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Elasticity along a straight line demand curve

Syllabus: Explain why PED varies along a straight line demand curve and is not represented by the slope of the demand curve.


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Now you know that the PED is different on different parts of a straight line demand curve. However you also know that a straight line demand curve has a constant gradient so the gradient of a straight line demand curve cannot be the same as the PED along the curve

Let┤s Do Some Economics
In May 2016 Paper 3 there was this question for 4 Marks

Q1b (ii) Explain why, for a linear demand curve, the price elasticity of demand is not represented by the slope of the demand curve. (4 Marks)

The markscheme says you could answer in these ways:
 
Level    Descriptor                                                                                                                                                                    
0         The work does not reach a standard described by the descriptors below.                                                                                    0

1         The written response is limited. 1–2

            For explaining that the gradient of a linear demand curve is constant along the curve, but PED changes, and that demand is more elastic at higher             prices.

2         The written response is accurate. 3–4

            For explaining that the gradient of a linear demand curve is constant along the curve. However, the rates of change of price and quantity are not             constant. As price increases, the % change in price diminishes while the % change in quantity demanded increases. Therefore, the slope, which is             constant, cannot represent the formula: PED = %ΔQd / %ΔP.
OR

            an explanation that PED=slopeÎ P
                                                       Q
            Since the slope ΔQ is constant along a straight line, PED is equal to a constant number x P whose value constantly changes along the demand
                                 ΔP                                                                                               Q
            curve. Therefore, as we move along the demand curve, PED changes.
Also:
            A response which uses dQ in this explanation should be rewarded.

                                            dP
            A response which explains that, as price increases, the price becomes a larger portion of income, hence the consumer becomes more responsive to             changes in price, should be awarded a maximum of [3].