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Given $x_{m}$ in Slutsky form $$\frac{\partial x_{m}(p_{x},p_{y},I)}{\partial p_{x}} = \frac{\partial x_{m}}{\partial p_{x}} \rfloor_{U=constant} - x_{c} \frac{\partial x_{m}}{\partial p_{x}} \\ = \text{substitution effect} + \text{income effect}$$ From Nicholson and Snyder (Microeconomic Theory 12th Ed.) (p. 158) "The sign of the income effect $-x_{c}... 2 When solving this problem, it is important to notice that whenever you have a tax, there will be a difference between the price that the buyers pay and the price that the sellers will receive. Let$p_D$be the price that the buyers pay and let$p_S$be the price that the sellers receive. The price$p_D$is the one that is relevant for the buyers, so it ... 2 Let$p$be price vector, let$m$be income and let$u$be utility. Let$e(p,u)$be the expenditure function which gives the minimal expenditure necessary to get utility level$u$and let$v(p,m)$be the indirect utility function, which gives the maximal utility that can be obtained ad prices$p$given income$m$. The Hicksian demand for good$i$,$h_i(p,u)\$ ...