6b. Computing Marginal Rate of Substitution

In this video, I provide an example to show how to compute marginal rate of substitution using a utility function. This video uses calculus and assumes familiarity with the formula MRS = MUx/MUy, which I derive in Lecture 6A.

If you want a non-calculus version of the content of this video, see Lecture 6.

For a description of my teaching activities, check out my teaching website at http://www.tonycookson.com/teaching.

This video is part of my series of videos on microeconomics that supplement my textbook "Intromediate Microeconomics." The book (which does not use calculus) is available for purchase ($18 for an E-book with solutions) at http://www.lulu.com/cookson

For a list of videos and links to these videos (organized by topic), check out the Intromediate Microeconomics video web page:

http://blog.thisyoungeconomist.com/p/learn-microeconomics.html

Category:

Education

Tags:

• microeconomics with calculus
• microeconomics tutorials
• microeconomics
• marginal rate of substitution
• marginal utility
• MU
• MRS
• intromediate microeconomics
• intermediate microeconomics
• consumer theory
• Cobb-Douglas
• utility

[newportdeport]

So I understand the calculus behind all this, but I just don't seem to logically understand the end result. That is, what does -dy/dx = MUx/MUy actually mean!? I would think that the amount of y that you give up for x has to be equal to the amount of marginal utility that you give up for y in exchange for x. But instead, this formula shows that its equal to the amount of MU that you give up for x in exchange for y! Is this correct?

[intromediateecon]

@newportdeport Maybe an easier way to see the intuition is through my non-calculus based video (Video 6). The intuiton is that one more x gives MUx more utility, so how much y do we have to take away to make the consumer indifferent to the whole exercise? Just enough to get back to the indifference curve, call that amount W (which reduces utility by W*MUy). The total change in utility is MUx + W*MUy or 0 (b/c the consumer is indifferent). Solve for W and you get it. See Vid 6 for details.

[dbjaqy1]

i missed the last couple of steps u made that led to getting 1.5 (y/x) particularly because of the glare on the board and the size of the writing, why do u have to scrunch everything into one side of the board when you haven't used the left side at all?

[intromediateecon]

@dbjaqy1 I didn't realize there was a glare when I was filming this, but it was painfully apparent when I went to edit the video. I tried to mitigate this problem with the text popups throughout the video. Sorry for the confusion.

Here are the steps. MUx = 0.6*[X^-(0.4)]*[Y^(0.4)] while MUy = 0.4*[X^0.6]*[Y^-(0.6)].

Simplifying the previous: MUx = 0.6*(Y/X)^(0.4) while MUy = 0.4*(Y/X)^-0.6.

Take the ratio: MRS = MUx/MUy = (0.6/0.4)*(Y/X)

[mbarnes105]

honestly you made it way more difficult then you should have....

[srslayerz]

i learn better 7 mins from you than 2 hours with my econ prof

[NamClassic]

You  make econ so easy!!!!

[dbjaqy1]

how do u just multiple 0.6x^-.4 by (1/x)^.4, doesn't that need to be done on both sides of the equation? so it would be MUx * (1/x)^.4

[freeze4real]

how do ou find the mrs with only the consumption bundles? i watched your lecture 6a and i couldn,t understand it.

[theysayisayable]

Very helpful!