Talk:Price elasticity of demand

Giffen and Veblen goods
It seems to me that the discussion of Veblen and Giffen goods has no business in this article. They're related more closely to income and cross price elasticities of demand, which this article notably neglects to mention. That part should be deleted or moved to a more appropriate article, and preferable modified to reflect the lack of empirical support for the existence of these goods in the first place.
 * I don't know when this section was added, but if it relates to the current version of the article, I disagree. My experience of economics (A-Level i.e. ages 17-8) uses these types of goods as the exception to the "always" negative PED rule, and I think they have a similar use in the article, surely. OTOH, I agree about linking this article more strongly to other similar articles. It was really in a bad place until a couple of edits I gave it, hopefully an improvement, but, as I say, I'm no expert. - Jarry1250 [Humorous? Discuss.] 18:29, 3 January 2010 (UTC)


 * Giffen goods are definitely relevant here as they have to do with own price elasticity. Note also that "income effect" does not refer to "income elasticity" but to the effect of price on income, hence on demand. It's a bit apples and oranges. Veblen goods may or may not be related, depends on how you model that. Either way though, the above is right that if the article is going to mention these, the lack of empirical support for their existence should also be mentioned.radek (talk) 02:26, 6 March 2010 (UTC)

Giffen and Veblen links
Also, the links to Veblen and Giffen should probably be directly to the Veblen good and Giffen good pages. Right now they are linking to redirect pages that have all kinds of links on them. Mr. Shoeless (talk) 14:46, 3 January 2010 (UTC)
 * Done for the links in the lead. - Jarry1250 [Humorous? Discuss.] 18:29, 3 January 2010 (UTC)

Reorganization
The mathematical definition is simple and contains everything you need to know about the topic. The rest is just idle chatter. Move the mathematical definition to the top.


 * ✅. - Jarry1250 [Humorous? Discuss.] 18:23, 28 February 2010 (UTC)

Different Shapes of Elasticity Curves
This article seems to implicitly treat the elasticity curve as if it were a straight line. I would like to see this article discuss different shapes and models for the elasticity curve. For example, some people use a logarithmic curve for convenience or certain practical reasons (even if it does not reflect reality). On the more realistic end, I have seen people use an S-shaped curve, where the inflection point of the curve represents the competetive price. Would anyone who knows more about this topic care to add this material? I think it would greatly enrich this page. Cazort (talk) 22:05, 8 July 2008 (UTC)


 * Now, at least, the article makes so such assumption. - Jarry1250 [Humorous? Discuss.] 18:23, 28 February 2010 (UTC)

Ambiguous statement about ambiguity
In this sentence: "Price elasticity is almost always negative, although analysts tend to ignore the sign even though this can lead to ambiguity" - what does "even though this can lead to ambiguity" mean exactly? In what sense? Is this simply saying that most of the time in literature when somebody's talking about price elasticity they're talking about it's absolute value and that a person unfamiliar with the convention might get confused? Or is it referring to the possibility of Giffen goods mentioned right next to this sentence? Either way, the statement about ambiguity is itself ambiguous.radek (talk) 02:23, 6 March 2010 (UTC)
 * Somewhat ironic, yes. I can't recall where that bit came from, but I would guess that it is supposed to me that if someone said to you, "the PED of this good is 0.5" you would have to guess whether they mean "-0.5" or a true "0.5" (upwards sloping demand). But yes, if you would prefer the omission of that phrase, sure thing. - Jarry1250 [Humorous? Discuss.] 12:17, 6 March 2010 (UTC)
 * NO! This is a sigificant matter that any reasonably complete and credible discussion of PED and some other elasticities should definitely address! Jarry1250 describes himself as a "grammar pedant," a persuasion that I share.  But I'm also an elasticity pedant, and some otherwise good textbooks are so ambiguous on this point that they leave students confused and frustrated.  In my 15+ years of teaching about PED to undergraduate and graduate students, this ambiguity is one of the most confusing aspects of a topic that's already one of the most bewildering subjects in undergrad microecon.  (I sincerely apologize if that introductory prepositional phrase comes across as immodest or smug, but my classroom experience has left some rather indelible impressions.)  Of the 2 dozen or so introductory-, intermediate-, and graduate-level texts I have on my bookself (never mind those crated up in storage), some simply ignore the negative sign that (because of The Law of Demand) is implicit in and integral to PED, a few others use the absolute-value formulation (which immediately confuses the non-mathematically inclined students), and at least 1 even explicitly says "we can safely ignore the negative sign"!  (Mathematically inclined students find the latter approach risible, even contemptible.  Sure, we can safely ignore the sign, until the student slavishly applies the [signless, memorized but not understood] formula on an exam question and forgets or fails to indicate that an X% change in price causes a Y% change in quantity demanded in the opposite direction, or vice versa.) Unfortunately, as the necessity of the present discussion so lamentably indicates ipso facto, few, if any, texts below the graduate level address the problem coherently.  Yes, this aspect of PED needs to be clarified (and I'll try to assist in doing so, Jarry1250).  And it probably doesn't deserve pride of place above the article's table of contents.  But it's an integral property of all 4 of the principal elasticities that any serious student of economics should be conversant in -- PED, cross-price, income, and even supply.  (In theory, supply curves can have negative elasticities under certain circumstances, i.e., "over some relevant range.") I hope to return to this topic soon, after first addressing some considerably more pressing difficulties with the current state of the "incidence of taxation" article.  Besides, that's the least I can do for a fellow grammar pedant ("We few, we happy few ...") who's also an expert in heraldry. And BTW, speaking of pedantry, don't get me started on using change in demand (supply) interchangeably with change in quantity demanded (or supplied).  Warm regards, Jack F. Twist 03:03, 26 March 2010 (UTC)  —Preceding unsigned comment added by Jackftwist (talk • contribs)

