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I'm struggling with this question. Please help out with the correct formula.

how to find the elasticity of log(y) =β0+β1log(x).

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1 Answer 1

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This is a standard log-linear model. $log(y)=b_0+b_1log(x)$

We know that elasticity is equal to $e=\frac{dy}{dx}.\frac{x}{y}$

We can differentiate the regression equation with respect to $x$ and then substitute the value of $\frac{dy}{dx}$ in the elasticity function to get the value.

$\frac{1}{y}.\frac{dy}{dx}=\frac{b_1}{x}$

Therefore $\frac{dy}{dx}=b_1\frac{y}{x}$

Now substitute it into the elasticity function $e=b_1\frac{y}{x}\frac{x}{y}$ which equals $b_1$.

Notice that this is a constant.

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