Question

Prove that for a perfectly competitive firm, P = MR

Would be greatly appreciated if answered in 5sentences please.

Answer 1

The perfect competition is a market structure with many buyers and sellers. As there is numerous buyers and sellers no one has any market power to change or set the price. Each buyer takes price as given as changing the price will change the demand instantaneously either in favor or against that particular buyer. Therefore, for any firm $\small P=\bar{P}$

The total revenue of a firm is

$\small TR=P\times Q$

For a perfectly competitive firm

$\small TR=\bar{P} \times Q$

$\small \therefore MR=\frac{\partial\left (TR \right ) }{\partial Q}=\bar{P}$............. (proved)