Price Elasticity of Demand

[archived_user]

Hi everyone,
This question came up in of of the past papers.
The price of a good decreases from $15 to $13. On the other hand, the quantity demanded of the good increases from 100 units to 120 units. I got 1.5 as the price elasticity, but the answer said 1.3 using midpoint calculation. Which one is correct?
Thank you,

 

[archived_user]

I think the 1.5 answer is the most correct.
Price demand elasticity formula is Var%Q / Var%P
Var%Q = 120 / 100 - 1 = 20%
Var%P = 13 / 15 - 1 = -13.33%
Ep = 20% / -13.33% = -1.5
However, if you calculate Var%P as the following, you get another number (which is wrong…)
Var%P = 15 / 13 - 1 = 15.38%
Ep = 20% / 15.38% = 1.3
The second Ep is wrong because 2 things. First, the latter price is 13, not 15, so the variation must be calculated as P1 / P0, not the way around. Second, the sign must be negative, because demand curve is negatively sloped (lower price, higher demand). So, the correct Ep should be -1.5, not +1.3.
Hope this helps.

 

[archived_user]

Harrogath wrote: Price demand elasticity formula is Var%Q / Var%P

Almost: it’s −Var%Q / Var%P. Economists want elasticities to be positive numbers, so you have to throw in the negative sign.

 

[archived_user]

Yup, you are right, although it is not much intuitive for me in that way.

 

[archived_user]

Harrogath wrote: Yup, you are right, although it is not much intuitive for me in that way.

The text I’m using in my business calculus class has it as |%ΔQ/%ΔP|, instead of −%ΔQ/%ΔP. For most goods there’s no difference – it’s a positive number either way – but for Giffin goods and Veblen goods you want to see the negative sign on the price elasticity of demand, to remind you that the quantity demanded increases when the price increases (and vice-versa).
I need to write to the authors and explain that, with the hope that they’ll correct it in the textbook. In the interim, I’m forced to go with, “… using the formula you learned in class (not the formula in the textbook, which is wrong) … .”