Btukfyl

I want to typeset these equations :

documentclass{article}

usepackage{amsmath,amssymb}

begin{document}

We have

[tilde{P}_i^{1-sigma}=sum_j^Nleft[prod_{(Mjisucc0)}tilde{p}_j^{1-sigma}theta_jprod_{k=1}^Ke^{beta_kD_{kji}}right]qquadforall j]

and

[sum_{i=1}^Nsum_{j=1}^Nleft[mathrm M_{ij}-exp(T_{ij}overset{smallfrown}{delta})right]T_{ij}=0]

as well as

[M_{ij}=frac{Y_iY_j}{Y^W}frac{prod_{h=1}^He^{delta_hD_{hji}}}{tilde P_i^{1-sigma}tilde P_j^{1-sigma}}]

also

[prod_i^{1-sigma}=sum_{j}^Nleft(frac{t_{ij}}{tilde P_j}right)^{1-sigma}cdotfrac{E_j}{Y_t}]



And these are inline:



begin{enumerate}

    item $tilde{P}_i^{1-sigma}=sum_j^Nleft[prod_{(Mjisucc0)}tilde{p}_j^{1-sigma}theta_jprod_{k=1}^Ke^{beta_kD_{kji}}right]qquadforall j$

    item $sum_{i=1}^Nsum_{j=1}^Nleft[mathrm M_{ij}-exp(T_{ij}overset{smallfrown}{delta})right]T_{ij}=0$

    item $M_{ij}=frac{Y_iY_j}{Y^W}frac{prod_{h=1}^He^{delta_hD_{hji}}}{tilde P_i^{1-sigma}tilde P_j^{1-sigma}}$

    item $prod_i^{1-sigma}=sum_{j}^Nleft(frac{t_{ij}}{tilde P_j}right)^{1-sigma}cdotfrac{E_j}{Y_t}$

end{enumerate}

end{document}