The Arc Formula



There are also times when we do not know the original price or quantity of a good.  When this occurs we use an average to substitute for the original price and quantity.  The way to calculate an average for the price elasticity of demand is to add together the numbers for quantity and divide by 2.  Mathematically this is written as;
Q1 + Q2  = Average value of Q
      2
We place this into the denominator for each part of the equation to obtain the new formula.
   Q2 - Q1       = %DQ
(Q2 + Q1)/2
    P2 - P1        = %DP
(P2 + P1)/2
This formula requires a lot of work, fortunately it can be simplified as is shown below;

Example:  Assume that a company can sell 400 widgets at $5 and 300 widgets at $7.  What is the price elasticity of demand?

Using the simplified formula:

Recall that the price elasticity of demand is positive.  This tells us that a one percent increase in price of widgets would decrease the quantity demanded by 0.857%.

The procedure for measuring the price elasticity of demand is:

  1. Determine the percentage change in quantity.  If you do not know the start point use the average, otherwise use the start point.
  2. Determine the percentage change in price.  If you do not know the start point use the average, otherwise use the start point.
  3. Divide the percentage change in quantity demanded by the percentage change in price.
The formula that gives us the price elasticity of demand is a ratio of the percentage change in quantity demanded to the percentage change in price.  If you have two of these three factors you can calculate the value of the remaining item.  This procedure is used frequently in industry and government.  For example, if you know the change in price and the price elasticity of demand you can calculate the change in quantity demanded.  The equation becomes
%DQ = EQd,P * %DP.
This equation will give an accurate reflection of the change in quantity for small changes in price and quantity.  You can also determine what the change in price needs to be to increase the quantity demanded.  This is written as:
%DP = %DQ/EQd,P.

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