Point-price elasticities
Okay, this section is confused. If you can use calculus, then you don't have to worry about the end points. But the whole point is that if you're dealing with empirical data, which is discrete, you can't use calculus. So you have to calculate the elasticity with something like what's given in the first formula. To do that you approximate the elasticity at a point via the so called "mid point method" which is what the formula of this section refers to. But this is different than using calculus.radek (talk) 02:37, 6 March 2010 (UTC)
 * Per my reply to another section, any details you may have about real life usage of PEDs would very much be appreciated. Having rearranged the various bits yesterday, I was about to write a section of the average point method (I do believe it is referred to as the arc method in the textbooks I have read) but I was simply too tired. Will try to do so today. - Jarry1250 [Humorous? Discuss.] 12:21, 6 March 2010 (UTC)
 * Section added. - Jarry1250 [Humorous? Discuss.] 14:11, 6 March 2010 (UTC)
 * Yes that section helps. I'll try to clarify the issue in the preceding section when I get a minute.radek (talk) 07:17, 7 March 2010 (UTC)

constant elasticity
A demand function of the form $$P=aQ^{-\beta}$$ where a and beta are constant, has constant price elasticity of $$1/\beta$$. In fact these type of functions are commonly used in empirical studies - and this is where all those numbers in the "Selected price elasticities" come from. Otherwise, the elasticity wouldn't be constant and a single number (w/o additional information) wouldn't be very informative. So the section contradicts somewhat the material in the point price elasticity section (which I tried to clarify a bit).radek (talk) 02:44, 6 March 2010 (UTC)
 * Yes, I do believe you've shown up my own lack of knowledge about PEDs in real life: anything you could add or amend would very much be appreciated. - Jarry1250 [Humorous? Discuss.] 12:19, 6 March 2010 (UTC)

Selected sample price elasticities
This whole section should be removed, but as someone who hasn't edited Wikipedia in a year, I'm not going to do it. Every economics article that estimates elasticities of demand comes up with a different range of estimates. At the very least, the years over which these elasticities were estimated should be recorded in the main text of the article instead of in footnotes (regardless of whatever Wikipedia standards exist, this would be standard practice in economics). 199.136.107.76 (talk) 22:36, 8 February 2016 (UTC)

Are the price elasticities of Ford Motor Company, Coca Cola and Mountain Dew really positive? I dont have those references available to check. For Ford that might in theory make some limited sense, but for Coca Cola And Mountain Dew I really cant imagine that it could be correct. I don't want to correct those to negative because maybe there is some really weird economic thing happening here that justifies positive elasticity and I dont just understand it. But then that really should be explained in that chapter why the elasticity is positive for these commodities. Right now it is very confusing. 88.114.246.209 (talk) 19:09, 8 March 2010 (UTC)
 * As noted in the article, PEDs are often quoted as positive, even if they are really negative (as I am sure they are here). I'm thinking it may be worth adding in the minus signs, but I haven't copies of the books quoted. - Jarry1250 [Humorous? Discuss.] 19:33, 8 March 2010 (UTC)


 * It doesn't really matter whether you show the empirically estimated elasticities as positive or negative, as long as you're consistent, regardless of which sign the original source used. That's the standard practice across all the textbooks I checked.  But to minimize potential confusion among Wiki's general readership (like the astute observer above), it would help to include a footnote or other explanatory comment about which convention you've chosen to follow regarding the sign.  BTW, doing original research on empirical estimates of elasticities of demand (or supply) isn't likely to put any faculty member on the fast track to academic promotion and tenure in most U.S. universities (unless it happens to be on a topic of current political importance, like, say, health care in the U.S., or to a lesser degree, energy).  As a result, many of the empirical estimates one finds -- and yours is by far 1 of the most exhaustive lists I've ever seen -- tend to cite studies that go back many decades. E.g., the authoritative source for the PED of many agricultural products in the U.S. is, I kid you not, Henry Schultz's classic study, The Theory and Measurement of Demand, published in 1938.  (No, that's not a typo -- 1938!) To meet the highest standards of reliable sourcing, though, the origin of each estimate or group of estimates should be shown separately, although that may be impossible to do without access to the original source texts.  Otherwise, it's usually acceptable to say, "as cited in ... [the source you actually do have access to]."  --Jack F. Twist 04:00, 26 March 2010 (UTC)  —Preceding unsigned comment added by Jackftwist (talk • contribs)

The .01 estimate on insulin is bogus. Firstly the reference in Boyes and Melvin (2002) is on page 141, rather than 140. Moreover, it's an end of chapter exercise: "Suppose the price elasticity of demand for the first group is .01 and that for the second is 4.0". Insulin is indeed often presented as a classic example of a perfect or nearly perfect inelastic demand curve. But that's pedagogy, not empiricism. I substituted in "Physicians visits for pediatric care". Similarly the info on movie visits was from an exercise, not a study. (Original edits made on Oct11, 2009 by anon on Elasticity (economics) article: info merged into this one in Feb2010. Only 3 edits made, now corrected.) Measure for Measure (talk) 21:54, 27 May 2010 (UTC)

Mert Daryal (1999 - 2 working papers) reported that the demand for marijuana was inelastic (estimates ranged from -0.1 to -0.5). The eggs example is bizarre, but seems to be backed by Huang and Lin (2000) http://www.ers.usda.gov/Publications/TB1887/. Accordingly, I will delete the marijuana example, but keep the eggs pending further study. Does anyone know why demand for eggs would be so inelastic? Feel free to put marijuana back, if you confirm that Frank did a careful review of the literature and opted for a higher elasticity. Measure for Measure (talk) 08:21, 8 September 2010 (UTC) Thinking it over, the estimate from Huang and Lin concerned direct household demand for eggs in the US -- but there is restaurant and food processing demand to consider as well. Also, I found another estimate from South Africa putting egg demand at -0.55. Frankly, the H&L figure of -0.1 looks to me like an outlying estimate in their 14 food consumption system: OTOH, I've confirmed that it indeed was cited by Krugman, Wells and Olney in Essentials of Economics (2007). What to do, what to do... Measure for Measure (talk) 22:25, 8 September 2010 (UTC) Eggs: Found a Canadian estimate of -0.35. I'll provide a range of estimates ... though I personally harbor doubts about the Huang-Lin figure of -0.1. Admittedly the standard error wasn't bad and eggs may have only weak substitutes. Thoughts? Measure for Measure (talk) 00:34, 10 September 2010 (UTC)

