Calculate elasticity of a power function

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CGHMaastricht

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Sep 16, 2016
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How do I compute the elasticity of the function f(x) = x^a?

My work:

I think the way to find it is to use the formula for Elasticity:

f'(x)*(x/f(x)) (f'(x) being the derivative of the function f(x))

so I can get that derivative to a*x^(a-1)

and multiply is by (x/f(x)) which is (x^1)/(x^a)

to get a*x^(a-1) * (x^1)/(x^a)

I think I can use exponents rule to take it to

ax^(a-1) * x^(1-a)

but I can't work out how to take it any further

Help would be much appreciated!
 
CGHMaastricht said:
How do I compute the elasticity of the function f(x) = x^a?

My work:

I think the way to find it is to use the formula for Elasticity:

f'(x)*(x/f(x)) (f'(x) being the derivative of the function f(x))

so I can get that derivative to a*x^(a-1)

and multiply is by (x/f(x)) which is (x^1)/(x^a)

to get a*x^(a-1) * (x^1)/(x^a)

I think I can use exponents rule to take it to

ax^(a-1) * x^(1-a)

but I can't work out how to take it any further

Help would be much appreciated!
Click to expand...

ax^(a-1) * x^(1-a) = a*x^(a-1+1-a) ... take it from there
 
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