Monopolistic competition in a flexible economy VS perfect competition in a flexible economy

We can allow for full price/wage flexibility in a Calvo price/wage-setting by assuming there is 0 probability of not being able to re-optimize. Thus, all firms and/or all households re-optimize their prices and wages in each period, respectively.

But this does not mean we have perfect competition, right? Since households still have monopoly power over their wages and firms still have monopoly power over the prices they set.

So we can have monopolistic competition in a fully flexible economy which is different from perfect competition in a fully flexible economy (without Calvo pricing), right?

Yes, monopolistic competition is different from price rigidity. You cannot have meaningful price rigidities without market power (otherwise nobody would buy the good a price different from marginal costs). But monopoly power does not depend on having sticky prices.

Hi Prof. Pfeifer, many thanks for the response. Let me kindly ask this follow up question.

I have seen some papers where they simply set the probability to re-optimize to 1 to allow for full price/wages flexibility, instead of re-solving the model with prefect competition assumptions (i.e., \frac{W_t}{p_t} = MRS_{c,l} = MP_l). So although both setups will have full price/wage flexibility incorporated in them, results will be different, right? Which is prefered? Or both are ok if you are just comparing a flexible economy to a rigid.

Now it seems to me that what we really want is a flexible economy, not necessarily perfect competition. Thus, perfect competition is just a means to allow for flexibility in the economy. And thus a monopolistic competition in a fully flexible economy is also perfectly fine.

It always depends on the exercise you are trying to do. If you are only trying to analyze the effects of price rigidity, then you should obviously keep market power equal in both models.