Quadrature (mathematics): Difference between revisions

Revision as of 00:33, 31 August 2013

In mathematics and economics, the arc elasticity is the elasticity of one variable with respect to another between two given points. It is the ratio of the percentage change of one of the variables between the two points to the percentage change of the other variable. It contrasts with the point elasticity, which is the limit of the arc elasticity as the distance between the two points approaches zero and which hence is defined at a single point rather than for a pair of points.

Formula

The y arc elasticity of x is defined as:

E_{x, y} = \frac{% change in x}{% change in y}

where the percentage change in going from point 1 to point 2 is usually calculated relative to the midpoint:

% change in x = \frac{x_{2} - x_{1}}{(x_{2} + x_{1}) / 2};

% change in y = \frac{y_{2} - y_{1}}{(y_{2} + y_{1}) / 2} .

The use of the midpoint arc elasticity formula (with the midpoint rather than the initial point (x₁, y₁) used for calculating percentages) was advocated by R. G. D. Allen for use when x refers to the quantity of a good demanded or supplied and y refers to its price, due to the following properties: (1) it is symmetric with respect to the two prices and quantities, (2) it is independent of the units of measurement, and (3) it yields a value of unity if the total revenues (price times quantity) at the two points are equal.^[1]

The arc elasticity is used when there is not a general function for the relationship of two variables, but two points on the relationship are known. in contrast, calculation of the point elasticity requires detailed knowledge of the functional relationship and can be calculated wherever the function is defined.

For comparison, the y point elasticity of x is given by

E_{x, y} = \frac{\partial x}{\partial y} \cdot \frac{y}{x} = \frac{\partial \ln x}{\partial \ln y}

Application in economics

The arc elasticity of quantity demanded (or quantity supplied) Q with respect to price P, also known as the arc price elasticity of demand (or supply), is calculated as

(% change in Q) / (% change in P)

Example

Suppose that two points on a demand curve, $(Q_{1}, P_{1})$ and $(Q_{2}, P_{2})$ , are known. (Nothing else might be known about the demand curve.) Then the arc elasticity is obtained using the formula

E_{p} = \frac{\frac{Q_{2} - Q_{1}}{(Q_{1} + Q_{2}) / 2}}{\frac{P_{2} - P_{1}}{(P_{1} + P_{2}) / 2}} .

Suppose the quantity of hot dogs demanded at halftime of football games is measured at two different games: at one measurement it is 80 units, and at the other measurement it is 120 units. The percent change, measured against the average, would be (120-80)/((120+80)/2))=40%.

In contrast, if the percentage change were measured against the initial value, the result would be (120-80)/80= 50%. The percent change for the opposite trend, 120 units to 80 units, would be (80-120)/120 = -33.3%. The midpoint formula has the benefit that a movement from A to B is measured as the same as a movement from B to A in absolute value. (In this case, the movement from 120 to 80 would be measured as -40%.)

Suppose that the change in the price of hot dogs, which led to this change in quantity demanded from 80 to 120, was from $3 to $1. The percent change in price measured against the midpoint would be (1-3)/2 = -100%, so the price elasticity of demand is 40%/(-100%) or -40%. It is common to refer to the absolute value of the price elasticity as simply price elasticity, since for a normal (decreasing) demand curve the elasticity is always negative and so the "minus" part can be made implicit. Thus the demand of the football fans for hot dogs has 40% elasticity.

