MC equation in RBC models


In a RBC model we know that we have the perfect competition assumption, and therefore


In some Real business cycle models researchers normalize the P_{t} to 1. Therefore


In model equations we can derive an equation for marginal cost or for price level in optimization step of the firm. When we normalize P_{t} to 1 is it necessary to write price level equation or marginal cost equation in the model block equations in Dynare ?

Because I did not see the MC equation or price level equation in model block in these type of RBC models but in New Keynesian DSGE models I know that we enter MC equation in the model block equations in Dynare and we have incomplete competition and wages and prices stickness in New Keynesian DSGE models.

When you normalize price to 1, then you don’t need to enter it. For example, with the following budget constraint P_t C_t = W_t L_t + R_t K_t, factor prices are nominal and you need price to compute real variables. With C_t = w_t L_t + r_t K_t models, prices (w_t, \;r_t) are real as you have fixed price = 1…i.e., the price does not change or vary over time. It is 1 in all periods…

I am not sure the question was well-defined. In the RBC model, the firm is a price taker, i.e. there is no explicit optimization with respect to prices and therefore no equation related it. The question whether P_t=1 is on of the numeraire. In the RBC model, only relative prices are uniquely determined.