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# Slutsky equation with marshallian demand

2018-10-06 12:53:44

We have marshallian demands for goods 1 and 2:

$x_1^* = \frac{I}{2p_1}$ and $x_2^* = \frac{I}{2p_2}$

where $I$ is income and $p_i$ is price.

We need to solve the slutsky equation for income effect and substitution effect as such:

$\frac{D (x_i)}{D (p_j)} = \frac{D(H^i(p1, p2, i))}{ D(p_i)} - x_j*\frac{D(x_i^*)}{D(I)}$

So in balance marshallian demand is the same as the compensated demand.

I solved the left hand side of equation and got a result of $0$.

Then I moved on to the income effect and got the following result:

$-\frac{I}{2p_j}*\frac{1}{2p_i} = -\frac{I}{4p_jp_i}$

Substituting the results from above in to the slutsky equation gives a positive result for substitution effect. I thought that that the substitution effect is always negative. Can anyone help me out?