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True, false or uncertain: If there is no money illusion, once all price elasticity is known, the income elasticity of commodity demand can be calculated.

My answer is false. I don't think it's possible to get the income elasticity from the price elasticity. But obviously my answer doesn't use the condition that "there is no money illusion".

So maybe I am wrong.

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Let $x_i(p,m)$ be the demand for good $i$. If there is no money illusion, this function is homogeneous of degree zero: $\forall t > 0$ $$ x_i(tp, tm) = x_i(p,m) $$ Next use Euler's theorem for homogeneous functions. You will find that you can write the income elasticity as minus the sum of all price elasticities.

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