Main Page: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
mNo edit summary
No edit summary
 
(306 intermediate revisions by more than 100 users not shown)
Line 1: Line 1:
{{Orphan|date=November 2006}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
In [[economics]], the '''Total Revenue Test''' is a means for determining whether [[demand]] is [[elasticity (economics)|elastic]] or inelastic. If an increase in price causes an increase in total [[revenue]], then demand can be said to be inelastic, since the increase in price does not have a large impact on quantity demanded. If an increase in price causes a decrease in total revenue, then demand can be said to be elastic, since the increase in price has a large impact on quantity demanded.


Different commodities may have different elasticitiy depending on whether people need them (necessities) or want them (accessories).
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


'''Examples:'''
Registered users will be able to choose between the following three rendering modes:  


1. Product A currently sells for $10. The seller decides to increase the price to $15, but finds that he ends up making less money. This is because he is selling fewer of the product due to the increased price, and his total revenue has fallen. The demand for this product must be elastic.
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


2. Product A currently sells for $10. The seller decides to increase the price to $15, and finds that his revenue ends up increasing. The demand for this product must be inelastic.
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


== Mathematical explanation ==
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


The mathematical link between them comes from the formula of the price elasticity of demand:
==Demos==
:<math>E_d = - \left(\left(Q_2-Q_1\right)/ \left(P_2- P_1\right)\right) \cdot \left(P_1/Q_1\right)</math>
Where <math>P</math> stands for Price, <math>Q</math> for quantity demanded, <math>\left(Q_2-Q_1\right)</math> for change in quantity demanded, <math>\left(P_2-P_1\right)</math> for change in price.<ref name="Economics">{{cite book |author=Campbell R McConnell|title=Economics : principles, problems, and policies|publisher=McGraw-Hill.|location= New York |year=1987|isbn=0-07-044958-9 : 9780070449589}}</ref>


Using the idea of limits, it’s easy to convert the formula into:
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
:<math>E_d = - \frac{dQ}{dP} \cdot \frac{P}{Q}</math>
or even
:<math>E_d = - f'(P) \cdot \frac{P}{Q}</math>


On the other hand, total revenue is given by <math>TR=P \cdot Q</math>.


Since Q is a function of P, <math>Q = f(P)</math> total revenue can be rewritten as
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


:<math>TR=P \cdot f(P)</math>
==Test pages ==


To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


The differential of total revenue with respect to P is thus:
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
:<math>\frac{dTR}{dP} = 1 \cdot f(P) + P \cdot f'(P)</math>
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
But <math>Q = f(P)</math>, so <math>\frac{dTR}{dP} = f'(P) \cdot P + Q</math>.
 
After both multiplying and dividing by <math>Q</math>, the equation can be rewritten as:
:<math>\frac{dTR}{dP} = Q\left(f'(P) \cdot \frac{P}{Q} + 1\right)</math>
 
The last step is to substitute the elasticity of demand for <math>f'(P) \cdot \frac{P}{Q}</math> to obtain:
:<math>\frac{dTR}{dP} = Q(-E_d + 1) = Q(1 - E_d)</math>.
 
To find the elasticity of demand using the mathematical explanation of the total revenue test, it’s necessary to use the following rule:
 
If demand is elastic, <math>E_d > 1 \!\ </math>, then <math>\dfrac{dR}{dP} < 0 \!\ </math>: price and total revenue move in opposite directions.
If demand is inelastic, <math>E_d < 1 \!\ </math>, then <math>\dfrac{dR}{dP} > 0 \!\ </math>: price and total revenue change in the same direction.  
If demand is unit elastic, <math>E_d = 1</math>, then <math>\frac{dR}{dP} = 0</math>: an increase in price has no influence on the total revenue.
 
==Graph explanation==
Total revenue can be represented by a square or a rectangle formed by connecting the following four points on the demand graph: Price (P), Quantity demanded (Q), Point on the Demand Curve (A) and the origin zero (0) (the intersection of the X axis and the Y axis).
 
Look at the picture.
[[File:Total revenue test.gif|left|thumb|upright|400px]]
This rectangle or square is the measure of total revenue.
 
When price or quantity change the square changes. The change in total revenue caused by price is called the [[price effect]]. The change in total revenue caused by quantity is called the quantity effect.
 
Look at the graph. When price changes from <math>P_1</math> to <math>P_2</math> the price effect is represented by the rectangle <math>P_1 P_2 CA</math> and the quantity effect is formed by rectangle <math>Q_1 Q_2 BC</math>.
 
So, if the square of price effect is greater than the square of the quantity effect the demand is inelastic and <math>E_d < 1 \!\ </math>.
If the square of price effect is less than the square of the quantity effect the demand is elastic and <math>E_d > 1 \!\ </math>.
If effects are equal the demand is unit elastic (or unitary elastic).<ref name="Focus: : High School Economics">{{cite book |author=Michael Watts|title=Focus: : High School Economics|publisher=National Council on
Economic Educ.|location=|year=2001|isbn=1-56183-614-1}}</ref>
 
==References==
{{reflist}}
 
[[Category:Elasticity (economics)]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

Retrieved from "https://en.formulasearchengine.com/index.php?title=Main_Page&oldid=329754"