Arc Elasticity of Demand

Arc elasticity of demand is a measure of the responsiveness of the quantity demanded of a product to a change in its price, calculated over a range of prices. It is expressed as the percentage change in quantity demanded divided by the percentage change in price, where the percentage changes are calculated using the midpoint formula. The midpoint formula is used to avoid the problem of different elasticity values for price increases and price decreases.

The formula for calculating arc elasticity of demand is as follows:

Arc Elasticity = ((Q2 - Q1) / [(Q2 + Q1) / 2]) / ((P2 - P1) / [(P2 + P1) / 2])

Where Q1 and Q2 are the initial and final quantities demanded, and P1 and P2 are the initial and final prices.

Arc elasticity of demand can be either elastic, inelastic, or unitary elastic, depending on the value of the coefficient. If the coefficient is greater than one, it is said to be elastic, if it is less than one, it is said to be inelastic, and if it is equal to one, it is said to be unitary elastic.

The advantage of arc elasticity over point elasticity is that it takes into account the effect of price changes on the quantity demanded over a range of prices, rather than just at one price. This makes it a more accurate measure of the responsiveness of demand to changes in price.

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