\tau_k)[R_e(\lambda)hk_e+R_S(\lambda)k_s]\\ &+(1-\tau_l)W(\lambda)l+(1-\delta_e(h))k_e/q+(1-\delta_s)k_s+T_{\lambda}\\ & -A_s(k_s^{t+1},k_s)-A_e(k_e^{t+1}/q,k_e/q;\eta), \end{split}\\ \intertext{ands^{t+1}=S(\delta)$} \intertext{Form a period$t+1$value Lagrangian:} \begin{split} \mathcal{L} & =E_0\sum\limits_{t=0}^\infty \beta^t U(c_t,l_t)+\Lambda_t\{(1- \tau_k^t)(r_e^t h k_e^t +r_s^tk_s^t) \\ & +(1-\tau_l^t)W(\lambda)l+(1-\delta_e(h))k_e/q+(1- \delta_s)k_s+T_{\lambda}\\ & -A_s(k_s^{t+1},k_s)-A_e(k_e^{t+1}/q,k_e/q;\eta)-c_t -k_e^{t+1}/q - k_s^{t+1}\}\\ \end{split}\\ \intertext{First Order Conditions Of Household:} \frac{\partial\mathcal{L}_{t+1}}{c_t} = \beta\theta\frac{1}{c_t}=\Lambda_t\\ \frac{\partial\mathcal{L}_{t+1}}{l_t} =\frac{\beta(1-\theta)}{l_t- 1}=\Lambda_t \tau_l^tw_t(\lambda)\\ \frac{\partial\mathcal{L}_{t+1}}{k_s^{t+1}} =2\phi_s k_s^t+1-2(k_s^t)^2- k_s^t=0\\ \frac{\partial\mathcal{L}_{t+1}}{k_e^{t+1}} =2e^\eta\phi_tk_e^t+1-2\kappa_e k_e^t-k_e^tq=0\\ \frac{\partial\mathcal{L}_{t+1}}{h_t} =r_e^t=\frac{1}{q(1-\tau_k^t)} bh^\omega-1\\ k_e^{t+1}=(1-\delta_s)k_s^t+i_s^t,\quad 0<\delta_s<1\\ \intertext{Dynamic Budget Constraints:} \begin{split}\\ c_t &= k_e^{(t+1)}\frac{1}{q}+k_s^{(t+1)}+(1-\tau_k^t)(r_ehk_e+r_sk_s)+(1- \tau_l)wl \\ &\quad+ (1-\lambda_e(h))k_e/q+(1-\lambda_s)k_s+T(\lambda)\\ &\quad- A_s(k_s^{(t+1)},k_s)-A_e(k_e^{(t+1)}/q,k_e/q;\eta) \end{split} \\Transversality\quad Condition \intertext{First Order Conditions Of Firms:} \shortintertext{F.O.C with respect to$k_e$:} r_e=\alpha_e z h^{(\alpha_e-1)} k_e^{(\alpha_e-1)}k_s^{\alpha_s}l^{(1-\alpha_e-\alpha_s)}\\ \shortintertext{F.O.C with respect to$k_s$:} r_s=\alpha_s z h^{(\alpha_e)} k_e^{\alpha_e} k_s^{(\alpha_s-1)}l^{(1-\alpha_e-\alpha_s)}\\ \shortintertext{F.O.C with respect to l:} w=(1-\alpha_e-\alpha_s)z h^{\alpha_e}k_e^{\alpha_e}k_s^{\alpha_s}\\ \shortintertext{F.O.C with respect to$h$:} r_e\widetilde{k_e}=\alpha_e z h^{(\alpha_e-1)}k_e^{\alpha_e} k_s^{\alpha_s} l^{(1-\alpha_e-\alpha_s)}\\ \ln{z_{(t+1)}}=(1 \rho_a)\ln{\overline{z}}+\rho_a\ln{z_t}+\varepsilon_{(a,t)}\\ \intertext{Government:} \tau=\tau_k(r_e h k_e +r_s k_s)+\tau_e wl\\ \end{gather} \end{document}  • David,YOU ARE MY HERO! – E.K Apr 1, 2018 at 22:23 • @E.K pleasse see the notes I added to my answer Apr 1, 2018 at 22:25 • Yes, I did. I sincerely appreciate your help . – E.K Apr 2, 2018 at 23:08 I would use no “intertext” at all. Note that exponents should be like ^{t+1} rather than ^(t+1) (similarly for subscripts). Also \[ is not a bracket. \documentclass{article} \usepackage{amsmath} \usepackage{mathtools} \begin{document} The Household Problem: $$V(k_e,k_s;s,z,q)= \max_{\substack{c_t,l_t,h_t,\\k_e^{t+1},k_s^{t+1}}} \{U(c_t,l_t)+\beta E[V(k_e^{t+1},k_s^{t+1};s^{t+1},z^{t+1},q^{t+1})]$$ subject to $$\begin{split} c+k_e^{t+1}/q+k_s^{t+1}&=(1-\tau_k)[R_e(\lambda)hk_e+R_S(\lambda)k_s]\\ &+(1-\tau_l)W(\lambda)l+(1-\delta_e(h))k_e/q+(1-\delta_s)k_s+T(\lambda)\\ & -A_s(k_s^{t+1},k_s)-A_e(k_e^{t+1}/q,k_e/q;\eta),\\ s^{t+1}&=S(\delta) \end{split}$$ Form a period$t+1value Lagrangian: $$\begin{split} \mathcal{L} & =E_0\sum\limits_{t=0}^\infty \beta^t U(c_t,l_t)+\Lambda_t\{(1- \tau_k^t)(r_e^t h