MRS for Cobb Douglas Utility: The EASY WAY!!!

[@valjeanjean1]

Finally a video where the math and calculus is explained!!! You have no clue what this means to so many students!!

[@BurkeyAcademy]

Thanks! I am glad it helped!

[@domsjuk]

Probably the most efficient and useful shortcut I ever learned in my (fortunately) short micro-math career. How it never occurred to my prof to teach this absolutely basic thing is beyond me. Thank you!

[@thomascags6879]

Why do professors make it so complicated in Universities! Thank you man got it! :)

[@hq1428]

I assume we are from the same uni hhhh

[@enochihuoma9661]

I think its is the same in many universities. They make simple things complicated

[@alexaa515]

This is quite possibly the most god breathed video EVER. Was literally bawling my eyes out today in the library trying to finish my homework. thank you so much

[@BurkeyAcademy]

Oh my! Glad you are all better now!

[@noidea6558]

THANK YOU SO SO MUCH, seriously you have no idea how much you saved me and my grades

[@jay_lu]

i love you for this video. my professor had my head burning with his lecture. this is so simple. thank you!!!

[@tasnamira4701]

You have no idea how much this helps! Thank you so so much. Uni really over complicated it for no reason.

[@BurkeyAcademy]

Absolutely. As long as the production function is a Cobb-Douglas type, of the form Q=A*L^a *K^b, the MRS is the same as the MRTS. If there is a multiplier (like the A), it cancels out of the MRTS equation since it will be on top and bottom. It is the same mathematics as for MRS.

[@matthewweber8588]

Your page is underrated. Thank you so much!!!

[@matthewweber8588]

please keep doing what you do

[@EOCmodernRS]

why on Earth does literally nobody use numbers? I don't understand without a practical example!

[@BurkeyAcademy]

Well, there are two types of videos- numerical and analytical. Usually as you move toward higher and higher levels of analysis, you see fewer and fewer numbers (and even fewer equations!) as you try to generalize to more and more general situations. I have both kinds of videos- most of them with numbers! Check out my video list in the right hand column on www.burkeyacademy.com/home/microeconomics for a large selection of numerical goodness!

[@josiahu]

Ikr ive been looking for 30 minutes all useless videos

[@philipadams9611]

This was incredibly well explained and really clarified many questions I had. Thank you so much!

[@Real4Bas]

OMG! You have saved me sir. I just couldn't understand it until now. Thank you!

[@Wizhi]

Thanks!!! Superior tutorial, finally I understood how I should solve my homework. Million of thanks for saving my day!!!

[@nayrarizk]

This video is an absolute lifesaver, thank you!!!

[@soybeans8139]

thank you so much for this video!!!! It's really made my life easier.

[@itswaterlily]

you wonderful human you. bless.

[@gHaDE351]

exactly what i need.. an explanation for newbies.. keep it simple dude.. :)

[@Iansmith4]

Okay thanks a bunch! So for example the question is Q=f(L,K)=5KL^(1/4) I can use the rules in the video and assume that the MRTS = 1/4K / L or K/4L, and I can disregard the 5 because it cancels out?

[@claudettewhippy6561]

finally - able to understand...MRS - COBB DOUGLAS AND MU

[@BurkeyAcademy]

.2/.4=0.5. Another way to write this is 1/2. Make sense?

[@João_Pedro_Sampaio]

Thanks, Profesor, you really help me to understand that step of content.

[@aliarehman9746]

Are these answers monotonic or non monotonic

[@gixmchizi]

nice tutorial very easy to understand compared to my lecurer.......please upload more content.........Brian G. Nairobi,Kenya.

[@muhammadmustafa281]

Thank you so much. very well and simply explained

[@NO.ONECARESLLC]

You’re the goat for goin over the calculus 🫶🏾

[@TawiSaran]

wow!!! well explained and so easy to understand!!!

[@yasminalonso4539]

how can i apply this on a utility function with a square root? Thank you!!!

[@BurkeyAcademy]

Do you know what power a square root represents?

[@Sharpshooter649]

Can it be used for other functions, like quasi-linear functions, or just COBB-DOUGLAS ?

