What does this $(\gamma _{0.clothes} + \gamma _{1.clothes} * \ kids)$ term mean in my linear demand equation?

Question

I have the following demand equation system (expenditure ratio model):

$w_{clothes}= \beta _ {clothes} + \alpha_{clothes} * \ kids + (\gamma _{0.clothes} + \gamma _{1.clothes} * \ kids)* \ income + u_{clothes}$

$w_{food}= \beta _ {food} + \alpha_{food} * \ kids + (\gamma _{0.food} + \gamma _{1.food} * \ kids)* \ income + u_{food}$

...

$w_{other}= \beta _ {other} + \alpha_{other} * \ kids + (\gamma _{0.other} + \gamma _{1.other} * \ kids)* \ income + u_{other}$

where $\beta_i$ and $u_i$ denotes the constants and the residuals, kids is a dummy variable (1, if the consumer has got kids), and $w_{"product"}$ is the proportion of "product" consumption of the total expenditure.

My question is, how can I interpret the term, for example, $(\gamma _{0.clothes} + \gamma _{1.clothes} * \ kids)$? Is this a dummy variable, or interaction or other? It looks like an other regression's coefficients in this equation. I have no idea, please help.

Thank you for your time and help.

Answer 1

If you multiply out any one of the equations,

$$w_{clothes}= \beta _ {clothes} + \alpha_{clothes} \cdot \ kids + (\gamma _{0.clothes} + \gamma _{1.clothes} \cdot \ kids)\cdot\ income + u_{clothes}$$

$$=\beta _ {clothes} + \alpha_{clothes} \cdot \ kids + \gamma _{0.clothes}\cdot income + \gamma _{1.clothes} \cdot \ kids\cdot\ income + u_{clothes}$$

it is evident that you have "kids" and "income" as regressors, plus an interaction term