User talk:Jackftwist/Jack's Test Page

--Jackftwist (talk) 22:50, 14 April 2010 (UTC) Econ PhD, taught for 16 yrs at undergrad & grad levels, 6 yrs in academic administration (partly overlapping with teaching time), 8 yrs in policy analysis as a practicing economist, mainly in labor-market issues; current interests mainly focus on introductory micro & macro, intermediate micro, and economic education. (And yes, my screen name is taken from that movie character)[reply]

Could you clarify which diagram you're talking about? Is it the the one that's convex to the origin (i.e., the decreasing costs case)? If so, I see how the diagram could leave that mistaken impression, and we'll try to tweak the diagram to fix it (if we can achieve the necessary degree of resolution in how the diagram gets rendered on the screen). The short answer to your question is no, —Preceding unsigned comment added by Jackftwist (talk • contribs) 01:21, 15 April 2010 (UTC)[reply]

Tea template test

{{tea}} —Preceding unsigned comment added by Jackftwist (talk • contribs) 17:32, 17 April 2010 (UTC)[reply]

--Jackftwist (talk) 17:24, 8 May 2010 (UTC)[reply]

Usage

{{subst:tea}}

Test: Cut-and-paste from Word

Interpretation

In microeconomics, the PPF shows the options open to an individual, household, or firm, in a 2-good world. The two-good world is a deliberate theoretical simplification, but economists usually think of the second good as a composite basket of all other goods. For example, by definition each point on the curve is productively efficient, but, given the nature of market demand, one point might be less profitable than another. Equilibrium for a firm will be the point on the PPF that is most profitable. ^[1] --Jackftwist (talk) 21:48, 17 April 2010 (UTC)[reply]

Price Elasticity Formula

E_{d}={\frac {\%\ {\mbox{change in quantity demanded}}}{\%\ {\mbox{change in price}}}}={\frac {\Delta Q_{d}/Q_{d}}{\Delta P_{d}/P_{d}}}

E_{d}={\frac {P}{Q}}\times {\frac {dQ}{dP}}

E_{d}={\frac {\frac {P_{1}+P_{2}}{2}}{\frac {Q_{1}+Q_{2}}{2}}}\times {\frac {\Delta Q}{\Delta P}}={\frac {P_{1}+P_{2}}{Q_{1}+Q_{2}}}\times {\frac {\Delta Q}{\Delta P}}

let $\displaystyle x(p,w)$ be the demand of goods $x_{1},x_{2},\dots ,x_{L}$ as a function of parameters price and wealth, and let $\displaystyle x_{l}(p,w)$ be the demand for good $\displaystyle l$ . The elasticity of demand $\displaystyle x_{l}(p,w)$ with respect to price $p_{k}$ is

E_{x_{l},p_{k}}={\frac {\partial x_{l}(p,w)}{\partial p_{k}}}\cdot {\frac {p_{k}}{x_{l}(p,w)}}={\frac {\partial \log x_{l}(p,w)}{\partial \log p_{k}}}

LaTeX Math Syntax - 1

$p(x+y)$ .

$\pi ^{h}=xp(x+y)-c(x)+sx$ where $xp(x+y)$ is total revenue, $c(x)$ is total cost

$\pi ^{f}=yp(x+y)-c(y)$ .

$xp_{x}+p-c_{q}+s=0$

$yp_{y}+p-c_{y}=0$ , where subscripted variables denote partial derivatives.

$y=R1(x;s)$ and $y=R2(x)$ .

$p=a-b(x+y)$

Notice (Info) Box Template

This info box contains instructions for substituting another template.

"New Messages" / "Talkbox" notification box example

New messages at User talk:Kingpin13

NOTE: This is only an example. There are no messages for JFT on Kingpin13's talk page.

Hello, Jackftwist. You have new messages at Kingpin13's talk page.
You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

- Kingpin¹³ (talk) 19:16, 5 May 2010 (UTC)[reply]

PED estimate for eggs (further comments)

Continuing the above discussion on this topic: Providing a range of estimates, as M4M proposes, is probably the most reasonable way to go.

Two of the standard determinants of the PED for a good may help explain why the PED estimates for eggs are so low, possibly even as low as (-) 0.1: (1) spending on eggs probably accounts for a very small percentage of a typical household's income, so the income effect of a change in the price of eggs would be correspondingly small; and (2) there may be few satisfactory substitutes for eggs purchased directly for household-consumption purposes. (See note at † below.)