Link to "Law of demand" article?
The first sentence below the formula for PED refers to the law of demand (LD) in parentheses but doesn't provide a link to the current Wiki "Law of demand" article, which is at Law_of_demand (http://en.wikipedia.org/wiki/Law_of_demand). (I'm new to Wiki editing, so I may not have used the proper syntax for the internal link. If not, apologies.)  Note, however, that while the current LD article is quite ambitious, it is quite weak in its present state, and it would also benefit from extensive copyediting. (Perhaps you deliberately didn't link to it for that reason.) The last "talk" entry for the article is almost 6 months old, so perhaps its original author has lost interest in it or now places a low priority on it. Nevertheless, the LD is obviously such a fundamental economic concept (as is PED!) that it needs to be a flagship article of the economics project if that project is to be worthy of its name! How does one suggest to the project managers/editors that they place this article in a higher-priority category? (Or alternatively, they may have cogent reasons for not doing so. If so, it would be helpful to know what those are.)  As time permits, I'll try to assist in cleaning up the current LD article and strengthening it, but I'm not sure how soon I can get to it. --Jackftwist (talk) 23:50, 26 March 2010 (UTC)
 * It used to be linked, but the linking was removed (not by me) because of the guidance at WP:OVERLINK and its being linked in the lead. Yes, you're right, the article does have a number of faults. Whilst you can try appealing to WP:WikiProject Economics, it's not AFAICT a very active project, and consequently, there are lots of gaps that need filling, and editors like you and me are needed to help (WP:SOFIXIT). So keep up the good work, and one day, we may have an encyclopedia :) - Jarry1250 [Humorous? Discuss.] 19:12, 27 March 2010 (UTC)
 * Thanks. LOL, upon reviewing several other sections of your article this morning, I found the link in the lead and another one later on. Thanks for all the references to the specific policies -- as a rookie at the Wiki-editing game, I'm still pretty overwhelmed by all the policies and procedures.  I'm a career college teacher and administrator, so I'm accustomed to the necessary evil of such a bureaucracy for a large project like this, but obviously it takes some getting used to.  I've used Wiki for years without having any inkling that all this structure exists behind the curtain.


 * I'd intended to spend some time posting a few more comments and suggestions about your PED article here today, but instead I ended up spending all that time reading policies, instructions, etc. I'm afraid I've just stumbled into a new black hole for my spare time!  --Jackftwist (talk) 00:28, 28 March 2010 (UTC)
 * Heh, all comments appreciated. We have all day, after all. Incidentally, I should condemn you to an immediate and very painful death, but I'm much nicer than that :) Just get stuck in - the great thing about Wikipedia is that all mistakes are easily fixed. - Jarry1250 [Humorous? Discuss.] 17:20, 28 March 2010 (UTC)

Some minor revisions to the 1st paragraph of the "Definition" section.
An obviously jumbled word somehow crept into the beginning of the 2nd sentence of the paragraph: "The formula useoefficients of price elasticity...." I put in a proposed revision.

I also changed "quantity" to "quantity demanded" in that sentence for the sake of clarity and completeness. It's crucial that the definition be as precise as possible in emphasizing that PED is concerned only with changes in quantity demanded. (Elasticity is one of the most difficult concepts in micro for most beginning econ students and for other potential readers/users -- WP's "customers"; they tend to get confused by the slightest ambiguity about which quantity we're referring to. An ounce of emphasis here doesn't preclude such confusion, but it can help avoid a pound of it.)

In addition, I added "services" to the definition as a token reminder that PED and the laws of supply and demand apply to both goods and services.

The only other noteworthy revision was to the beginning of the last sentence in the first paragraph to place more emphasis on the PED for the most typical types of goods and services. Although the Giffen and Veblen exceptions are interesting, they are almost negligibly rare anomalies compared to the overwhelming number of typical goods and services governed by the Law of Demand. (That's why it merits the rare status of a "Law"!) These exceptions do deserve discussion eventually (in a later section or a separate article), but I think this introductory paragraph would be strengthened by giving them only the briefest possible mention in passing here. Instead, this paragraph should focus attention on the crux of the issue that readers need to remember (the "take-away"), namely: because the demand for the vast majority of goods and services obeys the Law of Demand, their PED coefficients will always be negative.

Again, elasticity is one of the most difficult topics at the introductory level of microeconomics. Regardless of how interesting these exceptions may be to intellectually curious readers, to risk distracting students and other users from the paragraph's main point with minor exceptions too early in their learning process probably detracts from this section of an otherwise well-done article that's on the verge of becoming an extremely good one. Once the main point (i.e., the last sentence in the preceding paragraph) is made as clearly as possible, then devoting some time to the exceptions is much less likely to cause confusion or ambiguity.

(To avoid further belaboring this point here, I've placed some other comments about Giffen and Veblen goods on my Talk page.) I have one more revision along this line to suggest for strenghtening and streamlining the opening paragraph, I'm still working on the exact wording, so I'll return to it as soon as time permits.

I made a few other copyedits that were purely minor, e.g., deleting an occasional unnecessary word and otherwise polishing the prose just a bit.

