Questions tagged [slutsky-equation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
1answer
32 views

Reason behind the decomposition of price effect into substitution and income effects

I was studying the decomposition of price effect into substitution and income effects. I am finding it a bit complicated. This is what I have understood: (0) Let us assume that there are two ...
0
votes
1answer
15 views

How to derive substitution and income effect using Slutsky equation if we don't know which of the prices change?

We have the utility function $$U(x,y)=x + y$$ and we have to derive the substitution and income effects using Slutsky equation. But after I derive the Hicksian demand functions for e.g. x: $$h_x= \...
3
votes
1answer
31 views

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 ...
0
votes
0answers
20 views

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 ...
0
votes
0answers
36 views

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
0
votes
1answer
39 views

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 ...
0
votes
0answers
49 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. ...
0
votes
0answers
636 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 ...
1
vote
1answer
4k views

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 ...
-1
votes
1answer
745 views

Calculating income and substitution effects

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: $x,y >> 0$....
0
votes
1answer
112 views

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 ...