43. Pareto Efficiency and the Edgeworth Box

In this video, I explain the idea of Pareto efficiency. I define the idea, and I illustrate it with a simple numerical example. In the last section of the video, I relate the discussion of Pareto efficiency to the Edgeworth Box.

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

This video goes along with my textbook, "Intromediate Microeconomics" and it draws partially from some of the material in the supplement. Both the main textbook and its supplement are available for purchase at

http://www.lulu.com/cookson

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• Pareto efficiency
• economics tutorials
• economics
• microeconomics
• intromediate microeconomics
• consumer theory
• endowment economies
• general equilibrium
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[spamkingalpha]

Could you please make the examples a bit more complex? CD is idiot proof, maybe do an example with a quasi linear and an economic bad?

[intromediateecon]

@spamkingalpha By CD, I'm guessing you mean Cobb-Douglas. I just rewatched the video; there's nothing that imposes Cobb-Douglas utility in this video. I did assume strictly convex preferences and that both products are goods... aside from those restrictions, what I say here is perfectly general (it applies to quasilinear utility as a special case). But thanks for the comment. One of these days, I'll get around to making a video on bads, and maybe I'll do the special case of quasilinear, too.

[susanoo900]

Ok so aside from cobb-douglass, I have difficulties understanding where it is pareto efficient when you have a linear utility curve along with a perfect compliment curve. Could you do a video on PO's for that?

[intromediateecon]

@susanoo900 I didn't just do "Cobb-Douglas" utility in this vid. This video applies for any utility function with convex-to-the-origin indifference curves. Cobb-Douglas utility is special: U = [X^(a)]*[Y^(1-a)]

To your special cases: if you can draw the area that is preferred to a particular bundle for each person, you can find mutually preferred points in the Edgeworth Box. An allocation is not PO if there are mutually preferred allocations...this works for kinked ICs as well as smooth ones.

[susanoo900]

@intromediateecon Truthfully speaking I am having much difficulty understanding how to even reach the pareto optimum or even see it in IC's aside from linear-linear, cobb-cobb and kinked-kinked. You mentioned you can draw the area, I am actually quite confused by what you mean? Is it only when it is tangent that is PO?

[intromediateecon]

@susanoo900 If that's your difficulty, I suggest starting with some of my previous videos (video page link in the description of this video). For a discussion of what I mean by area of preferred bundles, see Lecture 5 and 7 (and then Lecture 36 and 37 for how to think about this in the Edgeworth Box).

Secondly, yes. Only when the ICs are "tangent" is the allocation PO. I say "tangent" rather than tangent b/c kinked ICs (perfect complements) technically don't have a slope at the "tangency."

[darascenuik]

3 people are pareto inefficient..

[SARAHBBRIGHT]

@SARAHBBRIGHT It says right off the bat it has to make someone worse off rather than the possibility. . .

[SARAHBBRIGHT]

I love your beginning, the Pareto optimal/efficient definition you gave is way better because, unlike the current textbook, it says it has to make someone worse off right off the bat!

[mrlokanc]

please could you expand on weak pareto efficiency vs strong pareto efficiency?

[spamkingalpha]

@intromediateecon Yes you are correct ... sorry I kinda skipped through the video and was getting frustrated after going through numerous videos and all of them just going over the general case. Could you maybe do an abstract case? Something like Ua=x+ln(y) Ub=x+ln(y) or even something more generic like an example with two economic bad's ... Also is there a way to introduce Risk into an edgeworth box calculation? If so it might make my problem sets a bit easier to figure out.

[sunkissed00004]

you are an economics angel! This is exactly what i was looking for!

[joehumungo]

In the case of perfect substitutes, is it always the case that the contract curve will lie to the top and left sides of the box? if so, why?

[MrSjebha]

Thanks for the vids. Could you illustrate & explain cases where 2 goods are both complements; both substitutes; one is a compliment & the other a substitute function. I'm struggling in figuring out the path of the contract curve, especially in the case where both goods are substitutes. [Please also explain with an illustration the concept of an optimal area/where you don't get a single efficient point but an area between complement curves]. Much appreciated