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| THIS PAGE CONTAINS AN ANALYSIS OF THE MIDPOINT FORMULA, AND ITS USE IN DETERMINING ELASTICITIES, INCLUDING THE PRICE ELASTICITY OF DEMAND. AN UNDERSTANDING OF ELASTICITIES IN GENERAL, AND THE PRICE ELASTICITY OF DEMAND ARE NECESSARILY PREREQUISITES FOR THIS SECTION |
Elasticity - The Midpoint Formula |
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The standard method for computing the price elasticity of demand
has one major drawback. It is based on the assumption that the
company is starting from a position of a specific price and quantity
sold, and is considering a change in price. But what about the
case where the company is not really "starting" from one
particular point, but instead only wants to compare the results of
two different possible prices. In other words, it does not care
whether one price is considered to be the beginning price and
the other is considered to be the ending price; it just wants to
compare the difference between two possible prices.
The drawback is that, using the standard method for calculating
the price elasticity of demand, you often get two different answers
depending on which price you call the beginning, and which price
you call the ending. In the first example used for that analysis,
recall that the prices being considered were: $2, with sales of 100
units, and $3, with sales of 75 units. The analysis used $2 as the
beginning price, and arrived at a price elasticity of demand of 0.5.
But suppose that $3, with the exact same sales of 75 units, was
used as the beginning price, and $2, with the exact same sales of
100 units, was used as the ending price. The same situation,
using the same numbers, but looking at them from the opposite
direction. In this case, the price elasticity of demand would be
calculated as follows:
The percentage change in quantity would be 25/75, or 33%. The
percentage change in price would be 1/3, or 33%. The price
elasticity of demand would be 33/33, or 1.
Going from $2 to $3 gives an answer of 0.5, but going from $3 to
$2 gives an answer of 1. Two different answers using the same
numbers. Neither method is better than the other if specifying a
beginning price is not relevant to the situation. To correct for this
discrepancy, the midpoint formula is considered to be a superior
method.
has one major drawback. It is based on the assumption that the
company is starting from a position of a specific price and quantity
sold, and is considering a change in price. But what about the
case where the company is not really "starting" from one
particular point, but instead only wants to compare the results of
two different possible prices. In other words, it does not care
whether one price is considered to be the beginning price and
the other is considered to be the ending price; it just wants to
compare the difference between two possible prices.
The drawback is that, using the standard method for calculating
the price elasticity of demand, you often get two different answers
depending on which price you call the beginning, and which price
you call the ending. In the first example used for that analysis,
recall that the prices being considered were: $2, with sales of 100
units, and $3, with sales of 75 units. The analysis used $2 as the
beginning price, and arrived at a price elasticity of demand of 0.5.
But suppose that $3, with the exact same sales of 75 units, was
used as the beginning price, and $2, with the exact same sales of
100 units, was used as the ending price. The same situation,
using the same numbers, but looking at them from the opposite
direction. In this case, the price elasticity of demand would be
calculated as follows:
The percentage change in quantity would be 25/75, or 33%. The
percentage change in price would be 1/3, or 33%. The price
elasticity of demand would be 33/33, or 1.
Going from $2 to $3 gives an answer of 0.5, but going from $3 to
$2 gives an answer of 1. Two different answers using the same
numbers. Neither method is better than the other if specifying a
beginning price is not relevant to the situation. To correct for this
discrepancy, the midpoint formula is considered to be a superior
method.
In economics class, the textbook or the instructor might define the midpoint formula as something like
this:
p.e.d. = [(Q2 - Q1) / ((Q1 + Q2) / 2)] / [(P2 - P1) / ((P1 + P2) / 2)]
Pretty intimidating, right? But luckily, you do not have to actually memorize this formula in order to know
how to do the calculations. You only need to understand the concepts behind it, and the calculations will
be easy.
This formula does not change the concept of the price elasticity of demand. Refer back to the beginning
of the elasticity section, and the first and most important concept of elasticity listed: elasticity (in this
case, the price elasticity of demand) is always going to be the percentage change in quantity divided by
the percentage change in price. The midpoint formula does not change that. The midpoint formula only
changes the method of arriving at these percentages; all you have to know is the concept behind the
different method of arriving at the percentages, and you know how to use the midpoint formula.
For the midpoint formula, instead of dividing the change in quantity by the beginning quantity, and the
change in price by the beginning price, simply divide the change in quantity by the average of the two
quantities, and the change in price by the average of the two prices. Using the average avoids having to
designate a beginning and an ending.
In the example above, the change in quantity is 25; the average of the two quantities is 87.5 ((100 + 75) /
2). The percentage change in quantity, then, using the midpoint formula, is 25 / 87.5, or 28.57%.
The change in price is $1; the average of the two prices is $2.50 (($2 + $3) / 2). The percentage change in
price, then, using the midpoint formula, is 1 / 2.5, or 40%.
The price elasticity of demand, using the midpoint formula, is 28.57 / 40, or 0.71 (your instructor may have
you use a different method for rounding).
Recall that the standard method yielded an answer of 0.5 for a price increase and 1.0 for a price decrease,
two different answers using the same numbers. The midpoint formula, which is considered superior,
yields only one answer, 0.71.
this:
p.e.d. = [(Q2 - Q1) / ((Q1 + Q2) / 2)] / [(P2 - P1) / ((P1 + P2) / 2)]
Pretty intimidating, right? But luckily, you do not have to actually memorize this formula in order to know
how to do the calculations. You only need to understand the concepts behind it, and the calculations will
be easy.
This formula does not change the concept of the price elasticity of demand. Refer back to the beginning
of the elasticity section, and the first and most important concept of elasticity listed: elasticity (in this
case, the price elasticity of demand) is always going to be the percentage change in quantity divided by
the percentage change in price. The midpoint formula does not change that. The midpoint formula only
changes the method of arriving at these percentages; all you have to know is the concept behind the
different method of arriving at the percentages, and you know how to use the midpoint formula.
For the midpoint formula, instead of dividing the change in quantity by the beginning quantity, and the
change in price by the beginning price, simply divide the change in quantity by the average of the two
quantities, and the change in price by the average of the two prices. Using the average avoids having to
designate a beginning and an ending.
In the example above, the change in quantity is 25; the average of the two quantities is 87.5 ((100 + 75) /
2). The percentage change in quantity, then, using the midpoint formula, is 25 / 87.5, or 28.57%.
The change in price is $1; the average of the two prices is $2.50 (($2 + $3) / 2). The percentage change in
price, then, using the midpoint formula, is 1 / 2.5, or 40%.
The price elasticity of demand, using the midpoint formula, is 28.57 / 40, or 0.71 (your instructor may have
you use a different method for rounding).
Recall that the standard method yielded an answer of 0.5 for a price increase and 1.0 for a price decrease,
two different answers using the same numbers. The midpoint formula, which is considered superior,
yields only one answer, 0.71.
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