
Today's Index
Yesterday's Index 176.0
Help us compile the AmosWEB Free Lunch Index. Tell us about your last lunch.
More About the Index



Imaginary numbers? Real or Not?



COMPOUND INTEREST: Interest that's added to a principal at regular intervals such that each subsequent interest calculation is based on the original principal and the added interest. For example, suppose you have a $100 savings account that pays 5 percent interest. Without compound interest, such that your 5 percent interest is paid only at the end of a year, you will have exactly $105 in one year. However, if your interest is compounded each month you end up with $105.12 after a year. The extra 12 cents comes from interest on the interest paid the first month, interest on the interest paid the second month, interest on the interest paid the third month... well I could go on.
Visit the GLOSS*arama




MIDPOINT ELASTICITY FORMULA: A simple technique for calculating the coefficient of elasticity by estimating the average elasticity for discrete changes in two variables. The distinguishing characteristic of this formula is that percentage changes are calculated based on the average of the initial and ending values of each variable, rather than initial values. An alternative technique is the endpoint elasticity formula. The midpoint elasticity formula is a common method of calculating elasticity, especially the price elasticity of demand, price elasticity of supply, income elasticity of demand, and cross elasticity of demand. This formula is most often used at the introductory level of economic instruction.The FormulaThe midpoint elasticity formula for calculating the response of changes in B to changes in A is given as:midpoint elasticity  =  (B2  B1) (B2 + B1)/2  ÷  (A2  A1) (A2 + A1)/2 
The first term on the righthand side of the equation is the percentage change in variable B. The second term is the percentage change in variable A. The individual items are interpreted as this: A1 is the initial value of A before any changes, A2 is the ending value after A changes, B1 is the initial value of B before any changes, and B2 is the ending value after B changes.The numerator of each term on the righthand side of the equation [(A2  A1) and (B2  B1)] is the discrete change in A and B, respectively. The denominator of each term [(A2 + A1)/2 and (B2 + B1)/2] is the base value from which the percentage change is calculated. A Special PercentageThese base values and the resulting percentage changes are unlike traditional methods of calculating percentage changes. For example, under traditional methods a price that rises from $10 to $12 is a 20 percent increase. This is calculated as the discrete change in price of $2 (= $12  $10), divided by the initial value of $10. However, using the midpoint approach, the discrete change is still $2 (= $12  $10), but instead of using the initial value of $10, the base value is the average of $10 and $12, that is $11 [= ($10 + $12)/2]. This approach results in percentage change of 18.18 percent.While this seems like another example of making a simple task excessively complicated, such is not the case. This is actually intended to generate identical elasticity calculations over a given segment of a curve, whether the variables increase or decrease. This is particularly important for the demand curve and the price elasticity of demand. An Simple ExampleA Standard Demand Curve 

 The time has come for a numerical example to illustrate the midpoint elasticity formula. The demand curve to the right will help. Suppose the demand price of Wacky Willy Stuffed Amigos (those cute and cuddly armadillos and tarantulas) INCREASES from $10 to $12. This price increase causes the quantity demanded to decrease from 5 to 4 Stuffed Amigos. Using a simple, traditional percentage change method of calculation, the price increases by 20 percent, a $2 increase from an $10 initial price. This simple method also results in a 20 percent decrease in the quantity demanded, a decline of 1 Stuffed Amigo from an initial value of 5. This seems relatively simple and straightforward. The price elasticity of demand is thus equal to 1.Or is it? What is the coefficient of elasticity for this same range of the demand curve, if the price DECREASES from $12 to $10 causing the quantity demanded to increase from 4 to 5? In this case, the change in price is 16.7 percent, a $2 decrease from an $12 initial price, and the change in quantity is 25, an increase of 1 Stuffed Amigo from an initial value of 4. This results in a coefficient of elasticity of 1.5. Over the same segment of the demand curve, a price INCREASE indicates a different coefficient of elasticity than does a price DECREASE. This can become confusing, which is where the midpoint formula comes into play. Using the Midpoint FormulaUsing the midpoint formula, a price increase from $10 to $12 gives a change of 18.18 percent, a $2 increase from a midpoint base of $11 [= ($12 + $10)/2]. This is the same 18.18 percent change for a price decrease from $12 to $10. The resulting quantity change between 4 and 5 gives the same percentage change of 22.22 percent, a change of 1 Stuffed Amigo from an midpoint base of $4.5 [= ($4 + $5)/2], whether quantity is increasing from 4 to 5 or decreasing from 5 to 4. As such, the price elasticity of demand is 1.22 regardless of the direction of the price and quantity changes.Alternative SpecificationsOne alternative method of specifying the midpoint elasticity formula can be had by eliminating the "/2" from both the numerator and denominator terms on the righthand side of the equation. Eliminating this unneeded step results in a formula of:midpoint elasticity  =  (B2  B1) (B2 + B1)  ÷  (A2  A1) (A2 + A1) 
Another variation of this midpoint formula is possible by rearranging terms slightly, resulting in:midpoint elasticity  =  (B2  B1) (A2  A1)  x  (A2 + A1) (B2 + B1) 
Both of these alternatives are designed to ease the calculation process just a little. And all three formulas produce identical results. Moreover, for increasingly small changes in the two variables A and B, the midpoint elasticity formula more closely approximates point elasticity.
Recommended Citation:MIDPOINT ELASTICITY FORMULA, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 20002015. [Accessed: January 25, 2015]. Check Out These Related Terms...      Or For A Little Background...       And For Further Study...        
Search Again?
Back to the WEB*pedia



State of the ECONOMY
U.S. Population
January 20, 2015
320,197,621
Up again...U.S. Census Bureau
More Stats


GRAY SKITTERY [What's This?]
Today, you are likely to spend a great deal of time at a going out of business sale trying to buy either a bookshelf that will fit in your closet or a birthday greeting card for your grandfather. Be on the lookout for gnomes hiding in cypress trees. Your Complete Scope
This isn't me! What am I?


Sixty percent of bigfirm executives said the cover letter is as important or more important than the resume itself when you're looking for a new job


"The creative is the place where no one else has ever been. the You have to leave the city of your comfort and go into wilderness of your intuition. What you'll discover will be wonderful. What you'll discover will be yourself."  Alan Alda, Actor


NAA National Association of Accountants


Tell us what you think about AmosWEB. Like what you see? Have suggestions for improvements? Let us know. Click the User Feedback link.
User Feedback

