43. Pareto Efficiency and the Edgeworth Box

[darascenuik]

3 people are pareto inefficient..

[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!

[SARAHBBRIGHT]

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

[mrlokanc]

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

[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.

[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

[Meddd123]

thaaaaaaanks

[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."

[polvotierno]

Ok... I watched lecture 12. Let´s look at MRS in the edgeworth box. Could you add the MRS for Person A and B at each point along the pareto set? Then graph those. From that new graph could you determine the optimal point of the pareto set using elasticities or differentials?

[intromediateecon]

@polvotierno ANY point in the Pareto set is Pareto optimal (which is what I say at 6:57 in this video). Hence, looking for "the optimal point of the Pareto set" doesn't make sense because they are all optimal.

If you want the "best" allocation, you'll have to come up with some sensible measure of "best" other than Pareto (i.e. maximizing total utility), but to do so, you'll have to make assumptions about the utility functions and how much weight to give each of them... that can get messy.

[polvotierno]

Wouldn´t there be diminising marginal utility which would end up putting more distance between the utiity curves the farther out from the axis-origin you go?

[intromediateecon]

@polvotierno Not necessarily. Three points on this: (1) Diminishing marginal utility (DMU) has nothing to do with distance between indifference curves. (2) DMU isn't necessary or sufficient to have a downward-sloping demand curve. (3) Because of 1 and 2, DMU is an *assumption* that we may or may not want to make. It is one of those sharper criteria I was talking about in the video. I discuss more on DMU in Lecture 12, you should really check it out.

[polvotierno]

Can you measure the distance between utility curves to get a sense of elasticity?

For example, if person B has very little goods, it may take just a bit more for them to get to the next level of utility, whereas person A already has so much that to give a little to person B probably wont make them jump to a lesser utility curve?

Therefore the utility curves of person B are closer together than for person A.

Do you see? Utility curves measure increases in being better off.

[intromediateecon]

@polvotierno I think you're trying to loosely say, "Why don't we maximize total utility?" And, as a corollary, "If we are at a tangency where moving along the Pareto set increases A's utility more than it decreases B's utility, why don't we do it?"

These ideas seem sensible on their face, but the trouble is that they require interpersonal comparisons of utility. For another video of mine where I show why using cardinal utility is problematic, see Lecture 12 of this series of videos.

[polvotierno]

Is there any way of evaluating the points on the pareto efficiency line as far as elasticities?

For example, moving along the line of the elasticity of demand, one can optimize revenue. Can one optimize the allocation of goods according to the elasticity of the pareto efficient line?

[intromediateecon]

@polvotierno No. I'm not sure what it would mean to think of an elasticity along the Pareto set. All of the points on the Pareto set are "efficient" points in the Pareto sense. None is "better" than the others. All are allocations that are not necessarily misallocated.

If you start on the Pareto set, the slope of that line would just tell you what direction you would have to go to stay at a point of mutual tangency. It wouldn't tell you anything like maximizing revenue.