Why is marginal revenue equal to both average revenue and price in a perfectly competitive setting?

Question

it's a 5 points question..

do i have to draw graph or something for this?

Answer 1

Firstly, I think this is a bit of a long question for only 5 marks. But I'll try to explain as best as I can. You can do it through logic or algebra.

I'll assume that you already know that a profit maximising firm produces where marginal revenue (MR)= marginal cost (MC).

A perfectly competitive market is composed by price taking firms: consumers believe that all products are identical, firms enter and leave the market freely, there is perfect information and there are no transaction costs. Since products are homogenous (or undifferentiated) no firm can charge more than another firm without losing all it's customers- therefore, firms in a perfectly competitive setting face a horizontal demand curve. Considering the firm's revenue is TR=price*qty, when the firm sells one more unit, the revenue increases just by P. (Drawing a diagram here helps)- hence the marginal revenue=P. I would then use the algebraic explanation for why AR=P

Now, I think it's easier through algebra.... so here

Total Revenue (TR)= Price(P)*Quantity(Q)

Average Revenue (AR)=TR/Q=P*Q/Q (Q's cancel out)

So AR=P

Marginal Revenue(MR)= ΔTR/ΔQ

ΔTR- since firms are price takers, P does not change. Hence we can rewrite ΔTR=P*ΔQ

So MR=ΔTR/ΔQ=P*ΔQ/ΔQ (ΔQ cancels out)

So MR=P=AR(=MC)

Hope it helps!