k_e^t +r_s^tk_s^t) \\ & +(1-\tau_l^t)W(\lambda)l+(1-\delta_e(h))k_e/q+(1- \delta_s)k_s+T(\lambda)\\ & -A_s(k_s^{t+1},k_s)-A_e(k_e^{t+1}/q,k_e/q;\eta)-c_t -k_e^{t+1}/q - k_s^{t+1} \end{split}$$ First Order Conditions Of Household: \begin{align} \frac{\partial\mathcal{L}_{t+1}}{c_t} &= \beta\theta\frac{1}{c_t}=\Lambda_t\\ \frac{\partial\mathcal{L}_{t+1}}{l_t} &=\frac{\beta(1-\theta)}{l_t-1}=\Lambda_t \tau_l^tw_t(\lambda)\\ \frac{\partial\mathcal{L}_{t+1}}{k_s^{t+1}} &=2\phi_s k_s^t+1-2(k_s^t)^2- k_s^t=0\\ \frac{\partial\mathcal{L}_{t+1}}{k_e^{t+1}} &=2e^\eta\phi_tk_e^t+1-2\kappa_e k_e^t-k_e^tq=0\\ \frac{\partial\mathcal{L}_{t+1}}{h_t} &=r_e^t=\frac{1}{q(1-\tau_k^t)} bh^\omega-1\\ k_e^{t+1}&=(1-\delta_s)k_s^t+i_s^t,\quad 0<\delta_s<1 \end{align} Dynamic Budget Constraints: $$\begin{split} c_t &= k_e^{(t+1)}\frac{1}{q}+k_s^{(t+1)}+(1-\tau_k^t)(r_ehk_e+r_sk_s)+(1- \tau_l)wl \\ &\quad+ (1-\lambda_e(h))k_e/q+(1-\lambda_s)k_s+T(\lambda)\\ &\quad- A_s(k_s^{(t+1)},k_s)-A_e(k_e^{(t+1)}/q,k_e/q;\eta) \end{split}$$ First Order Conditions Of Firms: \begin{align} r_e&=\alpha_e z h^{(\alpha_e-1)} k_e^{(\alpha_e-1)}k_s^{\alpha_s}l^{(1-\alpha_e-\alpha_s)} &&\text{(with respect tok_e$)}\\ r_s&=\alpha_s z h^{(\alpha_e)} k_e^{\alpha_e} k_s^{(\alpha_s-1)}l^{(1-\alpha_e-\alpha_s)} &&\text{(with respect to$k_s$)}\\ w&=(1-\alpha_e-\alpha_s)z h^{\alpha_e}k_e^{\alpha_e}k_s^{\alpha_s} &&\text{(with respect to$l$)}\\ r_e\widetilde{k_e}&=\alpha_e z h^{(\alpha_e-1)}k_e^{\alpha_e} k_s^{\alpha_s} l^{(1-\alpha_e-\alpha_s)} &&\text{(with respect to$h)}\\ \ln{z_{t+1}}&=(1-\rho_a)\ln{\overline{z}}+\rho_a\ln{z_t}+\varepsilon_{(a,t)} \end{align} Government: $$\tau=\tau_k(r_e h k_e +r_s k_s)+\tau_e wl$$ \end{document}  • I used because I followed an example given by others. Thank you so much. – E.K Apr 2, 2018 at 23:11 • @E.K Separating the various parts allows for much greater flexibility. Apr 2, 2018 at 23:14 i only try to correct errors in your first two equations and improve their appearance. In this i introduce new environments \substack{...} and replace split with multlined: \documentclass{article} %\usepackage{amsmath} \usepackage{mathtools}% also load amsmath \begin{document} \noindent The Household Problem: \begin{gather} \begin{multlined}[0.8\linewidth] V(k_e,k_s;s,z,q) = \max_{\substack{c_t,l_t,h_t,\\ k_e^{(t+1)},k_s^(t+1)}} \{U(c_t,l_t)\} \\ + \beta E\Bigl[V\bigl(k_e^{(t+1)}, k_s^{(t+1)}; s^{(t+1)}, z^{(t+1)}, q^{(t+1)}\bigr)\Bigr] \end{multlined} \shortintertext{subject to} \begin{multlined}[0.8\linewidth] c+k_e^{(t+1)}/q+k_s^{(t+1)} = (1-\tau_k)\bigl[R_e(\lambda)hk_e+R_S(\lambda)k_s\bigr] \\ +(1-\tau_l)W(\lambda)l+(1-\delta_e(h))k_e/q+(1-\delta_s)k_s+T_(\lambda)\\ - A_s\bigl(k_s^{(t+1)},k_s)-A_e(k_e^{(t+1)}/q,k_e/q;\eta\bigr), \end{multlined} \intertext{ands^{(t+1)}=S(\delta)$. Form a period$t+1\$ value Lagrangian:}
\vdots
\end{gather}
\end{document}


similar cleaning of errors are required in all remaining rows. this task i left to you, if you interested for shoved approach of writing your equations.

main errors are noted in David Carlisle answer.

• Thank you for your new way to fix my errors. Wish you a good day.:-)
– E.K
Apr 2, 2018 at 23:12