Gobbet_5_Answer_1_Problem_Set - Gobbet # 5: Elasticity...

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Gobbet # 5: Elasticity Material adapted from the course text, Harris: Environmental and Natural Resource Economics , 2006 and from Frank and Bernanke: Principles of Economics, 2001 Solution: Price Elasticity of Demand – “The degree of consumer responsiveness to a change in the price of a good or service at a given price” (Harris). Placing this definition in mathematical terms we have the equation of elasticity: . ε = (ΔQ/Q) / (ΔP/P) In words this says that elasticity is equal to the change in (Δ means change in) quantity demanded divided by the quantity demanded, all divided by the change in price divided by the price. Hence, we can also say that the elasticity is the percentage change in quantity divided by the percentage change in price. Because it is expressed as a ratio of percentage changes, the resulting elasticity is unit free. This means that we can compare the elasticity or relative responsiveness of diverse goods such as coal and food. Rearranging a few terms we can put this equation in a simpler form. First, we multiply the top and bottom of our fraction by the reciprocal of the denominator and noting that the resulting denominator cancels out ( 29 ( 29 ( 29 ( 29 1 * * P P Q Q P P P P P P Q Q ∆ = ∆ = ε Rearranging, gives ε = (ΔQ * P) / (ΔP * Q) If we rearrange further and split this into two fractions we have ε = (ΔQ/ΔP) * (P/Q) We know that the slope of our demand curve (think rise over run from high school algebra) is equal to the change in price over the change in quantity or ΔP/ΔQ, so our term on the left is
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Gobbet_5_Answer_1_Problem_Set - Gobbet # 5: Elasticity...

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