References

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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[1]

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+In [[mathematics]] and [[economics]], the '''arc elasticity''' is the [[Elasticity (mathematics)|elasticity]] of one variable with respect to another between two given points. It is the ratio of the percentage change of one of the variables between the two points to the percentage change of the other variable. It contrasts with the ''point elasticity'', which is the limit of the arc elasticity as the distance between the two points approaches zero and which hence is defined at a single point rather than for a pair of points.
+==Formula==
+The ''y'' arc elasticity of ''x'' is defined as:
+:<math>E_{x,y} = \frac{\% \mbox{ change in } x}{\% \mbox{ change in } y}</math>
+where the percentage change in going from point 1 to point 2 is usually calculated relative to the midpoint:
+:<math>\% \mbox{ change in } x = \frac{x_2 - x_1}{(x_2 + x_1)/2};</math>
+:<math>\% \mbox{ change in } y = \frac{y_2 - y_1}{(y_2 + y_1)/2}.</math>
+The use of the midpoint arc elasticity formula (with the midpoint rather than the initial point (''x''<sub>1</sub>, ''y''<sub>1</sub>) used for calculating percentages) was advocated by [[R. G. D. Allen]] for use when ''x'' refers to the quantity of a good demanded or supplied and ''y'' refers to its price, due to the following properties: (1) it is symmetric with respect to the two prices and quantities, (2) it is independent of the units of measurement, and (3) it yields a value of unity if the total revenues (price times quantity) at the two points are equal.<ref>{{cite journal |first=R. G. D. |last=Allen |year=1933 |title=The Concept of Arc Elasticity of Demand |journal=[[Review of Economic Studies]] |volume=1 |issue=3 |pages=226–229 |jstor=2967486 }}</ref>
+The arc elasticity is used when there is not a general function for the relationship of two variables, but two points on the relationship are known. in contrast, calculation of the point elasticity requires detailed knowledge of the functional relationship and can be calculated wherever the function is defined.
+For comparison, the ''y'' point elasticity of ''x'' is given by
+:<math>E_{x,y} = \frac{\partial x}{\partial y} \cdot \frac{y}{x} = \frac{\partial \ln x}{\partial \ln y}</math>
+==Application in economics==
+The arc elasticity of quantity demanded (or quantity supplied) Q with respect to price P, also known as the arc price elasticity of demand (or supply), is calculated as
+:<math>(\% \mbox{ change in }Q)/(\%\mbox{ change in }P)</math>
+===Example===
+Suppose that two points on a demand curve, <math>(Q_1, P_1)</math> and <math>(Q_2, P_2)</math>, are known.  (Nothing else might be known about the demand curve.)  Then the arc elasticity is obtained using the formula <br>
+:<math>E_p =\frac{\frac{Q_2-Q_1}{(Q_1+Q_2)/2}}{\frac{P_2-P_1}{(P_1+P_2)/2}}.</math>
+Suppose the quantity of hot dogs demanded at halftime of football games is measured at two different games: at one measurement it is 80 units, and at the other measurement it is 120 units.  The percent change, measured against the average, would be (120-80)/((120+80)/2))=40%.
+In contrast, if the percentage change were measured against the initial value, the result would be (120-80)/80= 50%.  The percent change for the opposite trend, 120 units to 80 units, would be (80-120)/120 = -33.3%.  The midpoint formula has the benefit that a movement from A to B is measured as the same as a movement from B to A in absolute value.  (In this case, the movement from 120 to 80 would be measured as -40%.)
+Suppose that the change in the price of hot dogs, which led to this change in quantity demanded from 80 to 120, was from $3 to $1. The percent change in price measured against the midpoint would be (1-3)/2 = -100%, so the [[price elasticity of demand]] is 40%/(-100%) or -40%.  It is common to refer to the ''absolute value'' of the price elasticity as simply price elasticity, since for a normal (decreasing) demand curve the elasticity is always negative and so the "minus" part can be made implicit.  Thus the demand of the football fans for hot dogs has 40% elasticity.
+==See also==
+* [[Elasticity of a function]]
+* [[Elasticity (economics)]]
+==References==
+<references/>
+[[Category:Elasticity (economics)]]

Quadrature (mathematics): Difference between revisions

Revision as of 00:33, 31 August 2013

Contents

Formula

Application in economics

Example

See also

References

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Quadrature (mathematics): Difference between revisions

Revision as of 00:33, 31 August 2013

Formula

Application in economics

Example

See also

References

Navigation menu

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