If the price elasticity of a linear demand curve is −1 at the current price, an increase in price will lead to:

A) no change in total revenue. B) an increase in total revenue. C) a decrease in total revenue.

Answer is given as C. Please explain

If the price elasticity of a linear demand curve is −1 at the current price, an increase in price will lead to:

A) no change in total revenue. B) an increase in total revenue. C) a decrease in total revenue.

Answer is given as C. Please explain

C should be correct.

Just make an example with numbers:

current price revenue level: 10 US$ x 10 units = 100 US$

Price increase +10%. The elaticity is -1, meaning that there is a negative proportional relation between price and units (price increases by 10%, whereas units drecrease by 10%):

future price revenue level: 10 US$ x 1,1 x 10 units x 0,9 = 99 US$

Total revenue drecreased by 1 US$ as indicated by C.

Best,

Oscar

Hi,

i have a question here as the price elasticity of demand is -1, it falls under the category of inelastic demad as per demand curve…so in this case, Revenue should increase if the demand is inelastic…please clarify…

Regards,

NK

A price elasticity of demand of -1 indicates unit elasticy (which is neither elastic nor inelastic). Wikipedia says:

“When the price elasticity of demand for a good is *unit (or unitary) elastic* (E_{d} = -1), the percentage change in quantity is equal to that in price, so a change in price will not affect total revenue.”

So you might be wondering why a change in price doesn’t affect total revenue as indicated by the statement. This is only true in a marginal view. Only in the point of E = -1, you won’t see a change in revenue in respect to price since revenue is at a maximum. The definition of a maximum is that the value of the derivation is zero in that point.

But if you consider a price increase in a general way, this will lead to lower revenues because revenue is already on a maximum für E = -1. Therefore, any other price indicates a lower revenue.

However, I think the question is not completely clear-cut.

It doesn’t fall under the category of inelastic demand; it falls under the category of _ **unitary elastic** _ demand.

The question is clear-cut.

The key is that the demand curve is _ **linear** _.

With a linear demand curve, the point where price elasticity of demand is −1 is the point where revenue is _ **maximized** _; an *increase* in price or a *decrease* in price will lead to **lower revenue**.

While it’s true that the definition of unitary price elasticity of demand is that the percent change in demand is the (negative of the) percent change in price, that’s true only for an infinitessimal change in price. It’s a calculus thing. The total revenue function is a parabola (opening downward), and the point of unitary elasticity is the high point of the parabola: moving either direction leads to a lower total revenue, even though the slope at the high point is zero.

That’s what I said ;).

I’ve an academic background and academics (especially economists and I think especially German economists) tend to look at the infinitesimal change. That’s and because of the wiki text is why I mentioned it .

But of course in a practical view, the argument change in price leads to lower revenues is completely right and sufficient.

S2000magician:

maddin91: Neha\_09:Hi,

i have a question here as the price elasticity of demand is -1, it falls under the category of inelastic demad as per demand curve…so in this case, Revenue should increase if the demand is inelastic…please clarify…

A price elasticity of demand of -1 indicates unit elasticy (which is neither elastic nor inelastic). Wikipedia says:

“When the price elasticity of demand for a good is

unit (or unitary) elastic(E_{d}= -1), the percentage change in quantity is equal to that in price, so a change in price will not affect total revenue.”So you might be wondering why a change in price doesn’t affect total revenue as indicated by the statement. This is only true in a marginal view. Only in the point of E = -1, you won’t see a change in revenue in respect to price since revenue is at a maximum. The definition of a maximum is that the value of the derivation is zero in that point.

But if you consider a price increase in a general way, this will lead to lower revenues because revenue is already on a maximum für E = -1. Therefore, any other price indicates a lower revenue.

However, I think the question is not completely clear-cut.

The question is clear-cut.

The key is that the demand curve is _

linear_.With a linear demand curve, the point where price elasticity of demand is −1 is the point where revenue is _

maximized_; anincreasein price or adecreasein price will lead tolower revenue.While it’s true that the definition of unitary price elasticity of demand is that the percent change in demand is the (negative of the) percent change in price, that’s true only for an infinitessimal change in price. It’s a calculus thing. The total revenue function is a parabola (opening downward), and the point of unitary elasticity is the high point of the parabola: moving either direction leads to a lower total revenue, even though the slope at the high point is zero.

Too good …thanks

My pleasure.