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Given the demand function q=D(x)=(square root) 459-p Find the elasticity function, E(x)

User RonTheOld
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Final answer:

To find the elasticity function E(x) for the given demand function D(x) = √(459 - p), one must differentiate the demand function with respect to price and use the price elasticity of demand formula. Additional information about the elasticity of a different demand curve P = 2/Q helps illustrate how elasticity can vary with price changes.

Step-by-step explanation:

Elasticity of Demand Function

The question pertains to finding the elasticity function, E(x), of a given demand function, which is D(x) = √(459 - p). To find the elasticity function, we need to use the formula for price elasticity of demand:

E(p) = (p/q)*(dq/dp)

However, we are provided with additional context from a different demand curve P = 2/Q, where the elasticity is calculated as the price changes from 5 to 4 and from 9 to 8. The demand curve is explained to be inelastic in a given range when the value is less than one. To calculate the percentage change in quantity for this other demand curve, one would use the following method:

% change in quantity = (Q2 - Q1) / ((Q1 + Q2)/2)

This provides insight into how elasticity is calculated, but the initial question focused on finding E(x) for the demand function D(x) = √(459 - p), which would require differentiating the given function with respect to p and then applying the formula for elasticity to find E(x).

User Rodrigo Ferreira
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