I have a small - potentially dumb - question regarding the modeling of the Government side. In my model the Government taxes households. There are two kinds of taxes (tau): labour and capital. Accordingly, I need to specify an equation for the Government’s “problem”. My guess is : T_t = tau_h * w * h_t + tau_k * r * k_t. The variable T appears in the right-hand-side of the household’s equation as the Government is supposed to provide them with a lump-sum transfer.
My first question is how to name the variable T, do you think “Government expenditure” is correct?
Second, I have see some people model it as G_t = tau_h * w * h_t + tau_k * r * k_t + T. Could someone tell me what the difference is ? What is this G ? Is this a more appropiate way to model it ?