[@BurkeyAcademy]

No, I tried to make it clear that this shortcut only works for Cobb-Douglas- watch the video to see why. Every other kind of function is going to have very different looking derivatives, and MU, and thus MRS. However, there are some different ways (monotonic transformations) to transform a Cobb-Douglas that still represent Cobb-Douglas preferences. One example is to take the log of U: U=a*ln(x) + b*ln(y): The MRS will still be ay/bx.

[@15v1c1]

does it work all the time sometimes for me it is opposite like a=0.5 b=0.5 i get mrs l/k when it shuld be k/l

[@BurkeyAcademy]

If you want the slope with L on the x axis, then treat L like you would x. If Q=L^.5*K^.5, the MRTS=.5K/.5L=K/L.

[@15v1c1]

@@BurkeyAcademy mrts is measured mpl/mpk so i guess that was why i got it wrong as mrs is measured using this method

[@brieflygorgeous_]

Thank you SO MUCH for this video!

[@astheticshoes]

So monotinicity transforms the cobb-douglas function to: U= x1^a . x2^1-a So wouldnt it be solved as: (du/dx1)/(du/dx2) ,therefore; -a/(1-a) . x2/x1 ? Is this as simple as it gets?

[@BurkeyAcademy]

Yes, that would be the MRS! And there isn't a way to meaningfully simplify that further.

[@astheticshoes]

@@BurkeyAcademy you're amazing love your work !!

[@daragh2]

in the end, how does .7y = 7y and .1x = x ?

[@BurkeyAcademy]

I just multiplied the top and bottom of the fraction by 10. So if (.7y)/(.1x) is exactly the same thing as (7y)/(x).

[@casandrandhlovu1683]

thanx so much for this video......it was simple to understand cobb douglas

[@valiytora6094]

Thanks for the video. Can I ask a simple question? The last example you wanted us to solve is U=x^0.7*y^0.1, right? Isn't a+b always equal to 1? On my textbook, Cobb-Douglas production function is: QO=A(K^aL^(1-a)) 109=A(30^.3*70^.7) A equals to 2, right? Can you please explain to me what "A=2" means here? Why do we need to calculate this? Thanks again

[@BurkeyAcademy]

Great questions. Question 1: a+b does not have to be =1. However, for Cobb-Douglas utility functions you CAN force a+b to be = 1, and it can still represent all possibly Cobb-Douglas Utility functions. Let me make a video about that- I have been meaning to, and can explain it very well that way very quickly. I am going to do my best to make a video about it in the next few hours. Please remind me if you don't see one soon, OK? Question 2: Same thing... let me make a short video response to this to try to explain WHY someone might force you to do this. Typing a response would bee hard and confusing! I'll go get a cup of coffee and see if I can get started!

[@valiytora6094]

BurkeyAcademy Thanks alot. Your not-ready-yet video made me hit the subscription button :) Okay lets wait :)

[@BurkeyAcademy]

These "quick" videos sure take a lot of time!!! Here is #1: kzbin.info/www/bejne/bqK8iKmqjcZ9hZI

[@BurkeyAcademy]

Your second video is up. Cheers-

[@ellykalchenko323]

Thank you very much) wow, now i understand this topic!)

[@sjohal92]

Thanks for the help. but does this work for MRTS when there are integers in front of X and Y, for example, q=10F^1/3 * K^2/3 ? Doesn't seem to be working for me, unless I've missed something silly.

[@BurkeyAcademy]

Yes it does! The integers cancel out, since when you take the partial derivatives the 10 will appear in the numerator and denominator. One thing to be careful of is where you put your Pk and Pf-- that may be messing you up.

[@smf9890]

I'm getting a different answer for the first example. I get MUx= 0.2y^0.4 x^-0.8 and MUy=0.4x^0.2 y^-0.6 and then MRS = 0.5yx^-1.Why is that different than the shortcut/easy way?

[@BurkeyAcademy]

0.5y*x^-1 is exactly the same thing as 1/2(y/x) or y/2x. 0.5=1/2, x^-1=1/x. (1/2)*y*(1/x)=y/2x.

