Microeconomics question: how to use Midpoint Formula?

The midpoint formula can be best understood by breaking it down into sections that have meanings by themselves.

First of all, you need the data that will be used in the midpoint formula. Plug in the numbers you are given and solve.

At a price of $12, quantity would be: 12 = 20 - 0.2Qd; or 0.2Qd = 20 - 12; or 0.2Qd = 8; or Qd = 40 So at a price of $12, quantity is 40.

At a price of $13, quantity would be: 13 = 20 - 0.2Qd; or 0.2Qd = 20 - 13; or 0.2Qd = 7; or Qd = 35. So at a price of $13, quantity is 35.

Now you have your numbers for the calculations of the elasticity of demand. The midpoint formula uses the same concept of the standard method, it just uses a different approach to the different sections of the calculations (that is why it is easiest to understand if you broke it down to the different sections, and only apply the changes to the places where they are needed; it is easier to understand, and you don't have to memorize anything).

The price elasticity of demand is always defined as:

The percentage change in quantity divided by the percentage change in price. The midpoint formula uses a different method to calculate each part of this, but you will understand better if you do the calculations on each part separately, then combine them for the final answer.

If you were to use the standard method, you would have had to decide whether $12 or $13 is the beginning price; each would give a different answer. The midpoint formula is designed for one and only one answer regardless of which price comes first.

Back to the formula: the percentage change in quantity, using the midpoint formula, is:

(difference between the two given quanitities) divided by (average of the two quantities), then times 100. In this case, it would be: (difference between 40 and 35) / (40 + 35)/2, or 5/37.5, or 0.1333, then times 100 for 13.33

The percentage change in price is calculated using the exact same concepts, except you would use the price numbers instead of the quantity numbers:

(difference between 12 and 13) / (12 + 13)/2, or 1/12.5, or 0.08, then times 100 for 8.

Put these calculations together into your equation of: percentage change in quantity divided by percentage change in price, and you get your final answer:

13.33 / 8 = 1.67

Your answer key has a negative 1.67 instead of a positive 1.67. This is true because of the fact that the price and quantity change in opposite directions. This is normally considered a given, and isn't used in the above calculations. Changing the formulas for the sole purpose of making them come out to a negative number is an unnecessary complication. You only need to be aware that the negative sign will be present as long as the price and quantity move in opposite directions.

Midpoint Formula Economics

Midpoint Formula Econ

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RE:

Microeconomics question: how to use Midpoint Formula?

Can someone show me how to work this out?

Demand is given by P=20 - .2QD, between the prices of $12 and $13. The answer is negative 1.67.

Thanks so much,

Kate