Elasticity of demand

Elasticity of demand

Lessons

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.

  • Introduction
    Elasticity of Demand Overview:
    a)
    Elasticity formula

    b)
    What does Elasticity tell you?


  • 1.
    Calculating and Determining Elasticity

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

    a)
    Find ϵ(p)\epsilon (p)

    b)
    What is the price elasticity of demand when p=20p = 20? What should the company do to increase revenue?

    c)
    What is the percent change of quantity if p=20p = 20, and pp increases by 2%2\%?


  • 2.
    The demand curve for computers is given by p=400q2p = 400 - q^{2}.
    a)
    Find ϵ(p)\epsilon (p)

    b)
    What is the price elasticity of demand when q=10q = 10? What should the company do to increase revenue?

    c)
    What is the percent change of price if q=10q = 10, and qq decreases by 3%3\%?


  • 3.
    Maximizing Revenue using Unit Elasticity

    The demand curve for glasses is given by q=6003pq = 600 - 3p. For what value of pp maximizes revenue?


  • 4.
    The demand curve for glasses is given by p=6002q2p = 600 - 2q^{2}. For what value of pp maximizes revenue?

  • 5.
    Advanced Problems With Elasticity

    The demand curve for shoes is given by p2+q2=1000p^{2} + q^{2} = 1000. What is the elasticity of demand if price is $2525?