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Question

The demand function for a product is modeled by p=20-0.02x, $0 \leq x \leq 1000$ where p is the price (in dollars) and x is the number of units. (a) Determine when the demand is elastic, inelastic, and of unit elasticity. (b) Use the result of part (a) to describe the behavior of the revenue function.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 6To find the elasticity of the demand, we use the formula

$\begin{aligned} \eta &=\dfrac{p/x}{dp/dx} \end{aligned}$

We find first $\dfrac{dp}{dx}$ by using the sum and difference rule. Thus,

$\begin{aligned} \dfrac{dp}{dx}&=-0.02(1)x^{1-1}\\ &=-0.02 \end{aligned}$

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