Find the elasticity of demand at the price P=7 with the demand given by P+1.15x=500
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The demand function is given as P + 1.15x = 500 where P is the price and x is the quantity demanded. Price elasticity of demand is the ratio of the rate at which the demand changes and the rate at which the price changes.
The demand x as an expression of the price P is given by: `x = (500 - P)/1.15`
The price elasticity of demand is given by `PED = ((dx)/(dP))*(P/x)`
`(dx)/(dP) = -1/1.15`
At P = 7, x = `9860/23`
Substituting the given values in the expression for price elasticity of demand gives: `PED = (-1/1.15)*(161/9860) ~~ -0.0141`
The price elasticity of demand is approximately -0.0141
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p + 1.15x = 500
7 + 1.15x = 500
1.15x = 493
x ≈ 428.7 (rounded to the nearest tenth)
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