--Jackftwist (talk) 02:14, 30 March 2010 (UTC)

A potentially interesting and useful external site
I ran across the following external link among the references in one of the (too many) other WP articles on various aspects of "demand." The site might be of interest to both users of all those articles and to contributors to them:

http://demonstrations.wolfram.com/topic.html?topic=Microeconomics&start=1&limit=20&sortmethod=recent

I haven't yet had time to download the software necessary to run the simulations, but based on the thumbnails for each topic, the site looks like a very promising supplement to many of the articles in the Economics Project, but only a supplement, primarily as a "see also" link -- by no means a substitute for the articles themselves. Nor would I necessarily consider this site to be an authoritative source that would meet WP standards and guidelines on quality of sources. (On the other hand, to better illustrate their topics, most of the demand-related articles would benefit from adding graphs similar to those in some of the thumbnails at this site!) --Jackftwist (talk) 18:30, 5 April 2010 (UTC)

Question on Total revenue and Price Elasticity
Ok, I am not sure if the article is inaccurate or if I am just missing something/doing wrong math. Let's say price goes from 50 to 99, a change of 98%. Demand goes from 150 to 60, a change of -60%. The price elasticity of demand would be -.61 (rounded). Revenue decreases from 7500 to 5940. According to the current article, "When the price elasticity of demand for a good is inelastic (|Ed| < 1), the percentage change in quantity demanded is smaller than that in price. Hence, when the price is raised, the total revenue of producers rises, and vice versa." In the example I've shown, total revenue decreases with a price increase. I feel like I am missing something, or is the article really wrong? Thanks

Did some digging, and might of found my problem. I was using percent change[(new-old)/old)], when I should of be using "relative change" [ {(new-old)}/{(new+old)/2}]. Wrong way: http://economics.about.com/cs/micfrohelp/a/priceelasticity.htm Right way: http://www.businessbookmall.com/Economics_19_How_Elasticity_of_Demand_Affects_Total_Revenue.htm

The wiki article does say "% change", fooled me! Maybe changing the wording in the equation would be beneficial?

Puffcheese (talk) 05:54, 20 April 2010 (UTC)
 * A lot of the conclusions that can be drawn from PED - much of its usefulness in fact - come from small changes in price. It does, as you show, become absurd for large changes. But there may also be some merit in what you say about methodology. - Jarry1250 [Humorous? Discuss.] 16:57, 20 April 2010 (UTC)

A closer look at your problem

 * Puffcheese -- Your question is excellent, and it raises a problem that comes up often. It also points out a couple of things we need to clarify in the article.  The apparently contradictory result you originally got was caused by 2 separate things.
 * First, as Jarry pointed out, the % changes were very large.
 * To understand the second part of the problem, assume the demand curve between your 2 points is a straight line. It turns out that one of your points is way above the point on the demand curve where the PED = - 1 (unitary elasticity), and the other point is way below where PED = -1.  As the Total Revenue (TR) diagram in the article shows, TR reaches its maximum at the P and Q where PED = - 1.  So in your example, you're comparing a point where TR is rising (that is, a Q to the left of the max TR point) with one where TR is falling (a Q to the right of the max point).  In a case like that, whether TR rises or falls between the 2 points on the demand curve depends on how far they are above and below the unitary elasticity point.


 * The important thing to remember is that the basic definition of PED is always %∆Q / %∆P. But the next question (and source of frequent confusion) is, how do we compute the percentage changes? In general, there are at least 3 possibilities for doing that:


 * 1. Compute it the way we all learned to compute percentages back in grammar school arithmetic, as you did at first:  [(new - old) / old] × 100%  (If you got an increase in pay, that's almost certainly how you'd compute the percentage pay increase -- it's just seems like the natural way to do it.)
 * But, as you discovered, that can sometimes create problems, especially when computing elasticities, because percentage changes aren't linear and they're not symmetric -- the calculated percentage change depends on which price and quantity you pick as the "new" one and the "old" one. (This is easy to see from a simple example:  if you increase something by 100%, that is you double it, then you decrease it by 100% but from its new level, you don't end up back where you started -- instead, you go all the way to zero.)
 * This problem is compounded when you have a situation like your example, where the 2 points are on opposite sides of where PED = -1.


 * 2. We can get around the symmetry problem by using the method you found:  by computing the change relative to the average price and quantity, that is {(new-old)}/{(new+old)/2}.  This is called the arc elasticity in the PED article; it's also called the "midpoints formula," because (new+old) / 2 is the midpoint.


 * 3. Unfortunately, we can't apply the 3rd method to your specific problem, because this method applies only when the changes in P and Q are extremely small.  In that case, no matter which points you pick as the new and old ones, the % changes will be almost equal.  But you've got large % changes in your example.
 * Just to complete the picture, though, this method is called the point elasticity, as defined in the article. As shown there, it involves taking the derivative of the demand function.


 * BTW, if you remember your algebra or analytical geometry, you can find the equation for the straight line between your 2 points. It's
 * P = 131.66 − 0.54Q, or equivalently, Q = 241.71 − 1.84P (allowing for some rounding error)
 * From either form of the demand function, you can can figure out the P and Q where this straight line intersects the vertical and horizontal axes by setting Q=0 and solving for P, then setting P=0 and solving for Q.
 * Once you know the intercepts, you can determine where the midpoint of this straight line is: its coordinates are (Q/2, P/2), where Q and P are the intercepts found in the previous step.
 * The ED of any straight-line demand curve always = 1 at its midpoint, and only at its midpoint ... always!
 * Again, as the PED article discusses, Total Revenue (TR = P×Q) is maximized at the midpoint.
 * Note that the midpoint for the entire demand curve is somewhere between the 2 points given in your question. That's part of the reason why TR didn't change in the direction your original elasticity predicted it should.
 * You could also use the point elasticity formula given in the PED article, along with a bit of calculus and algebra, to figure out where PED = -1 for this linear demand curve.