[@smf9890]

BurkeyAcademy Thanks so much! As you can probably tell, this kind of thing isn’t my strong suit. 😬 Thanks for the video and the quick response!

[@Faith-yg1rv]

If the values of x and y are given say MRS at x,y = (2,3) We follow the same steps right?

[@BurkeyAcademy]

Plug the values of x and y into the MRS equation to get the slope at that point.

[@abelinho2004]

do you have videos with gravelle-rees excercises solved?

[@BurkeyAcademy]

No, this is the first time I have heard of that book. Solving all of the exercises for one certain book is not something that would be interesting to do. But, if there is a TYPE of problem you would like help understanding, let me know.!

[@BurkeyAcademy]

MRTS(L for K) would be as you say, yes.

[@BurgerLegacy]

This might be a stupid question but, how did the decimal numbers become whole numbers in the end results? o_o

[@akshaydaga]

4/2 = 2 & 0.4/0.2 = 4 Its the ratio.

[@annadaa1525]

Thank You Sir 😊🙏🏻

[@Fernandosplanet]

in my text book has MRS= -U1/U2. with the negative in front. whats the difference? I think it should be negative since the indifference curve is downward sloping.

[@BurkeyAcademy]

Yes, technically the slope is negative if both x and y are goods, and the slope of the budget line is negative as well. So, when solving MRS=Px/Py, I just cancel the negatives. Also, while the slope is negative, the MRS is a quantity that can be thought of as an absolute value: How many y you are willing to trade for 1 more x.

[@kimdan391]

I wish you to be happy all the time as you made me so

[@Micheal0128]

Thx dude 🎉

[@treyboy275]

Do you have an easy way to find optimal bundle using cobb douglas?

[@BurkeyAcademy]

I have a lot of videos on that, here is one: kzbin.info/www/bejne/o4WXo4mqabCelbs If you need something different, let me know!

[@garinflohr7369]

What if you had a constant in front of the x? Does that go away?

[@BurkeyAcademy]

+Garin Flohr Yes, it does- because when you take the derivative the constant will be in the numerator and denominator, and will cancel.

[@BurkeyAcademy]

Yeah, I know, I misspoke. :) You decide whether it makes you less painless, or not unpainfuller... or ... or something.

[@itsmepm7209]

Thank u very much sir , u explained well

[@cool121092]

thanks man this will help me in price theory

[@trey7961]

why does the 7 at the end go next to the Y ?

[@BurkeyAcademy]

The exponent on the X always goes with the Y.

[@Iansmith4]

does this work for mrts too?

[@stellaunya5192]

Thank you SO MUCH

[@simongoorden9673]

Thanks a lot man

[@Alice__]

Thank you!

[@bb86ify]

God bless you!!

[@loi-reneeletts2275]

Got it. Thank you.

[@haroonarif2824]

THANK YOU

[@welearnbetter7466]

helpful video

[@lounatiko]

Masterpiece

[@bahru4245]

vallla eyyw mikro sorumzun aynisini cozmusunz thx a lot

[@Epikur95]

Thank you !!

[@patrickbryant-u4n]

Legend!

[@karo66776]

Thank uuuuu❤❤

[@1993pennanthills]

'if you learn this trick it will make things much much less painless'....I don't want that!!

[@zainabns5501]

You.... Sound like Tony Stark :D

[@cynolly]

thanks a lot

[@peternjoroge6424]

nice

[@willdodds7838]

WHoever you are i LOVE YOU

[@BurkeyAcademy]

Love you too, bud.

[@peternjoroge6424]

good

[@GDInspirations]

My teacher made it so complicated :/

[@joeyzhou8919]

you forgot that MRS is always = - ; so you missed the negative

[@BurkeyAcademy]

Most economists, and most textbooks call MRS the absolute value (and similarly with the marginal rate of transformation). Similar to the price elasticity of demand, we are not interested in the sign, but the magnitude. Yes, there are a few sources that insist on the (-) sign, but it isn't important as long as you are consistent.

[@Dem0niccA]

[@johnknight1816]

Thank you!

[@yeabseratesfaye7788]

Thanks!