Revenue and Elasticity of Demand

1. Note that [i]Elasticity[/i] [math]=[/math] [math]-\frac{p}{q}\cdot\frac{dq}{dp}[/math] [math]\approx[/math] [math]\frac{p\cdot\left(-\Delta q\right)}{q\cdot\Delta p}[/math] when [math]\Delta p[/math] is small.[br][i]Loss due to the lower demand[/i] [math]=[/math] [math]p\cdot\left(-\Delta q\right)[/math] is the part of the gold area outside the blue region. [br][i]Gain due to the higher price[/i] [math]\approx[/math] [math]q\cdot\Delta p[/math] is the part of the blue area outside the gold region.[br][br]1. When Elasticity<1, what is the effect of a small price change [math]\Delta p[/math] on the revenue? What is larger in this case: the [i]Gain due to the higher price[/i] or the [i]Loss due to the lower demand[/i]? [br][br]2. Move the point [math]p[/math] to make Elasticity > 1 . What is the effect of a small price change [math]\Delta p[/math] on the revenue?[br][br]2. Move the point [math]p[/math] to make Elasticity=1 . What is the effect of a small price change [math]\Delta p[/math] on the revenue?[br]

Information: Revenue and Elasticity of Demand