# RBC model with monopolistic competition

Hello everyone,

I have a question on RBC model with monopolistic competition. All the textbook material about RBC model I have seen assumes a perfect competition market where the general price level is normalized to 1.

While with monopolistic competition, you have one more variable: marginal cost (MC), so what is the additional first-order condition should I add to the model?

I guessed that the condition should be p = markup* MC, but it seems not correct. If the price p is normalized to 1, then MC would be constant over time. But this is weird since a positive TFP shock should drive down the MC.

Thanks!

Hi ttc,

The condition you probably have in mind is actually the pricing rule of the form
P_{it}=\frac{\epsilon}{\epsilon-1}MC_{t}P_{t}
Dividing through by P_{t} yields
\frac{P_{it}}{P_t}=\frac{\epsilon}{\epsilon-1}MC_{t}
In the absence of nominal rigidities all firms adjust their price to the same optimal price, so price dispersion is always zero, i.e. \frac{P_{it}}{P_t}=1 in all periods. It does not prevent the marginal cost from falling in response to a positive TFP shock .

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