p=500/x+2 x=23 find the price elasticity of demand for the demand function

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mariloucortez | High School Teacher | (Level 3) Adjunct Educator

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You are given `P = 500/x +2` .

What is price elasticity at x =23?

Elasticity can be calculated by:

Elasticty of P with respect to x = `(dP)/dx * x/P`

Get the derivative of Apply quotient rule: `d(u/v) = (udv-vdu)/v^2`

on `500/x` . Recall derivative of constant is 0.

So `(dP)/dx = (500*1 - x*0)/x^2` .

`(dP)/dx = 500/x^2`

Plug-in in the formula:

Elasticity of Demand = `(dP)/dx * x/P`

Elasticity of Demand =`500/x^2 * x/(500/x +2)`

Elasticity of Demand =`500/x^2 * x/((500+2x)/x)`

Elasticity of Demand =`500/x^2 * x^2/(500+(2x))`

Elasticity of Demand =`500/(500+(2x))`

Substitute 23 in x.

Elasticity of Demand = `500/(500+2*23)`

Elasticity of Demand = `500/546`

Elasticity of Demand = `250/273`

Thus, Price Elasticity of Demand is 0.9158. Since it is less than 1, the demand is price inelastic.

Sources:

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