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# Questions tagged [slutsky-equation]

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### Question about the relationship between Weak Axiom and Slutsky Matrix

We know that if a differentiable Walrasian demand function $x(p,w)$ satisfies Walras' law ($p^Tx=w$), homogeneity of degree zero ($x(\alpha p,\alpha w)=x(p,w)$), and the weak axiom of revealed ...
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### How to prove that the substitution effect is negative when price of another good is changed?

In Slutski equation, we have: $$\frac{\partial x_i(p,w)}{\partial p_j} = \frac{\partial h_i (p,u)}{\partial p_j} -\frac{\partial x_i(p,w)}{\partial w}x_j(p,w)$$ If $i \neq j$, the substitution effect ...
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### Slutsky Substitution Matrix

How do we find out whether a Slutsky Matrix is negative semi definite, given the matrix? After derivation of the Slutsky matrix is their a simple way to tell whether it is negative semi definite
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### Why do the income and substitution effects cancel for log preferences? Trouble reconciling Slutsky decomposition

I've read (pg 10) in Gourinchas' notes on consumption that the income and substitution effects cancel for log preferences, and I tried to prove this to myself doing the Slutsky decomposition for the ...
47 views

### What are the impacts of a small increase of the wages on consumption, labor supply and production?

We have given the utility function $\displaystyle U(v(c)-k(l))$ where $\displaystyle u$ and $\displaystyle v$ are increasing and concave functions and $\displaystyle k$ is increasing and convex. ...
519 views

### Is the Hicksian demand curve steeper or flatter than Slutsky demand?

Putting price on the vertical axis and quantity on the horizontal axis, is the Slutsky demand steeper or flatter than the Hicksian demand curve? If I calculate the Slutsky and Hicksian substitution ...
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### Income and substitution effect for perfect substitutes

I was recently asked about what the income and substitution effects are for perfect substitutes are. Given the rather peicewise nature of the demands for each good in a utility function considering ...
Consider a simple quasi-linear utility function of the form $U(x,y)=x +ln(y)$. For this problem, assume that you have “enough” income, so that the optimal consumption bundle is where: $x,y >> 0$....
### Income effect $-\frac{\partial x_i}{\partial m} x_i$ or $\frac{\partial x_i}{\partial m}x_i$?
Recall that the slutsky equation is: $$\frac{\partial x_i}{\partial p_i}=\frac{\partial h_i}{\partial p_i}-\frac{\partial x_i}{\partial m}x_i$$ I know $\frac{\partial h_i}{\partial p_i}$ defined as ...