# Monopoly - Where is the Markup formula derived from?

Problem:

My lecturer wrote the marginal revenue formula before writing the markup formula, indicating some sort of similarity between the two.

How it was written on the board:

Market Power being $\text{P>MC}$

$\text{MR} = \text{P (1+1/η) = MC}$ (This being profit maximising condition for a monopoly)

Can be written as:

$\text{MC/P = 1+1/η}$

Markup: $\text{(P-MC/P)= -1/η}$

Question:

As much as I can see the similarity, I can't understand how he got to $\text{(P-MC/P)= -1/η}$ from $\text{MC/P = 1+1/η}$?

Index:

P = Price, MR = Marginal Revenue, MC = Marginal Cost, η = Elasticity

• Perhaps it was or supposed to be $\frac{P - MC}{P} = - \frac{1}{\eta}$? Jan 18, 2018 at 1:55
• The markup formula is correct, in saying the more elastic demand was, the lower the markup visa versa, the more ineleastic demand was the higher the markup. Because the left side of the equation is percentage change in MC, so the higher P>MC then it makes sense that the markup would follow. My question is, did he derive the markup formula from the MR formula..? Jan 18, 2018 at 3:43
• To be clear: is your problem that, starting from $P(1+\frac{1}{\eta})=\text{MC}$, you don't know how to get $\frac{P-\text{MC}}{P}=-\frac{1}{\eta}$? Because that can be achieved with straightforward algebraic manipulation. As a first step, write $P-\text{MC}=-\frac{P}{\eta}$. Jan 18, 2018 at 7:36
• Champion mate, it was a whole lot simpler than I thought.. Thank you for that Jan 19, 2018 at 8:03

## 1 Answer

It is just a missing parenthesis issue. The expression

$$\text{(P-MC/P)= -1/η}$$ should have been written

$$\text{((P-MC)/P)= -1/η}$$

• The parenthesis don't make a difference for going from MC/P = 1+1/η to (P-MC/P)= -1/η... where did the +1 go on the right side of the equation? Jan 18, 2018 at 6:52
• @Arthur Just carry out the math. Jan 18, 2018 at 7:19