Midpoint Formula For Price Elasticity

As was described earlier, elasticity measures the responsiveness of the quantity demanded tochanges in price. There is a mathematical formula used to calculate elasticity. That formula isdiscussed below.

Many students have a math phobia, especially when it relates to subject matter outside of the field of mathematics. The midpoint formula should not cause too much math anxiety. If you look at the formula below, most of what you are doing is adding and dividing. **The purpose of the formula is to discover the responsiveness in quantity demanded to a change in price.**

The Midpoint Formula

Price per candy bar | Q demanded per week | Total Revenue | Elasticity Coefficient |

.40 | 3 | $1.20 | |

.35 | 4 | $1.40 | |

.30 | 5 | $1.50 | |

.25 | 6 | $1.50 | |

.20 | 7 | $1.40 | |

.15 | 8 | $1.20 |

** Mid point formula **

**Ed = % change in Q demanded = ****change in**** Q **

** % change in Price **** (Q _{1} + Q_{2}) / 2 **

**change in **** P **

**(P _{1} + P_{2}) / 2 **

where Q_{1} = initial or old quantity

Q_{2} = final or new quantity

P_{1} = initial or old price

P_{2} = final or new price

**The e****xample ****below is using is using the numbers for ****moving from 3 candy bars to 4 candy bars ****(the price change of going from 40 cents to 35 cents) from the table above.**

** 1 **** ( change from 3 to 4 candy bars)**

**_______****(3+ 4) / 2 ****_______**** ( ****(Q _{1} + Q_{2}) / 2**

**)**

** .05 **** (change from 40 cents to 35 cents)**

** (.40 + .35) / 2 **** ( ****(P _{1} + P_{2}) / 2 **

**)**

What you get after you do the math from the numbers above is in the left hand column of numbers below. After you do the math at that step you get the numbers to the right of the first equal sign. When you do the math at that step, you get the final answer to the right of the second equal sign (2.1433) The answer means the price change is elastic since the number is greater than one. In other words, you have 1 ÷ 3.5 which equals .2857 Underneath the division sign, you then have .05 ÷ .375 which equals .133 Next you divide .2857 by .133 which gives you 2.1433

** 1 = .2857 .2857 = 2.1433 **

** 3.5 **** .133 **

** .05 = .133**

** .375 **

To figure out the remaining price elasticities from the candy bar table above, simply substitute the new numbers from the next price change. For the next price change, in parenthesis for quantity demanded you would put 4 and 5, and in parenthesis for price you would put .35 and .30.

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