# Single-price profit-maximizing output for a Monopoly

Hi, since the equation to find the price of profit-maximizing output for a monopoly is :
MR = P (1 - (1/Elasticity))
What happens when the elasticity is less than 1? The price is then multiplied by a negative number.

If price elasticity < 1 then, as the formula shows, marginal revenue actually declines with the production of more units.

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This formula is usually used to find P, after weâ€™ve been given either MC or MR (because MC=MR) and the own-price elasticity.
For example, if the MC is currently 40\$ and the elasticity is 1.5, what is the profit-maximizing price?
40 = P (1 - (1/1.5))
Price will be 120\$

So I am wondering how we can solve this if the elasticity is lower than 1, because the term in parentheses will be negative.

When price elasticity is less than 1 (inelastic), it means that MR is negative also.

So MR is negative, the parenthesis part is negative, and you solve for the price.

If price elasticity > 1 then MR is positive
If price elasticity = 1 then MR is zero
If price elasticity < 1 then MR is negative

If it helps: Price elasticity of demand - Wikipedia

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In the CFA curriculum, price elasticity for normal goods is negative, not positive.

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This also

Sorry to ask so many questions, but how can MR possibly be negative? To my understanding that means the company would actually have to pay (negative revenue?) to sell an extra item. Similarly, since MC would equal MR, the cost would also be negative?

No worries buddy!

First, let me just say that if s2000 says price elasticity on the CFA exam for normal goods is typically negative, thereâ€™s your solution right there for the important things in life (your upcoming test). S2000 is gospel.

But letâ€™s look at how MR can be negative through a simple scenario, remembering that marginal revenue is the additional revenue a company generates by selling â€śmoreâ€ť units of a product or service.

Consider this - hand sanitizer selling for \$3 per package might sell 100 units in a week, for \$300 in revenue, but the same hand sanitizer at \$2 per package might sell only 110 units in a week â€“ indicating its relatively constant demand â€“ for a revenue of \$220. If you want to sell 10 more units of hand sanitizer you need to then take an \$80 revenue loss, as the seller. In this case, lowering the price to sell more units is a money-losing proposition due to its price inelasticity (less than 1).

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It canâ€™t

With price elasticity of demand being negative, it wonâ€™t be.

So having a negative price elasticity of demand would solve the problem. But is the formula of any use with a positive price elasticity < 1 ? That would make the term in parentheses negative.

Itâ€™s in my responses above buddy.

Sorry, I was replying to s2000 as he is saying that MR canâ€™t be negative. So Iâ€™m a bit confused now

Probably not.

A positive price elasticity occurs with Giffen goods and Veblen goods.

Giffen goods are inferior goods; itâ€™s hard to imagine a monopoly producing an inferior good.

Veblen goods seem to violate the usual rules of economics, so if a monopoly were producing a Veblen good, that formula might well not apply.

Donâ€™t overthink it per se. If it helps you can read about negative marginal revenue briefly at

Or

Just look for the â€śnegativeâ€ť keyterm in those texts. But I wouldnâ€™t get stuck in a rabbit hole on this. The formula works for price, sometimes MR can be negative but thatâ€™s when elasticity is between 0 and 1. Then you solve for price. Itâ€™s the example about hand sanitizers above. But like s2000 says, the CFA is likely going to test you on scenarios where you wonâ€™t need this type of esoteric mental gymnastics.

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