What is the midpoint formula?


The midpoint formula is a popular mathematical formula that is used in a range of scientific courses such as mathematics and economics to determine the halfway point between two data points. In economics, especially, it is used to determine the coefficient of elasticity when you are measuring either supply of a product or demand of the product and it looks at two points in the curve to determine the midpoint. The aim of the midpoint formula is to help you find the midpoint. The formula is pretty handy in economics as it helps economists when they are measuring the consumer habits and how their habits may change in relation to changes happening to price, the quantity of supplies being made, and the quantity of a product being demanded.


Midpoint definition


In order to understand what it means to find a midpoint, the midpoint formula equation will help you solve the elasticity of demand and supply in different scenarios and models. The midpoint formula, in its quest to find the midpoint, calculates the percentage changes which are based on the differences between the beginning and ending values.


The standard midpoint formula


To find the midpoint, the standard equation used is shown below:


Midpoint = (b2 – b1) / (b2 + b1 / 2) / (a2 – a1) / (a2 + a1 / 2)

A1: initial value of product A

A2: Ending value of product A

B1: Initial value of Product B

B2: Ending value of product B


The Midpoint Formula in Actual Examples


Example 1


Michael wants to find the average change in the elasticity of two products; let us say product A and product B. The price of product A increases from an initial figure of $16 to an ending figure of $24. On the other hand, the prices of product B change from an initial price of $10 to an ending value of $16.


Determining the elasticity change without using the midpoint formula

You can determine the midpoint using the traditional method.  This can be done as follows:

For product A, Michael gets a change of 24/16-1×100=50%.

For product B, Michael gets a change of 16/10-1×100=60%


Using the midpoint formula to determine change in elasticity

For product A: ($24-$16)/ ($24+$16)/ 2=$8/$20=46%

For product B: ($16-$10)/($16+$10)/2=$6/$13=40%

Applying the midpoint formula;


Midpoint = (b2 – b1) / (b2 + b1 / 2) / (a2 – a1) / (a2 + a1 / 2)

=($16-$10)/($16+$10/2)/($24-$16)/($24+$16/2)= 0.46/0.4= 1.15


Example 2

Using the same example as above, but assuming the products fall in price, from $24-$16 for product A and $16-$10 for product B.  The calculations would be as shown below:


Using the traditional method

For product A: Change is $16/$24-1×100=-66.67%

For Product B: Change is $10/$16-1×100=-37.5%


Using the midpoint formula to calculate the same elasticity yields

For product A: ( $16- $24 / ( $16 + $24 ) / 2 = -$8 / $20 = -0.46 = -46%

For Product B: ( $10 – $16 ) / ($10 +$16) / 2 = -$6 / $13 = -0.4 = -40%



As seen above, the midpoint uses percentage changes at the initial values and percentage changes at the end values leading to higher accuracy compared to the traditional method.


Midpoint Formula Homework Help


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