MC equation in RBC models

General DSGE Modeling
1

Hi.

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

P_{t}=MC_{t}

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

P_{t}=MC_{t}=1

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.

2

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…

3

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.