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Point elasticity and arc elasticity make the difference?

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Point elasticity and arc elasticity make the difference?

• Replied by Kavita Kapoor on Tuesday, January 15 2013, 03:23 PM · Hide · #1
When we measure Arc Elasticity, we are measuring the PRICE ELASTICITY OF DEMAND between two points on the demand curve.
We can also measure the elasticity of any one point on the curve which is called point elasticity.
Point Elasticity will be different at each point of the demand curve.
Mainly we use calculus to measure Point Elasticity.
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Replied by garima on Tuesday, January 15 2013, 03:24 PM · Hide · #2
Price Elasticity of Demand: The percentage change in Quantity Demanded that results from a 1% change in Price.
In other words, the percentage change in Quantity Demanded caused by a percentage change in P.

There are two basic ways to measure elasticity. We can use a Point Elasticity measure, or an Arc Elasticity Measure:

Point Elasticity Measure:

|change in Q/Q |divided by= | P * change in Q | divided by= e
| change in P/P | | Q * change in P |
Arc Elasticity Measure:

| (Q2-Q1)/[Q1+Q2] | = e
| 2 |divided by
| (P2-P1)/[P1+P2] |

Eg:
Suppose we have the following demand curve, P = 100-Q/2 with the accompanying
Point A: P = 80, Q = 40 , Total Revenue = \$3200

Point M: P = 50, Q = 100, Total Revenue = \$5000

Point B: P = 20, Q = 160, Total Revenue = \$3200

Then
Point Elasticity at Point M: P = 50, Q = 100:

At (100,50):

e = | 50/100 * -50/25 | = 1 At the midpoint, e = 1. This is a Unit Elastic point.

Point elasticity at Point A: P = 80,Q = 40:

e = | 80/40 * -2 | = 4 Curve is elastic at (40,80), since e>1.

Point elasticity at Point B: P = 20, Q =160:

e = | 20/160 * -2 | = 1/4 Curve is inelastic at (160,20), since e<1.

Using the Arc Elasticity Measure, or Mid-Point Formula:

Midpoint forumula: Calculate the elasticity on the arc
from Point A to Point M, starting at Point A:

Let (Q1,P1) = (40,80) = Point A

Let (Q2,P2) = (100,50) = Point M

Q2-Q1 = 100-40 = 60 (Q2+Q1)/2 = 140/2 = 70

P2-P1 = 50-80 = -30 (P2+P1)/2 = 130/2 = 65

e = [60/70]/[-30/65] = [130/70] = 1.86

NOTE: The arc elasticity equals the point elasticity at the midpoint
of the arc. That is why the arc elasticity formula is sometimes
called the midpoint formula.

For this problem, at the point P = 65, Q = 70, the point elasticity would
be:

e = | 65/70 * -2 | = [130/70] = 1.86
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