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What is the formula of the income elasticity at the mean values?

I have two variables, I is income and C is consumption. And I have 10 observations (sample size)

Regresison equation

$$C = a + bI $$

Assume $\bar{I}$ is mean of income and $\bar{C}$ is mean of consumption expenditure. Then, how can I calculate this elasticity?

Thank you.

Thank you.

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1 Answer 1

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Let $C(I)$ be the level of consumption as a function of income. Then the definition of elasiticity is : $$ \frac{d C(I)}{dI} \times \frac{I}{C(I)}. $$ Given your linear specification, you have that $\frac{d C(I)}{dI} = b$.

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