Why am I getting 3 different answers for Point Elasticity of Demand?

Question

First year Econ. Question:

Demand function: $P=50-4Q$ (Price in cents/kilo)

Supply function: $P=25+Q$

Equilibrium Price and Quantity: 30 cents, 5 kilos.

Price change: 40 cents, 2.5 kilos.

I've tried 3 different methods of calculating point elasticity:

• $\frac{\% \Delta Q}{\% \Delta P}$ = $\frac{-50\%}{133\%}= -.375$;
• $\frac{\frac{Q_{1}-Q_0}{Q_0}}{\frac{P_1-P_0}{P_0}} = \frac{\frac{2.5-5}{5}}{\frac{40-30}{30}}=-1.5 $
• $\frac{1}{slope}\frac{P}{Q}=\frac{-1}{4}\frac{40}{2.5} = -4$

The right answer is -4, but why the variability?

Answer 1

In your second option, you computed the elasticity at the original point, and in your third option, at the end point. In your first point, you did the same as in the second one, but with a mistake: you wrote $133%$ instead of $33%$.