11a. The Slutsky Equation and Demand Curves

[dabestplayer]

creepy smile at the beginning

[weeloo1234]

Second year undergraduate Economic History students at the LSE that you :))) You are better than our lecturer! You should apply here!

[charliefasurf1000]

@weeloo1234 oh dear, I just lost my faith in higher education - even shiny LSE... Anyway thanks @intromediateecon from Arhus School of Business (Denmark) students'

[leoyn]

God bless you!



[bryanj12341]

this helped me on my econ final, thanks much

[kennyry1]

@intromediateecon: Ah...of course, thanks for that, just wasn't seeing it for some reason. Thanks for your help.

[kennyry1]

@intromediateecon: Thanks for answering that for me, and thanks for the videos, they're great. Just one other question. I don't see how your application of Shephard's Lemma works. I took your advice and had a look at the wikipedia page, and it says that Shephard's result was that de/dp1 (which I presume is dC/dp1 in your notation) = the Hicksian (not the marshallian) demand. I don't see how adding the Marshallian demand to this, as your subtitle says, gets you to the Marshallian demand?

[intromediateecon]

@kennyry1 The whole identity is predicated on the fact that Xh = Xm. I bundled two steps into one at 4:54. Step 1: Apply Shephard's Lemma to get dC/dpx = Xh... Step 2: Use the fact that Xh = Xm in this derivation.

[kennyry1]

Why is this called the Slutsky Equation when it depends on the Hicks-Allen (rather than Slutsky) substitution effect?

[intromediateecon]

@kennyry1 Slutsky compensation (giving the consumer enough after a price increase to allow him to afford his old bundle) and Hicks compensation (giving the consumer enough after a price increase to allow him to be indifferent to the change and his old bundle) are different, but for small price changes, they approach each other.

Because Slutsky used Slutsky compensation to get the original Slutsky equation, we call it the Slutsky equation. Hicks came later with the way we now think about it.

[JohnAntonyFortune]

damn my final is in two days and I am so screwed ...

[Oscargs7]

Where did you study economy?

[intromediateecon]

@Oscargs7 Montana State University and University of Chicago

[nanni84]

Your videos are very helpful. Reading the Varian is kind of boring and you make it more interesting and understandable. You are a good teacher. Thank you :)

[TheJimmyt1]

Very helpful, thanks!

[KRKbert]

Why is the Varian textbook so hard to understand?

[intromediateecon]

@KRKbert

I think Varian's exposition is an acquired taste. Personally, I like it. Others disagree because he hides many of the interesting mathematical details in appendices (which can make it hard to parse). In a phrase, I don't know. Do you have any thoughts on why or why not?

[eswyatt]

Are the income and substitution effects equal for all Cobb-Douglas utility functions, or only ones with .5 & .5 exponents? I mean, would they be equal for X^.3Y^.7? All I can find are statements to the effect "the precisely offset one another." But plain and simple, are they always equal?

[intromediateecon]

@eswyatt I assume that you are talking about the income and substitution effects for the other good (the good whose price doesn't change).

I think this is true. The easy way to see this is in demand. Cobb-Douglas demand is such that expenditure share = exponent in CD utility * Income.

Let Px*X be the expenditure share, alpha be the exponent, M be income. Then,

X* = alpha*M/Px.... so if we changed the price of Y, X wouldn't respond in aggregate (shorthand for income and subst canceling).

[eswyatt]

@intromediateecon I'm just gong to have to stop being lazy and do some Slutsky decompositions to Cobb-Douglass functions with unequal exponents. I hope it's not a lot more messy because of that. Most intermediate books (the more ambitious ones, that is) stick with .5 and .5.

[intromediateecon]

@eswyatt

Clarification: In my previous response, I was assuming that the sum of the exponents was 1. That's perfectly reasonable to do in a utility maximization framework because if alpha + beta wasn't 1, we could use the utility function V = U^(1/(alpha+beta))... a monotonic transformation... and still get the same demand functions.

[eswyatt]

@intromediateecon Yes I recall that any utility function of that form can be "normalized" without doing violence to the "ordinal utility" result (oh the jargon!).

[eswyatt]

What book are you using? I assume Mas Coell, but your exposition is much simpler (I know because I can somewhat understand it!). I'd like to see something on logarithmic derivatives (elasticity). Absolutely maddening!

[intromediateecon]

@eswyatt Honestly, I didn't base my explanation on any particular book. Part of the reason I made this video was because I was frustrated with the overly technical exposition that is given in most books. My inspiration for this video was a lecture I had on this from Kevin Murphy (of UChicago) a few years ago.

[blingking4444]

@intromediateecon That's where I am having problem. My book is filled with symbols and equations I can't understand. I understand the concept and everything, but I can't seem to get the formulas and get the big picture. Do you know any book that teaches this course easily? BTW, your lectures are very helpful. I need a book so I can read it in a library or something.

[intromediateecon]

@blingking4444 I wish I knew of an easy book on this. This level of economics can be difficult. Of the set of books that I know, getting easier exposition comes with the cost of forgoing actual substance. Deaton and Muellbauer is about as easy as this material gets, but it is still full of formulas.... Or, you can go to an intermediate book like Varian (but you'll have to hope that the topic you want is covered in the math appendices). I just looked it up, this one is... page 157 of Varian.

[blingking4444]

@intromediateecon Thank you for a quick reply. I was able to get hold of the book from my local library. It is so much better than the book I use right now. I guess I will go ahead and keep renting the book when I need it. The Deaton and Muellbauer is hard to find though.

Thank anyways and keep up the good work with the tutorials.

[soulutiongroupie]

Thank you, this is great. Microeconomics are fun with dynamic explanations.

[tolgochka]

If it's possible to switched on the sound and make the full video how do you make the calculations to undertand it better.

[kushagra452]

Hi

There is a typo in the last equation (the slutsky euqation). you have used the shephard's lemma correctly and labeled the compensated demand as X^h but in the last line you have written it down as the Marshallian demand X^m. It should be X^h (Hicksian/compensated demand).

I really liked your explanation, and have listened to this lecture multiple times.

Cheers!

Kushagra

[intromediateecon]

@kushagra452 Thanks for the comment. It turns out that is not a typo. Because the solution to the expenditure minimization (Hicksian/compensated demands) and utility maximization (Marshallian/uncompensated demands) are the same here, we can use whichever solution we wish. I just chose to substitute for Hicksian demand to obtain an equation entirely in terms of Marshallian demands.

[kushagra452]

@kushagra452 Thanks for the clarification! Sorry I didnt notice that X^m = X^h for this problem.

[LFCzeppelin8]

really good explanation, thanks.

i have a couple of questions though. if the price of one good falls, the Hicksian and Slutsky demand curves for that good are different because the Hicksian holds utility constant, while Slutsky allows utility to rise, right? (specifically, in terms of slopes, Hicksian < Slutsky < Marshallian)?

and the Marshallian demand curve incorporates the Slutsky substitution effect AND the income effect?

[fladdog]

You really tackle the tough problems. this is excellent.

[sasamuraki]

thanks for the vid... gotta study it a bit more...

[mvho1]

Please post a video on how to maximize utility with the cobb douglas function! My math is a bitt iffy..

BTW Great vids thus far!

[intromediateecon]

On a related note to your request, I posted a video on how to minimize cost using calculus and the Cobb-Douglas functional form.

That video is Lecture 17A. A lot of the derivatives are the same, but the application and context is different.