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LORENZ CURVE: In general, a diagram illustrating the degree of inequality and concentration for a group. This is accomplished by plotting the cumulative percentage of a total amount obtained by cumulative percentages of the group. A common use of the Lorenz curve is the distribution of income, in which the cumulative percentage of income is measured on the vertical axis and the cumulative percentage of the population is measured on the horizontal axis. Perfect equality is indicated by a 45degree line (that is, 10% of the population has 10% of the income, 20% of the population has 20% of the income, etc.). The actual Lorenz curve inevitably lies below the 45degree line. The extent that the Lorenz curve differs from the 45degree line indicates the extent of inequality.
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ARC ELASTICITY: The average elasticity for discrete changes in two variables. The distinguishing characteristic of arc elasticity is that percentage changes are calculated based on the average of initial and ending values of each variable, rather than initial values. Arc elasticity is generally calculated using the midpoint elasticity formula. The contrast to arc elasticity is point elasticity. For infinitesimally small changes in two variables, arc elasticity is the same as point elasticity. Arc elasticity is best considered the average elasticity over a range of values for a relation. Like any average, some values within the range are likely to be greater and some less. However, it provides a quick approximation of elasticity when more precise and sophisticated calculation techniques are not possible.Working Through an ExampleA Standard Demand Curve 

 The demand curve displayed to the right can be used to illustrate the measurement of arc elasticity using the midpoint elasticity formula. If the price declines from $12 to $8, the quantity demanded increases from 4 to 6, from point X to point Z. Using this midpoint formula (with price designated as P and quantity designated as Q) average price elasticity of demand is:midpoint elasticity  =  (Q[Z]  Q[X]) (Q[Z] + Q[X])/2  ÷  (P[Z]  P[X]) (P[Z] + P[X])/2 
midpoint elasticity  =  (6  4) (6 + 4)/2  ÷  (8  12) (8 + 12)/2  =  (2) (5)  ÷  (4) (10) 
midpoint elasticity  =  0.4  ÷  0.4  =  1.0 
Ignoring the minus sign, the price elasticity of demand over this segment of the demand curve from X to Z is 1.0.An Average ValueThis value of 1.0 is actually an average for the entire range between points X and Z. Precise estimates of point elasticity shows that the elasticity is 0.67 at point X and 1.5 at point Z. Moreover, the elasticity is different at each point on a straight line demand curve such as this one. The only point in which the elasticity is exactly equal to 1.0 is at point Y, the midpoint between X and Z.This last observation is worth emphasizing. The midpoint elasticity formula effectively estimates the point elasticity at the very midpoint of the overall segment. This means that the elasticity of any point on a demand curve (point elasticity) can be obtained by calculating the arc elasticity with the midpoint elasticity formula such that the desired point is dead center in the middle, the midpoint of the arc.
Recommended Citation:ARC ELASTICITY, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 20002014. [Accessed: November 22, 2014]. Check Out These Related Terms...       Or For A Little Background...       And For Further Study...      
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State of the ECONOMY
Real average weekly earnings
September 2014
$357.16 Bureau of Labor Statistics
Up 0.2% from Aug. 2014 Constant 198284 dollars
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Post WWI induced hyperinflation in German in the early 1900s raised prices by 726 million times from 1918 to 1923.


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