Unitary Elasticity Of Demand Question (PED=1) [duplicate]

So I was having a bit of trouble reasoning with the answer for this particular PED question. It goes like this:

PED=1, Quantity Demanded=4,000 units when Price=$12 The question was: Find the price when Quantity Demanded=20,000 units So I tried the easy way to do this which was to use the price in which the Total Revenue remained the same, and I got the answer Final Price=$2.4.

My problem was that I tried another method and I am not getting the answer and I want to know why .

So PED= % Change in QD/ % Change in Price

We can see that the increase in Quantity Demanded is 400%. Shouldn't it stand to reason that the decrease in Price is also 400% (I know this is impossible because a price can't fall by more than what it is at the moment) but isn't the theory that the % fall in price will equal to and be offset by the % increase in QD, resulting in the revenue remaining the same?

I'm sorry if this question was unnecessarily long or even confusing, it's a bit difficult to understand my own thoughts so writing them out in paragraphs helps me understand why I'm asking this question in the first place ;).

• @Giskard, hello, thanks for your response. Been trying for the past few hours to understand the connection between the article you sent me and this question . Is it because I am using point elasticity of demand (% change in QD/% change in price) that the figure is wrong? In our textbook no distinction is made between point and arc elasticity , we're just given the above formula . – econnewbie Apr 25 '19 at 10:38
• So you're saying that we can use the point elasticity of demand formula for values of PED that are not equal to 1? Because if we use 1 we will somehow get erroneous values for Price and Quantity ? – econnewbie Apr 25 '19 at 10:41
• Unfortunately I am sure I cannot explain it any better than I already did under the linked question. – Giskard Apr 25 '19 at 11:36
• No worries at all. I've read it thoroughly and have started to understand, thank you for your help. – econnewbie Apr 25 '19 at 11:54