 * One final point: your demand curve might not be linear at all, or it might be linear only over a certain range.  But when you apply the arc elasticity (midpoints) formula, the result you get is the elasticity at the midpoint along the straight line between your 2 points (i.e., at the average of your 2 prices and 2 quantities), regardless of whether the demand curve is linear or not.
 * Again, nice job figuring out the solution. We'll try to clear this up a bit in the article.  --Jackftwist (talk) 23:38, 20 April 2010 (UTC)
 * We'll? :) - Jarry1250 [Humorous? Discuss.] 19:18, 21 April 2010 (UTC)
 * Whoever gets around to it first :) --Jackftwist (talk) 21:44, 22 April 2010 (UTC)

Jack's proposed changes
I've looked over the changes that Jackftwist mentioned on my talk page (here ) and I think they're all good and would improve the article.

More specifically: The beginning "Definition" section is very clear as is; all it needs is the citations. It looks complete enough to me as well.

In the Point-price elasticity section I agree that the given formula is unnecessarily general and "theoretical" - at the very least make it explicitly l=k (i.e. just use same index), especially since the definition of a cross price elasticity is already mentioned in the section above. Personally I'd just put in a simple partial differential formula here. Maybe leave wealth as an argument of the function. The key point about this section, aside from the definition, is the last sentence.

Arc elasticity section has some unnecessarily long sentences which should be broken up. Also I think it needs to be more explicit about the fact that this method is an approximation and why one would wish to use it (to explain to undergrads, because of limited number of price/quantity observations, etc.)

The last question is whether a mention should be made of how these methods are used in empirical research, though that may deserve a section of its own (which brings up other issues like simultaneity and identification).radek (talk) 05:37, 27 April 2010 (UTC)

Oh, in terms of citations - what do you think would be most appropriate/useful here? Undergrad textbooks (while I have a large collection of Macro ones, somehow the pubs don't seem to be as generous with the Micro ones)? Survey articles? As I imply above, something like Mas-Collel et al. is probably inappropriate here, except for minutiae and detail.radek (talk) 05:40, 27 April 2010 (UTC)


 * Re: the partial differential formula -- I agree; I think it's easy enough to simplify the notation, but at a minimum the indices have to match for the own-price elasticity, as you said.
 * In addition, several intermediate and advanced texts I looked at specifically referred to this formulation at the "partial elasticity" (for obvious reasons) and defined it separately from the simpler point-elasticity formulas (although it's still a point elasticity, too, in that it's evaluated at a point; it just has more than 1 independent variable).
 * If no one has any objection, it could be moved to its own separate subsection, after arc elasticity, which I concur is the really important one.
 * In fact, those same references discussed arc elasticity before the simple-derivative version of point elasticity, since the latter is mathematically a more advanced concept. They organized their coverage along these general lines:
 * 1. The fundamental definition: %∆Qd/%∆P = (∆Qd/Q d ) ÷ (∆P/P) = (∆Qd/∆P) ÷ (P/Qd).
 * Some of them refer to this as the (simple) "point elasticity," which it technically is if we know the slope (∆Qd/∆P) independently. E.g., for a linear D curve, (∆Qd/∆P) is constant -- once we know it, we can compute the elasticity at any given point, (Qd,P), with the proviso that the resulting value is accurate only for very small changes in P and Qd around that point (for reasons to be explained elsewhere in the article, i.e., that % changes aren't symmetric).  The point elasticity definition using simple derivatives is then just a refinement of the simpler formula.
 * 2. Arc elasticity
 * I also agree -- this should be emphasized as an approximation that we have to use in certain cases, like in empirical applications when we only know distinct points on the D curve, not the equation of the curve itself, hence we can't use the point elasticity.
 * 3. Point elasticity redefined as (dQ/dP) ÷ (P/Q), because sometimes we may know the D equation and can just use the derivative.
 * 4. Partial elasticity -- a generalization of point elasticity when we take into the account all the nonprice determinants of demand -- all the ceterises that have to remain paribus when we compute any of these elasticities.
 * I'm inclined not to get into the empirical research issue, if we can avoid it, for exactly the reasons you cite, except possibly just to allude to it in a general way. It might be too advanced a topic for a general encyclopedia article.  We could treat that as "not within the scope of this article."
 * A discussion of simultaneity and identification seems more relevant to separate articles on the D & S curves. Gwartney and Stroup devote a whole page trying to explain identification intuitively, and I didn't find it particularly clear or useful.
 * As far as sources go, my opinion is pretty laissez-faire.
 * Survey articles would definitely lend weight to the authoritativeness of this article, but they would likely be too advanced for use by most WP readers, who're probably just looking for a basic understanding.
 * Texts that are available on-line (like those found in the references for many articles, like this one and PPF) have the advantage that the average reader who wanted, say, an alternative explanation, would have access to them. But such text sources are sometimes in limited supply, in the sense that Google Books omits a lot of pages, sometimes at very key points, i.e., they have all the discussion leading up to the formula you want, then ... woops, they skip at least a couple of pages.
 * Some of them even delete all or most of the diagrams, which really limits their usefulness. (They cite "copyrighted material" as the reason. Does that mean the diagrams are covered by a separate copyrights from the rest of the text?  Omitting photos or cartoons is more understandable, because those may be covered by separate copyrights.)
 * Maybe you just need to lean on the publishers' reps a little harder, or plead more convincingly. :) I've got a whole shelf of intro and intermediate texts from the good old days, but they're pretty dated.  On the other hand, the basic principles of elasticity haven't changed that much!  --Jackftwist (talk) 22:58, 28 April 2010 (UTC)

In my view the section on 'Effect on total revenue' needs a few changes. At present is is stated that:

" The percentage change in total revenue is equal to the percentage change in quantity demanded plus the percentage change in price. (One change will be positive, the other negative".

