If the demand curve shifts right, what is the long run equilibrium effect on the market and firm?

I'm asking this question because I need to know if the answer I have is correct. My reasoning is, demand curve shifts right, marginal revenue will increase, meaning more firms enter the market. In the long run, the new firms will shift the supply curve right, lowering the marginal revenue curve down to the original curve. When the supply curve shifts right, will the market equilibrium be at the same price it was in the beginning, just at a higher quantity?