(1) Spending of eggs as a proportion of income — The U.S. Consumer Price Index for All Urban Consumers (CPI-U, a widely used measure of the U.S. consumer-price level) assigns a weight of only about 1.75% to its market-basket category "meat, poultry, fish, eggs." As described below, eggs are relatively inexpensive, so they probably account for a minuscule part of even that 1.75%. Hence, even doubling the price of eggs wouldn't significantly affect a "typical" household budget, so we'd expect the income effect of the price increase to be relatively small, which would in turn tend to reduce their PED. (Granted, the CPI-U has a number of well-known methodological flaws, but for our purposes, the weights of various items in its market basket of consumer goods and services are both readily available and reasonable reference points to use for comparison.)

At my local supermarket (in a high-cost-of-living area), the price of a carton of a dozen regular "large Grade A" eggs is $2.29 (about £1.45 at current exchange rates), plus sales tax — significantly cheaper than a gallon of gas! (Organic, cage-free eggs are $3.59 [≈ £2.25] a dozen.) Combined with the small weighting of eggs in a "typical" market basket, a change in egg prices wouldn't significantly affect a "typical" household budget, so we'd expect a relatively low PED.

(2) Lack of close substitutes or eggs — M4M alluded to this point in his comments.

As sources of protein and other nutritional dietary components, products like meat, poultry, fish, milk, and cheese are generally accepted as satisfactory, and possibly even preferable, substitutes for eggs (because of eggs' relatively high content of fat and LDL ["bad"] cholesterol relative to their protein content, even though this risk now appears to be significantly lower than originally thought).
- And we can't yet know whether the recent, widespread contamination of eggs with salmonella will have any long-term effect on the demand for eggs.
For other uses, though, the acceptability of egg-substitute products (e.g., EggBeaters™) is less clear^‡:
- Using egg substitutes to make scrambled eggs, omelets, or sauces may be completely acceptable to all but the most discriminating palates, but meringues and eggs "sunny-side up" would be a different matter!
- I don't know how well egg substitutes work in baking, although when packaged mixes already contain the necessary eggs, they've obviously been processed somehow.
But the cost of egg substitutes may have an even greater effect on their acceptability than how well they perform in use does:
- In the supermarket where I compared prices, the EggBeaters™ brand substitute costs the equivalent of about $5.25/doz (£3.25)—well over twice the price of regular eggs! The store-brand subsitute was the equivalent of about $4.20/dozen (£2.60), or over 80% more than regular eggs.
- It's probably not "typical" consumer behavior to respond to a price increase in one product by substituting a more expensive one, although there are circumstances where that response would make sense.

† Note: The discussion above assumes that the PED estimates cited for eggs apply just to final demand for eggs by consumers only, vs. (total) demand including demand for eggs to be used as an intermediate good in producing other goods and services, such as cakes, cookies (and packaged mixes for these and other baked goods), or in restaurant meals (e.g., breakfast dishes or Hollandaise sauce). If the estimates are for total demand instead of only final consumer demand, then that would broaden the definition of "eggs," which would tend to reduce the PED even further.

The breadth of a good's definition is, of course, another determinant of demand: the demand for, say, "toothpaste" in general is almost certainly less elastic than the demand for a particular brand of toothpaste, because if the price of one brand rises while the price of all other brands remain constant, some consumers will likely switch from the former to one of the latter, rather than reducing the total amount of toothpaste they use.
In the case of eggs, if the price of eggs rises, some consumers may buy fewer eggs to use in baking cakes, etc., "from scratch" and switch instead to using cake mixes. But because those mixes also contain eggs, the total demand for eggs might fall less (if at all) than final consumer demand for eggs by consumers would.

‡ According to the list of ingredients shown on their cartons, egg-substitute products like EggBeaters™ do contain egg whites, although the content is less than 1%.

