# Since we can use any elasticity measures and not just

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Since we can use any elasticity measures and not just OF/AF , if we know P or MR and one of the other measures, we can also calculate the remaining variables. Application 4: A Pitfall to Avoid, and How to Avoid It The most common elasticity measures we use are the own-price elasticities of supply and demand. With both of these measures, elasticity is given by the equation E Q•P = Q P / / Q P = Q P m 1 = m P Q , (M.6.5) where m is the slope of the demand or supply curve. Since the slope m is in the denom- inator of the expression, the smaller in absolute value it is (the ﬂatter the curve) the greater the absolute value of the elasticity. When the slope m is zero, and the supply or demand curve is horizontal, we say that the curve is perfectly or infinitely elastic. It is not always the case, however, that a ﬂatter curve is more elastic than a steeper curve passing through the same point. This particular association results from the fact that we think of quantity supplied or demanded as a function of price, Q = f ( P ), and yet we con- ventionally put P (the independent variable) on the vertical axis and Q (the dependent vari- able) on the horizontal axis. In Figure M.6.4, Diagram (a) depicts two supply curves, both passing through a point C . The price elasticity of supply for each curve at C is s = OF/AF . Since OF 1 / AF < OF 2 / AF, S 2 is more elastic than S 1 . This means that at point C, a 1% increase in price will cause a larger percentage increase in quantity supplied along S 2 than along S 1 . The price elasticity of supply is a measure of the ratio of the percentage change in the vari- able, Q , measured on the horizontal axis (in the numerator ) to a 1% change in the vari- able, P , measured on the vertical axis (in the denominator ). M6-4 MATH MODULE 6: ELASTICITIES Price, MR A P = F MR = H D C O G E Quantity D' FIGURE M.6-3

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In (b), in contrast, we have depicted output Q (on the vertical axis) as a function of a single variable input, L (on the horizontal axis). We want to determine the elasticity of output Q with respect to the input L , E Q•L = (∆ Q/Q )/(∆ L/L ) = ( L/Q )(∆ Q/ L ) = MP L /AP L . (M.6.6) The MP L is given by the slope of the tangent to the production function, ∆ Q/ L = AF/FC = AF/OG , while the AP L is given by the slope of the ray from the origin to the production function, Q/L = GC/OG . Hence E Q•L = (∆ Q/Q )/(∆ L/L ) = MP L /AP L = AF/GC = AF/OF . (M.6.7) Perhaps not surprisingly, when we measure the elasticity of the vertical variable ( Q ) with respect to the horizontal variable ( L ), our measure for elasticity (= AF/OF ) is the rec- iprocal of the elasticity ( = OF/AF ) when we measure the elasticity of the horizontal vari- able ( Q ) with respect to the vertical variable ( P ). What this fact means is that for the input- elasticity of output , the steeper the Q ( L ) function at a given point, the more elastic it is.
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