This runs into obvious problems, if one takes it at face value, expecting to be able to apply it as a general formula, even for big changes in quantity/profit. I understand that it is meant to apply at the small changes level, but think the page would benefit from stating this, in order to render the page fully correct and avoid potential misunderstandings on the part of those not sufficiently versed in economics/calculus to know to make the necessary assumptions (like myself).

I did originally make changes to the page to remedy the problem - making the mathematics necessarily a little less neat. Marek has reverted this, explaining the small changes assumption and suggesting that I raise it here on the talk section. Hopefully the insertion of a small reference to the small changes assumption may be agreeable to all.

See also Marek's talk page for our chat there.

Tfll (talk) 08:47, 21 February 2011 (UTC)

Determinants of elasticity: duration vs. durability?
Ever since I first read this article, I've never understood the last sentence of the "Determinants" subsection on "Duration" at all. It just doesn't seem very intuitive to me, at least as explained in the source. (That's not to say it's necessarily counterintuitive—merely that I don't find it intuitive, either.) Here's the full paragraph, plus a link to the original source: (The original source is, which is a tutorial for an intermediate micro course at Illinois State Univ. The tutorial cites as its source the short- and long-run PED for autos (-1.20 and -0.42, respectively) from Pindyck and Rubinfeld's highly reputable text.  Unfortunately, that text isn't available on-line at GoogleBooks or elsewhere, or at least not that I could find.  But it may be available in a library near you; see .)
 * Duration: for most goods, the longer a price change holds, the higher the elasticity is likely to be, as more and more consumers will demand less of the good because they have more time and inclination to search for substitutes. When fuel prices increase suddenly, for instance, consumers may still fill up their empty tanks in the short run, but when prices remain high over several years, more consumers will reduce their demand for gasoline by switching to carpooling or public transportation, investing in vehicles with greater fuel economy or taking other measures. This does not, however, hold for consumer durables, such as cars themselves; eventually, it may become necessary for consumers to replace their present cars, so one would expect demand to be less elastic. [Italics added for emphasis.]

Also unfortunately, that's the only elasticity example for a durable good that the tutorial cites. So Pindyck and Rubinfeld nothwithstanding, a few things still puzzle me about the tutorial's generalization. 1. Another highly reputable text, Kamerschen and Valentine's Intermediate Microeconomic Theory, asserts the opposite conclusion, although the authors provide no empirical support: Durable goods are thought to have more elastic demand curves than nondurables since there are alternatives to purchasing durable goods. Consumers can decide to use their old durables longer, or they can employ more careful maintenance and repair to keep their durable operable longer. (p. 52)

(GoogleBooks doesn't have this text, either, but it's widely available at university libraries. See   )

2. In addition, Kohler's Intermediate Microeconomics (3rd ed., pp. 82-83) provides both the short- and long-run elasticities for a few dozen goods and services. Unfortunately, relatively few of them are durable goods, and cars aren't among the examples they give. But for all the durable goods they do have elasticities for, including car tires, the long-term elasticities are higher than for the short-run—the opposite of the tutorial's generalization. (Based on my survey of about a dozen introductory and intermediate texts, most of the example elasticities they cite appear to be for the short-run.) (Again, GoogleBooks doesn't have this text, but it's widely available at university libraries:  )
 * So it may just be that cars are an exception compared to other durable goods.
 * The PED article cites the elasticity for Ford compact cars as -2.80, i.e., highly elastic, but that's likely to be a short-run estimate. In addition, as another of the determinants of elasticity explains, if substitutes are available for a particular company's branded product, the demand for that specific product (Ford compacts) is likely to be more elastic than the demand for the product in general (cars).

3. Finally, the tutorial's assertion about the PED for durable goods is in the context of the duration of a price change, which are 2 different things. So this seems a bit like an apples-and-oranges comparison. In general, many—maybe most—durable goods eventually reach the point where they malfunction, and the repair-vs.-replace analysis comes out on the side of replacing them.
 * In the case of major appliances like kitchen stoves, refrigerators, microwaves, dishwashers, TVs, air conditioners, furnaces, hot water heaters, computers, etc., many consumers may feel a sense of urgency about replacing some of these items, combined with the lack of close substitutes, that has little or nothing to do with whether the good is a durable or nondurable. (My air conditioner died completely during a heat wave a few summers ago, and my demand curve for a replacement was as close to perfectly inelastic as it could get!  It seems reasonable to expect similar reactions if one's furnace goes out in the middle of winter, or if the hot water heater fails and you don't view cold showers as a feasible option.)
 * So is it the good's durability that's really the dominant driving factor here?
 * As most of us already know, and Kamerschen and Valentine point out, in many cases, all the determinants of PED
 * ...need not operate in the same direction at the same time. One or more may be working against the others, and the magnitude of elasticity will depend upon the relative strength of the opposing forces.  For example, a commodity, such as a refrigerator, may be regarded as a necessity with no close substitutes, which would tend to make the demand inelastic.  Yet it may also comprise a large portion of a family's budget, which would tend to make the demand elastic. (p. 52)

**(Hmmm ... sounds similar to a car, doesn't it?)

Bottom line: I don't find the tutorial's generalization very convincing, especially with only one empirical example to support it. Unless we can find additional empirical evidence, I believe that sentence needs to be deleted. --Jackftwist (talk) 22:53, 6 May 2010 (UTC)

Definition of "price point"?
Could anyone provide a clear definition of "price point" and a source for definition, besides the current WP article Price_point? (Preferably, the source should meet WP standards for credibility, but we'll worry about that later.) The PED article refers to the term at Price_elasticity, but the only reference is to the WP article.

Price_point gives a reasonable discussion of what the term might mean, but it doesn't provide any references at all, other than to other WP articles, so its credibility is questionable.

