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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

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To 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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