--Jack --Jackftwist (talk) 17:57, 19 October 2010 (UTC)[reply]

Krugman's special case of linear PPFs

Please see my dissenting note at User_talk:Jarry1250/Archive_10#Inverted_PPF_figure. --Jackftwist (talk) 08:21, 12 August 2010 (UTC) http://scholar.google.com/scholar?hl=en&q=%22Production-possibility+frontier%22+%22economies+of+scale%22&btnG=Search&as_sdt=80000000000000&as_ylo=&as_vis=0 http://books.google.com/books?hl=en&lr=&id=tpdYD-6lGlsC&oi=fnd&pg=PA268=onepage&q&f=false#v=onepage&q&f=false --Jackftwist (talk) 23:20, 2 October 2010 (UTC)[reply]

Of dingoes, "and/or", and Footy - DRAFT (Noetica, MOS) - * NOT USED *

And/or (WP:MOS section)

Avoid the construct and/or on Wikipedia. In general, where it is important to mark an inclusive or, use x or y, or both, rather than x and/or y. For an exclusive or, use either x or y, and optionally add but not both, if it is necessary to stress the exclusivity.

Where more than two possibilities are presented, from which a combination is to be selected, it is even less desirable to use and/or. With two possibilities, at least the intention is clear; but with more than two it may not be. Instead of x, y, and/or z, use an appropriate alternative, such as one or more of x, y, and z; some or all of x, y, and z.

Sometimes or is ambiguous in another way: Wild dogs, or dingoes, inhabit this stretch of land. Are wild dogs and dingoes the same or different? For one case write: wild dogs (dingoes) inhabit ... (meaning dingoes are wild dogs); for the other case write: either wild dogs or dingoes inhabit ....

G'day, Mate! Thanks, but I'm not sure I was being all that shrewd. The hint on your Talk page about being an Aussie seems fairly clear to me, at least if one is willing to take a (very?) small leap of faith, given that you don't deny the "consensus."

I'll reply as soon as I can to your most recent post re the dingoes example, but it'll probably be a day or two ... or more. Interim reply (and please do critique it):

I completely bungled my set theory terminology in my post. My set theory is very old and rusty, and even at its best, it wasn't very good. When I said:

Assuming for the purpose of illustration that dingoes and wild dogs are identical (that is, neither one is a subset of the other), ...

the parenthetical "that is, ..." phrase was completely wrong. I meant identical to be taken absolutely literally. I also intended that is to be interpreted exactly the way you stated a little later, "that is, which is to say the same as". Unfortunately, what I said after that is didn't convey what I meant it to at all. I'd completely forgotten that every set is a subset of itself, although not a proper subset. (Oh well, my high-school text for my advanced algebra course didn't even mention it until the bottom of page 2, so how was I to know it was important?)

To be clear: Solely for the purpose of this illustration (disregarding that the followinig statement may in fact be incorrect), I intended dingoes and wild dogs to be sets that are completely overlapping (whatever the correct terminology is for that)—by which I intend to mean that the 2 sets meet all of the following criteria inclusively (if my terminology is correct):

(1) the 2 sets are identical: {wild dogs} ≡ {dingoes}

(2) neither set is a proper subset of the other,

(3) the 2 sets don't just partly overlap, and

(4) the 2 sets are not disjoint.

Is it proper to interpret "disjoint" as "mutually exclusive"? In any event, I think one might describe my intent to be that the two sets are mutually inclusive.

In nonmathematical terms (but not in 1-to-1 correspondence with the above), and again, solely for the purpose of this illustration:

All dingoes are (also) wild dogs, and all wild dogs are (also) dingoes.
There are no dingoes that are not wild dogs, and there are no wild dogs that are not dingoes.
The 2 terms are perfect synonyms.

If I might ask a favor, I'd greatly appreciate it if you could tell me the correct term for "completely overlapping" so I can use it in my post. (Is it just "identical sets"? I found that in my old algebra text, too.)

But even if the conditions above accurately describe our respective assumptions for the purpose of trying to "disambiguate" (?) the grammatical usage of "or", unfortunately we still don't have a "meeting of the minds" about how well the dingo example per se illustrates this principle.

To the contrary, I think the dingo example confuses the issue rather than clarifying it.

And, to quote the inimitable Mrs. Slocumbe from Are You Being Served, "I am unanimous in this!" IMO the confusion (or my confusion, anyway) has at least 3 separate sources, or layers:

Any ambiguity stemming from the meaning of "or" in this grammatical context;
The ambiguity that you described so well of whether "dingoes" and "wild dogs"do, in fact, mean exactly the same thing; and
A linguistic difference between you Aussies and us Yanks: Many, perhaps most, of us Yanks simply aren't very sure what a dingo is, if we have any idea at all and even if we've heard the word.