I searched about 2 dozen on-line business and economics reference sources and found very few mentions of the term. Even in those few cases, "price point" was defined or used as just another term for price. (That's also what the WP article on Price says, but the "price point" article disputes that interpretation on its Talk page.) Alfred Marshall and some other economists of his era used it frequently in this sense.

A Google search didn't turn up anything specific, either (at least in the links on the first 5 of many, many pages). Other than the WP article on price on price point, the other relevant Google hits simply use the term as a synonym for price—it's just business jargon that's somehow meant to be more impressive than simply saying "price"! ("PricePoint" is also a brand name for several different things, including an on-line shopping site and an on-line source of prices of specific medical services in a few states.)

Any solid leads you could provide would be appreciated. Thanks. --Jackftwist (talk) 21:28, 10 May 2010 (UTC)

Lead: Price point appears to be a marketing concept, arising from the observation that, "Small differences in price, such as $11.95 versus $11.96, tend to have a disproportionate impact on sales." So businesses will round final prices to something like 99 cents or $9.99. Source: Marketing dictionary cited in http://www.answers.com/topic/price-points. Personally, I would not include this concept in this article, as it tends to be ignored in microeconomic principles texts, for good or ill. Regardless, the price point article itself could use some cites. Measure for Measure (talk) 19:22, 12 May 2010 (UTC)


 * Thanks. Yes, I found that answers.com citation, too, plus a few more along exactly the same lines!  I didn't mention it above because it seems to be the same sort of thing Price_point refers to in item 3 under "Causes" ("psychological" or "odd-number" pricing).  Coincidentally, in reviewing the coverage of elasticity in some old principles texts today, I ran across a few references to "price point" used merely as a synonym for "price," including in Samuelson's 8th ed. (1970).  (Why use 2 words instead of 1, I dunno.)  I agree, in the absence of some citations to more rigorous discussions of the concept, it probably doesn't belong in this article. --Jackftwist (talk) 22:05, 12 May 2010 (UTC)

External links - Facebook and Youtube??
Why are the two external links to Facebook and Youtube? Shouldn't something more useful be there, or else delete it? —Preceding unsigned comment added by 65.190.142.15 (talk) 00:28, 4 December 2010 (UTC)

Sources wrong?
I wanted to point out that I can't confirm the source for PED scores for rice. The link below would appear to be the Perloff quoted, but either the year is wrong or the source is wrong altogether.

http://are.berkeley.edu/~perloff/papers.htm — Preceding unsigned comment added by Trey333 (talk • contribs) 09:20, 8 February 2011 (UTC)
 * The reference attributes it to . Unfortunately, no online version exists. - Jarry1250 [Who? Discuss.] 21:42, 8 February 2011 (UTC)

Peer review
Should we subject this article to peer review? Lbertolotti (talk) 15:26, 12 August 2015 (UTC)


 * definitely Gagarine (talk) 20:03, 30 October 2018 (UTC)

External links modified
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 * Added archive http://web.archive.org/web/20070626000334/http://statistics.defra.gov.uk/esg/publications/nfs/2000/Section6.pdf to https://statistics.defra.gov.uk/esg/publications/nfs/2000/Section6.pdf

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Cannabis elasticity is too high
In a 2013 meta-analysis of 462 observations, the elasticity of cannabis is roughly -0.25.

http://onlinelibrary.wiley.com/doi/10.1002/hec.2902/pdf

The number quoted of -0.655 isn't incorrect bbut that study seems like an outlier. — Preceding unsigned comment added by Arielweil (talk • contribs) 20:06, 23 November 2017 (UTC)

Are the formula correct?
We have this formula for the definition of elasticity $$e_{\langle p \rangle} = \frac{\mathrm{d} Q/Q}{\mathrm{d} P/P}$$

I'm not sure is correct or at least is not the most "standard" form. Can someone double check?

Is this a bit more clear?

$$ e_{\langle p \rangle} = \frac{\mathrm{d} q }{\mathrm{d} p } \times \frac{p}{q} $$

(I'm not super good with calculus, so forgive me if I'm all wrong) Gagarine (talk) 19:57, 30 October 2018 (UTC)


 * Keep the notation consistent (capital letters) then it's fine, though I have no idea what the "standard" form is. :) Euan Richard (talk) 12:13, 28 November 2018 (UTC)

$$e_{\langle p \rangle} = \frac{\mathrm{d} Q/Q}{\mathrm{d} P/P}$$ is closer to the economic meaning of the definition, percentage response of Q to P. What you gave,$$e_{\langle p \rangle} = \frac{\mathrm{d} q }{\mathrm{d} p } \times \frac{p}{q}$$ is equivalent and more useful when you have a function to differentiate, but it loses the economic meaning, so it is generally taught in a later class, once students understand what elasticity really means. Erasmuse1 (talk) 20:32, 16 April 2020 (UTC)

Great explanation
Very detailed explanation, I understood the concept from this page.Break the clouds (talk) 00:18, 3 April 2019 (UTC)

Limitations of revenue-maximizing and profit-maximizing pricing strategies inconsistency
In the section entitled, "Limitations of revenue-maximizing and profit-maximizing pricing strategies", the second paragraph claim is dubious. As there are no sources given, I've included a citation needed template for it. My concerns with it on a theoretical grounds are as follows: My personal inclination is to delete that whole claim, as within the bounds of an intertemporal problem, it IS profit maximizing. However, as I'm a new editor, I wanted to get other's input before making deeper changes. Any thoughts are appreciated. EducatedRedneck (talk) 19:54, 23 March 2021 (UTC)
 * It does not cite a source for a claim which runs contrary to previous examples and conventional theory.
 * The claim is counterintuitive, also with no citations to back it up.
 * It asserts that the solution to the profit-maximizing problem either does not maximize profits, or else corporations are motivated by some other factor.
 * I think here the problem is not well-defined: the sentence seems to reference profit maximizing in a static (one time-period) sense, but then refers to the optimal strategy in a dynamic (intertemporal) sense. This mixing of static and dynamic metrics muddies the waters greatly.


