Skip to main content

Questions tagged [slutsky-equation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
4 votes
1 answer
122 views

Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation

Why is the partial derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2)$ for $p_1$ $$ \frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \...
j3141592653589793238's user avatar
3 votes
1 answer
153 views

A question on Intermediate Microeconomics 9ed by Hal Varian, Chapter 8 Slutsky Equation, Figure 8.8

In the example on Voluntary Real Time Pricing in "Chapter 8 Slutsky Equation", anyone can help to explain why the mentioned pricing scheme is a "Slutsky pivot"? In the textbook, it ...
dchao's user avatar
  • 97
3 votes
1 answer
162 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 ...
HXW's user avatar
  • 75
3 votes
1 answer
312 views

Marshalian and Hickisian Demands and Slutsky Equation

everyone. I have the following question: A consumer has the following indirect utility function: $ V(p_1,p_2,b) = (p_2k-b)p_1^{-1} \left[ \frac{2p_2k - 2b}{p_2} \right]^{-2}, x_2 < k$ a) Find ...
Pedro Cunha's user avatar
3 votes
0 answers
99 views

Effect of tax plus rebate on fuel consumption

I'm studying the Slutsky equation and an example in the text discusses the effect of a tax plus rebate on the consumption of fuel. Suppose the original price of fuel is $p$, tax is $t$, $x$ is the ...
AnotherJohnDoe's user avatar
2 votes
2 answers
452 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 ...
aintgeorge's user avatar
2 votes
1 answer
129 views

Complements/substitutes estimation from data (Slutsky matrix)

Estimation of complements/substitutes by Slutsky matrix from observable data Hello everyone, I was curious about the following problem: I can observe price $P_i$ of $n$ goods and the amount of goods $...
Athaeneus's user avatar
  • 834
2 votes
0 answers
100 views

CES in Slutsky matrix (weird results)

We have a Slutsky matrix: \begin{bmatrix} \partial x_{1}^H/\partial P_1 & \partial x_{1}^H/\partial P_2 & \dots & \partial x_{1}^H/\partial P_n \\ \partial x_{2}^H/\partial P_1 &...
Athaeneus's user avatar
  • 834
2 votes
0 answers
250 views

Concave preferences have negative SE [Proof]

Question from Intermediate Microeconomics by Hal Varian: Suppose that preferences are concave. Is it still the case that the substitution effect is negative? This is my point: If preferences are ...
carlos marena's user avatar
2 votes
0 answers
241 views

How to find the substitution and income effects?

The usual definition of Substitution Effect (pg. 30; also found in Varian) tells that the Slutsky SE is $x(p_x', I') - x(p_x,I) = x(2,15) - x(1,10) = \frac{15}{2 \cdot 2} - \frac{20}{2 \cdot 1} = -6....
Isa's user avatar
  • 87
2 votes
0 answers
187 views

Uncompensated and compensated demand functions

I came across this lecture note online and some of the points below confuse me. I have added the part that confuses me as an image and here is the lecture note for further reference, if needed. ...
Isa's user avatar
  • 87
1 vote
1 answer
16k 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 ...
EconJohn's user avatar
  • 8,407
1 vote
1 answer
171 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 ...
EconJohn's user avatar
  • 8,407
1 vote
1 answer
198 views

Using Slutsky method to understand substitution and income effect for luxury goods

If both goods are luxury goods, such as Channel vs Dior bags, how can you graph the substitution and income effect using the Slutsky method when the price of Channel bags fall? What I've tried: ...
Christina Joo's user avatar
1 vote
1 answer
1k 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 ...
MrAP's user avatar
  • 203
1 vote
1 answer
128 views

Income effect in perfect substitutes if the already cheaper good becomes more cheaper?

Consider a simple utility function U(x,y) = x+y such that Px < Py (which means only x is being consumed at optimal point, a corner solution). In this case, assume Px falls further. Now won't the ...
Polario's user avatar
  • 143
1 vote
0 answers
109 views

budget line for ration quota

In this situation there is a particular commodity, like rice, is both available at a subsidized rate from a fair price shop (ration shop) and at a higher price from the open market. Suppose a consumer ...
petearGriffin's user avatar
1 vote
0 answers
4k 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 ...
PGupta's user avatar
  • 227
0 votes
1 answer
434 views

Why does the Substitution effect always have to be negative?

I understand why the income effect can be positive or negative depending if the good is normal or inferior. but why does the substitution effect always have to be non-positive?
tessa's user avatar
  • 1
0 votes
1 answer
453 views

is income effect in the given quasilinear function equal to 0?

utility function given to me is as follows, $$u(x,y) = x+4 \sqrt{y}$$ which is a simple quasilinear function. There is a change in the given price vector, $(p_x,p_y) = (1,1) \to (0.25,1)$, and the ...
petearGriffin's user avatar
0 votes
1 answer
45 views

Explaining the relative share of the income & substitution effects of a price change

Let's say you have a Cobb-Douglas utility function, U = x^.1*y^.9 This will result in Marshallian demand functions x* = .1I / Px, and y* = .9I / Py. If you perform a Slutsky decomposition for x* as Px ...
Aa Z's user avatar
  • 1
0 votes
1 answer
80 views

Does an "optimal" MRS exist?

I was reading a case study in Hal Varian, where the author talks about essentially a surge pricing mechanism for incentivizing households to consume less electricity during peak hours (so as to not ...
Polario's user avatar
  • 143
0 votes
1 answer
988 views

How to prove Slutsky matrix's symmetry for L=2

I don't understand how to prove slutsky matrix is symmetric for L=2 $$\frac{\partial x_1}{\partial p_2}+\frac{\partial x_1}{\partial w}\cdot x_2= \frac{\partial x_2}{\partial p_1}+\frac{\partial x_2}{\...
Danjar27's user avatar
0 votes
1 answer
605 views

Calculate income and sustitution effect from utility funcion

Utility function $U(x_1 , x_2) = x_1 + 4 * x_2 $ $ p_1 = 3, p_2 = 8, m =120 $ $p_2$ changes from $8$ to $10 $ How can I calculate the income and substitution effect. I first thought about calculating ...
Coco Garazzo's user avatar
0 votes
1 answer
47 views

Confusion regarding the Slutsky equation

I'm reading Henderson and Quandt's Microeconomic Theory textbook and in the derivation process of the slutsky equation the final formula confused me a bit. The first term on the right of the equation ...
Adnan's user avatar
  • 1
0 votes
0 answers
93 views

substitution effect in slutsky equation

We know Slutsky equation decomposes the price effect into substitution effect and income effect, where the substitution effect is the partial derivative of Hicksian demand function against the change ...
Nonenicht's user avatar
  • 113
-1 votes
1 answer
2k 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: $x,y >> 0$....
user avatar
-1 votes
2 answers
213 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= \...
Svit's user avatar
  • 41