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?