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,
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.
Almost: it’s − Var%Q / Var%P. Economists want elasticities to be positive numbers, so you have to throw in the negative sign.
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) . . . .”
price of elasticity of demand = % change in Quantity Demand / % change in Price
= [(Q2 - Q1) / (.5 * (Q1 + Q2))] / [(P2 - P1) / (.5 * (P1 + P2))]
= [(120 - 100) / .5 * (120 + 100)] / [13 - 15 / (.5 * (15 + 13))]
= (20 / 110) / (-2 / 14)
= |-1.27| ~ 1.3; an elastic good. (absolute value > 1)
Edit: corrected elastic good
With all due respect, this isn’t correct: the correct formula is:
Price of elasticity of demand = − (% change in Quantity Demanded / % change in Price)
Somehow, you magically got rid of the negative sign in the last line of your calculation:
What you should have done was include a negative sign in your original formula.
Whether a good is normal or inferior cannot be determined from its price elasticity of demand; again, with all due respect, your conclusion is utterly wrong.
The way to determine whether a good is normal or inferior is to look at its _ income _ elasticity of demand:
Most goods will have positive _ price _ elasticities of demand, whether they’re normal or inferior. Some goods – Giffin goods and Veblen goods – have negative price elasticity of demand. Even then, you cannot use price elasticity of demand (exclusively) to determine whether a good is normal or inferior: Giffin goods are inferior goods while Veblen goods are normal goods.
Be careful.
You’re right about the inferior good, I apologize for that. I meant to say its elastic. The question asks about price elasticity, so it should be valued as an absolute value. Income elasticity is what should have been kept as a negative sign and be determined as an inferior or normal good, depending on whether the answer is a negative or positive.
But as far as the equation, I wouldn’t add the negative to it, but ¯_(ツ)_/¯
Again, you’re incorrect.
It should be the negative of the % change in quantity demanded divided by the % change in price. For most goods, this works out the same as if it were the absolute value: prices rise, quantity demanded falls, the negative of the relative percent changes is a positive number.
For Giffin goods and Veblen goods, however, the absolute value gives the wrong answer: it makes it appear that when prices rise, demand falls (and vice versa). You need to see that price elasticities for those goods are negative numbers, which you’ll never get with an absolute value in the formula.
Yes the slope of the demand is a negative, but following the book and the learnings from the CFA material, I’m trying to keep it consistent in case it shows up in the exam. The question is stated in regards to price elasticity of demand, not the income elasticity of demand, and if they ask about the price elasticity (not income elasticity), its going to most likely ask whether its going to be elastic or inelastic. Giffen goods or Veblen goods are related to questions on income elasticity, where the sign will matter (inferior/normal goods).
The point is that for Giffin goods and Veblen goods, _ this isn’t true _: the slope of the demand curve is positive.
If you read what I posted, you’d know that I’m quite aware of that.
One more time:
Price elasticity of demand = − (%ΔQuantity / %ΔPrice)
Price elasticity of demand ≠ |%ΔQuantity / %ΔPrice|
For most goods you’ll get the same answer. For Giffin goods and Veblen goods, the formula I give will produce the correct answer (a negative elasticity) while your formula will produce the wrong answer (a positive elasticity).
So what? The formula I give will produce the correct answer to questions of whether the demand for a good is price elastic or price inelastic, and will also produce the correct answer for Giffin and Veblen goods; yours won’t.
No, they’re not. That’s the point: what makes Giffin goods and Veblen goods unusual is their price elasticity, not their income elasticity. All inferior goods have negative income elasticity; all normal goods have positive income elasticity. Not all inferior goods have negative price elasticity (only Giffin goods do); not all normal goods have negative price elasticity (only Veblen goods do).
I’m trying to help the candidate who started this thread. By making many incorrect statements here, you’re harming that candidate.