If $\ln(y) = 5 - 0.1X $what is the elasticity of $Y$ with respect to $X$, when $X=10$?

Question

So i got the following model $\ln(y) = 5 - 0.1* X$ The elasticity of Y with respect to X, when $X=10$

i said -0.1 but apparently i'm wrong

Isn't the coefficient of X the elasticity of y when the model is a double log?

Is it rather -1?

Answer 1

The equation for the elasticity is:

$e=\frac{dy}{dx}\frac{x}{y}$

In your case, we have

$ln(y)=5-0.1x$, Now take the derivative of both sides and multiply by x:

$\frac{dy}{dx}\frac{x}{y} = -0.1x$

Therefore, at $x=10$, the elasticity is $-1$.