 * I've heard no input in the last month, so I've gone ahead and been WP:BOLD, deleting the section. If anyone would like to change it back, feel free to revert and I'd appreciate a discussion here. EducatedRedneck (talk) 18:38, 25 April 2021 (UTC)

Definition Formula
This seems to have been touched on earlier but may merit additional discussion. The definition equation is given as:
 * $$e_{\langle p \rangle} = \frac{\mathrm{d} Q/Q}{\mathrm{d} P/P}$$

But shouldn't the equation reference the partial derivatives rather than the absolute derivatives? Presumably, P is a function not only of Q but of other variables, as well, which if multiplicative would impact the result of the equation when it shouldn't. Thus I think it should be:


 * $$e_{\langle p \rangle} = \frac{\mathrm}{\mathrm}$$

or


 * $$e_{\langle p \rangle} = \frac{\mathrm}{\mathrm{d} P/P}$$

 SteveT (talk)  04:42, 12 August 2021 (UTC)


 * I think, given that here demand is considered to be a function only of price (i.e., Qd = f(P), from the Point Elasticity section) absolute derivatives are fine, and more consistent with the rest of the section. There is a section that explicitly mentions partials, so I think leaving the rest of the section as is better; beginners can learn easier, and more advanced users see the mention of partials. EducatedRedneck (talk) 18:37, 15 November 2021 (UTC)

What does the subscript lower-case p in angle brackets mean?
This article says: The formula for the coefficient of price elasticity of demand for a good is:


 * $$E_{\langle p \rangle} = \frac{\Delta Q/Q}{\Delta P/P}$$

where $$P$$ is the price of the good demanded, $$\Delta P$$ is how much it changed, $$Q$$ is the quantity of the good demanded, and $$\Delta Q$$ is how much it changed. But it does not say what the subscript lower-case p in angle brackets means. What is $$\langle p\rangle \text{ ?}$$ Sometimes angle brackets mean an average value, but what is lower-case p? And if it does mean the average value of lower-case p, that still doesn't say what it means to put that quantity, as opposed to some other, in the subscript. Obviously anyone grading students papers and finding this would deduct points for omission of the answers to these questions. Michael Hardy (talk) 20:45, 19 December 2021 (UTC)

Economics
To improve my level of knowledge 223.196.165.70 (talk) 02:35, 21 April 2022 (UTC)

minus sign
In economics we don't usually use the minus sign when defining elasticities. I think that this should be changed in the article. — Preceding unsigned comment added by 142.1.12.204 (talk) 15:24, 31 May 2022 (UTC)

Requesting an edit
I think it would be relevant to add in the "Selected price elasticites" section the following findings from a reliable source (scholars papers). What do you think? AM13prime (talk) 14:58, 14 June 2023 (UTC)
 * Patents
 * −0.30 to −0.50
 * Trademarks
 * −0.25 to −0.40 (international market)


 * @AM13prime I can add the trademark reference, as I could easily verify that. Can you point out where in the patent paper it specifies that? The only thing I was able to find was on p. 15, which specified -0.45 rather than the range you gave. I'm holding off on adding the Trademark reference so I can do it and the Patent reference at the same time. EducatedRedneck (talk) 15:55, 14 June 2023 (UTC)
 * Yes, sorry I think that is my mistake, -0.45 is the correct value from the paper. I think the range was initially added to Wikipedia by the authors in a version that was deleted, in order to have a range rather than a specific value (since it is an estimate). AM13prime (talk) 16:56, 14 June 2023 (UTC)
 * Also, I suspect I know the answer, but do you have any external affiliation with Gaétan de Rassenfosse? If so, you did exactly the right thing by posting an edit request, but are still expected to disclose that you have a WP:COI. (N.b.: I don't expect you to disclose what that connection is, only the presence or absence of such a COI-related connection.) EducatedRedneck (talk) 16:03, 14 June 2023 (UTC)
 * In theory, I have an external affiliation with Gaétan de Rassenfosse since he is my professor at university and I read his papers and I found out some findings which seemed relevant to be added to Wikipedia. Hence, I guess that when it comes to Wikipedia it is considered as a COI. How should I disclose it (I didn't quite understood that on the page WP:COI)? Thanks for your help, it is greatly appriciated! AM13prime (talk) 17:02, 14 June 2023 (UTC)
 * @AM13primeYeah, it's a confusing page; I had to give it several reads myself. I replied on your talk page about how to declare.
 * Alright, the edits are made. Thanks for the edit request, and helping to improve the article! EducatedRedneck (talk) 17:15, 14 June 2023 (UTC)

Lede Phrasing
@Siphomalobola has twice made a change to the lede of the article, which previously read: "A good's Price elasticity of demand ($$E_d$$, PED) is a measure of how sensitive the quantity demanded is to its price." to then read: "In economics, the Price elasticity of demand ($$E_d$$, PED) is a measure of how sensitive the quantity demanded is to its price." Per WP:BRD, we've done a couple bold edits and revert edits each, so it's time to discuss. I'd appreciate outside input as well. I assert this change is not an improvement because of the reference to quantity and price in the second half of the sentence. In the original formulation ("A good's PED"), it was clear that quantity and price were both referring to the good in question, and it also stresses that PED applies only in reference to a good. The new formulation ("In economics, the PED") leaves unneeded ambiguity, and could leave a casual reader with the impression that PED can exist without a reference good. Furthermore, I am not aware of any other discipline in which the phrase "price elasticity of demand" is used, so specifying "In Economics" is unnecessary. I'd like to hear others' perspectives on this. I have my own opinion, but I assume Siphomaloo has their own thoughts, which they find similarly compelling. EducatedRedneck (talk) 21:48, 27 July 2023 (UTC)