How to find price elasticity in the following demand system? We assume that the logarithmic function of $p_i$ equals the coefficients of the demand equation $w_i$. I have the following demand system:

$$ w_{a}=-0.03-0.01 \ \ nk +0.02 \ lcons $$
$$ w_{b}=-0.26-0.004 \ nk +0.08 \ lcons $$
$$ w_{c}= \ \ \ 0.96+0.03 \ \ nk -0.14 \ lcons $$
$$ w_{d}= \ \ \ 0.30+0.001 \ nk -0.05 \ lcons $$
$$ w_{e}= \ \ \ 0.07-0.005 \ nk +0.04 \ lcons $$
$$ w_{f}=-0.05-0.01 \ \ nk +0.04 \ lcons $$

Variable $w_i$ denotes the proportion of good $i$ of the total consumption (cons) of a family, and $nk$ (number of kids) is a dummy variable. $lcons$ is the logarithm of the total consumption. Plus, I know the income of the families.

I will appreciate your help with this situation.
The price elasticity is the derivative of the demand for each good over price. Demand is lcons * (wi) for each wi.