Elasticity of demand - Derivative Applications

Elasticity of demand

Lessons

Notes:

The Elasticity of Demand is the percentage change in quantity divided by the percentage change in price. In other words,

ϵ=%Δq%Δp=pqdqdp\epsilon = \frac{\% \Delta q}{\% \Delta p} = \frac{p}{q}\frac{dq}{dp}

Note that ϵ\epsilon will always be negative because the slope of the demand curve dqdp\frac{dq}{dp} is negative.

The Elasticity of Demand is very important because it tells us how to optimize our revenue.

1) When ϵ|\epsilon| > 1, then the good is elastic. This means %Δq\%\Delta q > %Δp\%\Delta p, thus decreasing price will increase revenue.

2) When ϵ|\epsilon| < 1, then the good is inelastic. This means %Δq\%\Delta q < %Δp\%\Delta p, thus increasing price will increase revenue.

3) When ϵ|\epsilon| = 1, then the good is unit elastic. This means %Δq\%\Delta q = %Δp\%\Delta p, so you are already at the optimal price which maximizes revenue

To maximize revenue, we set ϵ|\epsilon| = -1 and solve for pp so that we know what price maximizes revenue.

  • 1.
    Elasticity of Demand Overview:
  • 2.
    Calculating and Determining Elasticity

    The demand curve for cakes is given by q=4005pq = 400 - 5p.

  • 3.
    The demand curve for computers is given by p=400q2p = 400 - q^{2}.
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Elasticity of demand

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