The MoS article might as well use platypus, or any of the many other species that are unique to Australasia. (BTW, our Public Broadcasting Service happened to have a 3– or 4–part series a few weeks ago on the many remarkable species that are unique to your part of the world, but I don't remember if they mentioned dingoes!)

We don't have a comparable species or subspecies here, as far as I know. (Wolves, coyotes, and foxes, yes, but those are all clearly different species from anything we'd call a "dog". To us, the term "wild dogs" literally means feral canines of the domestic species.

I'd already read the WP article Dingo, but it wasn't very helpful because, for all the reasons you point out, the distinction (if any) can sometimes be blurry even to an Aussie—and, judging from the ambiguity in the article, to wildlife biologists and zoologists as well!

Dictionaries don't seem to help, either, because their definitions are necessarily brief (and perhaps because the editors couldn't figure it out, either!). They all say almost exactly the same thing:

a wild dog (Canis dingo) of Australia having a tan or reddish coat that is often considered a subspecies (C. familiaris dingo) of the domestic dog

[MWC11; Note: I added the emphasis to "often considered"]

So, "often considered" but not "always"? That hardly clarifies whether the two are identical or not! In fact, it seems (to me) to imply they're not necessarily identical.

I also wonder if there's some ambiguity implicit in "a wild dog"; i.e., do they mean "a type of wild dog (among 2 or more types)"? Or is the "a" present only to serve a purely grammatical function that is totally irrelevant to the substance of the definition?

Reply to my earlier post

Well! First, just let me put the kettle on.

Now, don't assume that all Australians say "g'day", or have the faintest idea about "footy". I gather you mean the game played with long balls, not a stick and a hard little red ball, right? I know nothing of such matters. On the other hand, I am frequently among kangaroos, so I do fit at least one stereotype. Not dingoes: but I did look after a friend's half-dingo-half-German-shepherd for a year, while he was overseas. Looked like the one at the top of Dingo article. A really clever animal.

I suggest you review the terms at Set_theory#Basic_concepts. "Overlapping" is not among them; but I used it informally to mean "having elements in common". By such a definition, every set would overlap with itself, except that it leaves out the null set (with respect to itself alone, and to itself and any other set), which has no elements yet is a subset of every set (including itself, of course). For that reason, "overlapping" is desperately loose, and best left out of any serious continuation. For a similar but more remediable quirk, see Intersection_(set_theory)#Nullary_intersection.

If you want to say that all wild dogs are dingoes, and all dingoes are wild dogs, you can indeed say "the set of dingoes is identical to the set of wild dogs". It gets complicated when you reflect on whether you mean this as a matter of definition, or as an accidental fact. I mean, it could be that there are many wild dogs, and some of them you want to call dingoes; then all the non-dingoes die out. In that case it is just accidentally true that the sets are identical, yes? Your notation "{wild dogs} ≡ {dingoes}" then looks questionable, hmm? A lot depends on – a lot else. But I'm too tired to get into any of it.

For the rest, what can I say? I am no deep authority on set theory, nor on dingoes. I do claim expertise with punctuation: its theory, its regimentation in practice, and something of its history. If you think things need to be taken forward with this newcomer, the slash "/", I'll watch with interest and I might participate. However, with respect: I think you have extracted from me a generous slice of my attention.

I hope you, in turn, will look at the new draft (see the pale green navbox) in this section of WT:MOS. It was a long time in the making, believe me. See also the latest tranches of discussion below it (latest chapters in an epic); and watch for a final version tomorrow.

Now: milk no sugar, right?

Noetica^Tea? 05:43, 19 July 2011 (UTC)[reply]

WP "Collapsed Box" Syntax Example

See Wordpad text file.

Font examples

Some adjustments as per suggestions above: [Placeholder.] (Right). [Placeholder.] (Wrong)

<span style="font-size:150%">[</span><span style="background:#efe; font-family: Georgia, serif;">Placeholder.</span><span style="font-size:150%">]</span> <span style="font-size:85%">(Right)</span>

The right/wrong are placed behind the examples so we don't need to concern about the capitalization when making it into a template. -- Sameboat - 同舟 (talk) 01:12, 28 July 2011 (UTC)[reply]

New comment:

Noetica & Memorable (MOS re Dashes)

"TMTCFY"? new "Dashes" section & "memorable"

I'm delighted to see the new "Dashes" section progressing (it appears) in the approval/adoption process.

