Math  /  Algebra

QuestionElasticity of Demand The demand function for a certain brand of backpacks is p=53ln(53x)(0<x53)p=53 \ln \left(\frac{53}{x}\right) \quad(0<x \leq 53) where pp is the unit price in dollars and xx is the quantity (in hundreds) demanded per month. (a) Find the elasticity of demand E(p)E(p). E(p)=E(p)= \square
Determine the range of prices corresponding to inelastic, unitary, and elastic demand. Demand is inelastic if \square , unitary if \square --Select-, and elastic if \square -Select--. (b) If the unit price is increased slightly from $53\$ 53, will the revenue increase or decrease? The revenue will increase. The revenue will decrease. The revenue will remain constant.

Studdy Solution
Analyze the effect of a price increase from $53 on revenue:
Since p=53 p = 53 corresponds to unitary demand, any increase in price will lead to a proportional decrease in quantity demanded, keeping revenue constant.
The revenue will remain constant.
The elasticity of demand is E(p)=p53 E(p) = -\frac{p}{53} . Demand is inelastic if p<53 p < 53 , unitary if p=53 p = 53 , and elastic if p>53 p > 53 . If the unit price is increased slightly from $53, the revenue will remain constant.

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