Demand Elasticity

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The elasticity of the demand shows the responsiveness of the quantity demanded to a change in the price.

It is defined as the proportional change in the quantity demanded, divided the proportional change in the price.

e = (ΔQ/Q)/(ΔP/P)

When the price increases (+), the quantity demanded decreases (-): the demand elasticity is usually negative.


demand elasticity

How to Calculate the Demand Elasticity

Method 1: starting point

The price of ice cream has increased from $10 to $12. As a consequence, the demand has decreased from 100 pounds daily sales, to 90 pounds daily sales.

To find out the demand elasticity, we find the percent change in the quantity demanded: ΔQ/Q = -10/100 = -0.1

The percent change in the price is: 2/10 = 0.2

And the elasticity is: -0.10 / 0.20 = -0.50

Method 2: midpoint or arc elasticity

Using the arc elasticity method, the base quantity and price are the averages:

  • The average quantity is: (100+90)/2=95
  • The average price is: (10+12)/2=11

The percent change in quantity, according to the arc elasticity method is: -10/95=0.105

The percent change in price is: 2/11=0.182

And the demand elasticity is: -0.579

Method 3: point method

The formula of the demand elasticity is:

e = (ΔQ/Q)/(ΔP/P)

And can be rewritten as:

e = (ΔQ/ΔP).(P/Q)

If the quantity demanded is a continuous function of the price Qd=f(P), the formula can be rewritten as:

e = (dQ/dP).(P/Q)

Where (dQ/dP) is the derivative of the quantity with respect to the price.

Using the given data, and assuming that the demand is a linear function with the form of Q = a - b.P , we can find that the demand function is:

Q = 150 - 5P

If we are asked to measure the elasticity of demand when the price is 10 using the point method, we take the first derivative of the demand function: dQ/dP = -5 (It is just the slope of the function).

And the demand elasticity is e = -5 . 10/100 = -0.50

Determinants of the Demand Elasticity

  • Availability of close substitutes: the more substitutes, the higher the elasticity.
  • The higher the participation of the income used to pay for the good, the higher the elasticity.
  • Long run vs. short run: the demand elasticity is higher in the long run.


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This content is for information and educational purposes only and should not be considered investment advice nor portfolio management. Past performance is not an indication of future results. Leveraged products can carry a high degree of risk.
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