It is possible to show that the marginal welfare loss from a labor (operatorname{tax}) is (V=t_{L} in

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It is possible to show that the marginal welfare loss from a labor \(\operatorname{tax}\) is \(V=t_{L} \in /\left[w-t_{L} \varepsilon\right]\) where \(\varepsilon\) is the labor supply elasticity evaluated at the net of tax wage received by the consumer, \(w\). Using this, show that the absolute value of the ratio of the tax interaction effect to the revenue recycling effect is given by \(I E / R E=\left(X^{*} / X^{+}\right)\left(\eta_{k /} / \epsilon\right)\) where \(\eta_{k x}\) is the price elasticity of demand for good \(X\) with respect to the wage rate. Assume elasticities are compensated elasticities. If on average we expect \(\eta_{k x}=\varepsilon\), what can you conclude about the size if IE relative to \(R E\) in this case? What is the significance of this result?

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