In your reply to one of A. di M.'s posts in the subsequent discussion, you used the abbreviation "TMTCFY". A search of 4 major online dictionaries of abbreviations, plus both a WP and a Google search, yielded no explanation of it, and I couldn't figure it out from the context. Am I missing something? (I'm not particularly fluent in that argot.)

Finally, in the section "Features of the Draft" of your "Preliminary Notes", you said, "... the principles themselves are simple and memorable." Memorable? MWC11 defines memorable as, "worth remembering : NOTABLE <a ~ occasion>." Although these rules might be "worth remembering" in one sense, I don't think they rise to the standard MWC11 intended, which IMO implies something of considerably greater significance. E.g., the day you were born was probably a memorable day to your mother; "To be or not to be, that is the question ..." is one of the most memorable lines in all of English-language literature; but "an en dash is not used for a hyphenated personal name"? Umm, not so much. It's simply of a different ilk altogether. And there are too many of them to be "easy to remember", at least for me (and my memory for grammar rules is pretty good, although quite short of yours, of course).

I'm not sure principles was the right word to use, either. Aren't they just rules? Or rationales for those rules? But I'll let that one slide for now. My prior quibble is sufficient unto the day. And now, one craves a cup of tea. – Jack --Jackftwist (talk) 18:22, 25 July 2011 (UTC)[reply]

That's “Too many things can f*** you”, innit? ― A. di M._plé^dréachtaí 23:37, 26 July 2011 (UTC)[reply]

That seems to make sense in the context. Many thanks. Odd that it didn't show up in at least my Google search, or perhaps it was just so many pages down in the search results that I ran out of patience and/or ;-) time before I got to that entry. Jack --Jackftwist (talk) 16:09, 27 July 2011 (UTC)[reply]

Jack, TMTCFY stands for "to make things clearer for you". I used it in answering A di M, who has a habit of using such abbreviated forms to the distress of his elders (you and me) who have no idea what he might mean by them. ITCN?

Now I turn to the word memorable. As a preliminary I should warn you (as a black-belt might in a casual skirmish): I collect dictionaries as well as style guides. I have OED and two editions of SOED installed on every computer in the house, and access to the current online version of OED, along with every major British and American dictionary, in hardcopy or some other form. Memorable, according to the current SOED, has been in English since the 15th century and has these meanings: "Worthy of remembrance or note, worth remembering, not to be forgotten; able to be remembered, easy to remember." Current OED gives this as its second sense: "2. Easy to remember, able to be remembered; memorizable." Citations include Shakespeare and Ruskin; the most recent citation is from 1991. Most American dictionaries agree, including the big brother of the one you cite above: MWNI3 ([Merriam-]Webster's Third New International Dictionary).

As for principles, that is chosen with great care. The contents of MOS are not rules in the fullest sense, because MOS provides guidelines rather than rules of policy for the project. They are rules in a weaker sense, of course: like the rules of a game that one can play or not, or cheat at or not. But principles rules out interpretations that rules principally evokes.

I hope you are content that the issue of positive and negative examples has been addressed. There will never be agreement on the best way to distinguish them; but the matter has been taken seriously.

Finally, I'm sorry for the late reply. I was exhausted after the marathon dashes drama, and just wanted silence for a couple of weeks.

Tea next time, OK? (Could you bring a couple of muffins?)

Noetica^Tea? 05:55, 5 August 2011 (UTC)[reply]

--Jackftwist (talk) 21:17, 20 August 2011 (UTC)[reply]

Draft reply

A period of recuperation from your "marathon dashes drama" was well deserved, indeed. No apology necessary. I've been much occupied elsewhere lately, too, and still am.

