Profit max price - did I forget how to do algebra??

I’m lost here. I have no idea how they put price in the second line since MC = MR. But even with it, I still don’t understand their explanation. Any help is appreciated.

What happens to the profit‐maximizing price for a monopoly when the expected price of the product increases dramatically and marginal product costs are unchanged?

Price goes up

Price goes down

Cannot be determined

You Answered Correctly!

In the equation that determines the optimal price for a product in a monopoly, increasing the expected sales price will decrease the optimal selling price. The profit‐maximizing level of output always occurs in the relatively elastic portion of the demand curve. This is because MC and MR will always intersect where MR is positive. We stated earlier that the relationship between MR and price elasticity is given as:


In a monopoly, MC = MR so


The monopoly can use this relationship to determine the profit‐maximizing price if it knows its cost structure and price elasticity of demand. For example, if MC is constant at $100 and market analysis indicates that Ep equals 1.25, the optimal price will be: 100/[1 − (1/1.25)] = $500