6a. Marginal Rate of Substitution and Marginal Utility (with Calculus) 

13 years ago and this shi still useful thank you so much my man

This guys smile before the videos start get me every time

Hey! That's my wife you're talking about! Shortly after this video, I replaced her camera work with that of a tripod.

It makes more sense when I watch it on RU-vid then when I see it in class.

@thienthan07 I'm not sure that one warrants an entire video. I'll give a hint instead of giving away the answer: An indifference curve is convex to the origin when it gets flatter as X increases (graph it if the words seem foreign). Referencing this video's topic, what does that mean about marginal rate of substitution as X increases?

@IGOTCREAM There are partial derivatives and regular derivatives in the video. df/dx is a regular derivative. At 0:39. I wrote it as a partial, but those d's should be standing up straight. du/dx and du/dy (the marginal utilities) are partial derivatives, and they come in through the chain rule's total differentiation. I hope that clarifies.

@quittner Lecture 6 gives a numeric example for this. This is the calc-based version of my explanation of marginal rate of substitution. In Lecture 6, I go through the same reasoning with numbers (and without calculus).

this makes everything a lot clearer! thanks from Belgium!

@mehdiand1job Lecture 6 (the non-calculus version of this one) relies on a numerical example. I don't know if that's what you mean by a simple exercise, but you may want to check out that video.

@renada89 Thanks! And, yes I have. That's video "29a" on my channel. It is under my "monopoly and imperfect competition playlist." You may find it more easily by going to my video web page (link in the description of this video).

it way better than my econ prof i udertand mrs immediately when i was warching this clip!

Another quick way is the take the inner(dot *)-product of the gradient of U with respect to dz = < dx, dy>. Now let 0 = grad(U) * dz = < MU_x, MU_y > * < dx, dy > such that (dU/dx)*dx = - (dU/dy)*dy. Solve for dy/dx. The rest is left as exercise. (You will find the MRS = |-dy/dx| = slope of the indifference curve.) My question is, do I just arbitrarily choose constants and separately set them equal to the U(x, y) to find my family of indifference curves? Or is there another approach?

why do we say that y is dependent on x? I get that we you the chain rule here and that both differentiation together must be zero to be on the same utility level. I saw another way to get there with the total differential, where is the difference to your way? dU = dU/dx * dx + dU/dy * dy = 0 if we solve this we also get: -dy/dx = MUx/MUy

@debomiralha Thanks for the suggestion. Given that you are the third one to request something like this in addition to what I have already done in the video, I'll put this request on my "to do" list.

I liked it...but would be nice if you used number to perform the diferentiation!It would be easier to understand!!but still great lecture!!

Just wondering... Why is MRS the "negative" of the slope of the indifference curve? Why not just the slope?

could you explain the differentiation? are you treating as a partial derivative?

A Bivariate Function not Multivariable U(X,Y,Z) this one is Multivariable

better than my prof!

wow! eureka...thank you so much for that wonderful explanation!

Why do you have y = 10?

thank you!! this is really helpfull

dude, srly, stop shaking the camera

I needed this!!!!!!!!!!!!!!

... great stuff!!

Thanks a lot.

WHY IS U = 10 WHEN 6 X 2 = 12??!?!?!?!?!?!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111111111111111111111111111

this need a simple exercice or something like that :)

DId anyone else think the thumbnail was Toms pic from Myspace lol

you are lovely thank you