The way you've indicated correct and incorrect examples in the "Dashes" section will just have to do. The ultimate success or failure of neither the WP enterprise in general nor the MoS in particular hardly rests on this matter. To paraphrase the saying about academic politics, the debates on these points are so bitter because the stakes are so small. (For a truly remarkable and egregious recent example, others might wish to see the Great Crêpes vs. Crepes Fracas, which you rescued almost singlehandedly from utter piffle through your contributions.)
(For other readers: This link should be to item 13 on the Crêpe Talk page. Click "[show]" in the medium-blue "discussion" header line to expand the box.)
Regarding memorable and principles: Ahem. I see. Yes. Well. Quite.
1. I assumed from the outset that your library of dictionaries and usage guides, as well as your on-line access to them, would dwarf my meager collection, so I had absolutely no intention or desire to provoke a "dueling dictionaries" match with you. But because your reply cites the 2nd sense of "memorable" from OED, I should note that my 1971 OED edition explicitly labels that sense "rare" [italics in the original]. Coming from OED, I took "rare" at face value. As for your reference to Shakespeare and Rushkin, such towering masters of the language can get away with using it, particularly in poetry, in ways the rest of us simply can't in ordinary discourse (e.g., WP Talk pages). If any editors on these pages have, in fact, risen to Shakespeare's or Rushkin's stellar level of literary and linguistic achievement, though, I have yet to make their acquaintance.
2. In the end the difference between your connotation and mine in both of these cases may be simply a matter of WP:ENVAR. So, "two peoples, separated by a common language" and all that.
3. But regardless of the merits of your rationales, my query for clarification of your usage in your original comment was in good faith, so what gives me the impression of a rather haughty, chiding tone in your reply seems somewhat ... uh ... indelicate? ... unseemly? ... perhaps a tad uncivil?
BTW, I thought you would have gathered from the 2 explicit references to "MWC11" in my comment above that I was already familiar with your very useful compilation of style guide and dictionary abbreviations, so you didn't need to decode "MWNI3" for me in your reply. But it's an entirely different matter with your use of (at best) obscure abbreviations like "TMTCFY"—and now "ITCN", which I don't recognize, either. (Are you just making these up as you go along? WTFO?) Besides, I rather preferred A. di M.'s interpretation of "TMTCFY"; it's clever instead of condescending.
Re our separate discussion above of "or dingoes", etc.: I'm still far from satisfied on that matter, but I doubt I'll ever have time to reply to your last post there. Maybe it's best for me just to let that sleeping wild dog (or dingo) lie, instead of risking getting bitch-slapped again. Time to just walk quietly away for now.

Sorry, no time for tea and muffins right now. (You'd probably just find fault with any muffins I brought, anyway.) Must dash. Ta. Jackftwist (talk) 21:04, 21 August 2011 (UTC)[reply]

"Holiday" & "WikiSloth" Templates

Jackftwist is away on vacation and may not respond swiftly to queries.

--Jackftwist (talk) 21:02, 7 August 2011 (UTC)[reply]

This user is a WikiSloth.

--Jackftwist (talk) 22:05, 7 August 2011 (UTC)[reply]

"Outdent" example

[indented post] x x x x x x x x x x ....

[Reply]

Blue Box Syntax

Hi, I'm User:name (talk • contribs • blocks • protects • deletions • moves),

Another example

Hello, ______ Welcome to Wikipedia! Thank you for your contributions. You may benefit from following some of the links below, which will help you get the most out of Wikipedia. If you have any questions you can ask me on my talk page, or place {{helpme}} on your talk page and ask your question there. Please remember to sign your name on talk pages by clicking

or by typing four tildes "~~~~"; this will automatically produce your name and the date. If you are already excited about Wikipedia, you might want to consider being "adopted" by a more experienced editor or joining a WikiProject to collaborate with others in creating and improving articles of your interest. Click here for a directory of all the WikiProjects. Finally, please do your best to always fill in the edit summary field when making edits to pages. Happy editing! Petrb (talk) 09:10, 7 January 2011 (UTC)[reply]

User boxes

PhD

This user has a Doctor of Philosophy degree in Economics.

Project Econ Info- & Navboxes

Infoboxes

{{Infobox Economist}}
{{Infobox Economy}}

{{Infobox Economist}} {{Infobox Economy}}

Navboxes

{{Economics}} {{Economics sidebar}} {{Economic history}} {{Economic systems sidebar}} {{Macroeconomics}} {{Consumption}}

^ Coelli, Time; Prasada Rao, D. S.; Battese, George E. (1998). An Introduction to Efficiency and Productivity Analysis. Springer. pp. 59–60. ISBN 9780792380627.

[1] Coelli, Time; Prasada Rao, D. S.; Battese, George E. (1998). An Introduction to Efficiency and Productivity Analysis. Springer. pp. 59–60. ISBN 9780792380627.

[1]