Production possibilities frontier
Allocative Efficiency and Marginal Benefit Marginal Utility and maximization
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- We've already spent a lot of time
- thinking about these six different scenarios,
- all of which sit on the production possibilities frontier,
- which means that in any of these scenarios
- we have achieved productive efficiency.
- And it's true not just of these scenarios,
- it's true of any of the points on this curve.
- So you have achieved,
- [for] any point on that curve, productive...
- -Let me give ourselves some real-state on the right-
- productive efficiency,
- which means.....
- Another way to think about it, is that
- as soon as you're at any point on that curve,
- if you want any more of one of these things,
- you have to give up some of the other.
- So for example, if you're at point C,
- and you if want more rabbits,
- If you want one more rabbit,
- you're going to have to give up some berries.
- Or, if you're at point C,
- and you want more berries,
- you're going to have to give up some rabbits.
- That's true of any point on the production possibilities frontier.
- A point over here
- -let me do this in a different color-
- So let's say that [for] this point right over here,
- you have not achieved productive efficiency here,
- because you can get more rabbits
- without having to give up any berries.
- And you could get to scenario B.
- Or, you could get more berries,
- and not have to give up any rabbits.
- And you would get to scenario D.
- So this right over here is inefficient.
- Now, all of these are all good.
- [In] all of these six scenarios
- we have achieved productive efficiency.
- But which of these do we pick?
- How do we decide [how] to allocate our time?
- So what I want to talk about in this video is
- "allocative efficiency".
- And it's somewhat subjective,
- based on the preferences of ...
- if we are the hunter gatherer, based on our preferences.
- But at least it gives us a framework for thinking:
- which of these meets our preferences the best?
- And to do that, I will review a little bit from the last video.
- In the last video, we talked about the marginal cost
- of each incremental rabbit.
- We said the opportunity cost of each incremental rabbit
- and the opportunity cost of one incremental unit
- that really is just the marginal cost.
- So let's just write these different scenarios.
- So these are the [scenarios],
- Let's write the scenarios, scene for short.
- And then let's think about the marginal cost
- of one incremental rabbit,
- -I just draw a rabbit here-
- of one incremental rabbit.
- And it's going to be given in berries
- All right, let's start with scenario F
- and this is all review from the last video.
- Sitting in scenario F,
- if we want to get one extra rabbit
- we are going to have to give up 20 berries.
- In senario E, if we are sitting in scenario E
- and we want even one more rabbit,
- we now have to give up 40 berries.
- So the marginal cost of that point of one more rabbit
- is forty berries.
- Now let's go to scenario D
- and I encourage you to pause and do this yourself.
- It'll help if you kind of work it out.
- Scenario D
- the cost of one extra rabbit is now 60 berries.
- You go to scenario C.
- The cost is now 80 berries.
- Finally we go to scenario B.
- And the cost of sitting in scenario B of getting one extra rabbit
- you are going to give up 100 berries.
- And I won't even go into scenario A
- because it will be impossible for you to have any more rabbits.
- You have no more berries to give up.
- So these are all the possible scenarios
- and the marginal cost of them
- and we can actually plot them on a line.
- So let me do that right over here.
- This will be useful.
- And so, let me draw one axis right over here.
- One axis over here,
- and let's call these the different scenarios.
- So let me do it in the same order.
- Let's call this scenario F,
- scenario E (I'll just do this in one color right now),
- scenario D, scenario C, and scenario B.
- Actually, instead of doing it that way,
- let me just talk about it in terms of
- the number of squirrels I have.
- In scenario F, if you remember...
- oh, not squirrels, rabbits.
- In scenario F, you have zero rabbits.
- zero, one, two, three, four, and five.
- So this is the number of rabbits,
- not squirrels,
- the number of rabbits
- that you are able to catch on average each day.
- And in the vertical axis,
- right now, I want to put the marginal cost,
- the marginal cost in berries.
- Let's see, it goes from 20 up to 100.
- So let's say that this is
- twenty, forty, sixty, eighty, and one hundred.
- So scenario F - that's when we had zero rabbits -
- and the marginal cost of trying to get another rabbit,
- you would have to give up twenty berries.
- So that is scenario F right over there.
- Scenario E - that's the one
- where we already had one rabbit
- and we are thinking about the marginal cost
- of getting another one. So that's scenario E.
- It's right over there.
- This is scenario D - the marginal cost is 60 -
- We already have 2 rabbits and
- are thinking about getting a third.
- That's scenario D.
- And then scenario C -
- we already have three rabbits
- and [we are] thinking about getting a fourth -
- That's scenario C.
- And then finally, we have scenario B,
- where we already have four rabbits,
- and we are thinking about getting a fifth
- and we would have to give up
- 100 berries to get that fifth rabbit.
- So that's scenario B right over there.
- So what I have just done is plotted the marginal cost
- along, these are points on our "marginal cost curve",
- our marginal cost as a function
- of the number of rabbits [that] we have.
- So let me connect all the dots.
- And in this scenario, it just happened to be a line.
- It doesn't always have to be a line,
- but in many introductory economics courses,
- it's often a line for simplicity.
- So let me make this a line right over here.
- This is our marginal cost as a function
- of the number of rabbits [that] we have.
- And actually, I should probably draw this axis.
- Let me copy and paste this.
- So let me cut that.
- And then let me paste it,
- because it really should sit
- on the zero point right over there.
- And ignore that little line right over there.
- So there you have marginal cost as a function of berries.
- But we still don't know which scenario to pick,
- and to think about that,
- I want to introduce something called
- the "marginal benefit",
- and I'll write it as MB.
- The marginal benefit of an incremental rabbit,
- and once again we're going to write it in berries.
- The way to think about the margin benefit,
- is if we are the hunter-gatherer,
- we're saying,
- if we're sitting in one of these scenarios,
- how much would we pay to
- some hypothetical convenience store in berries.
- Maybe that convenience store only sells bunnies
- and they only accept berries.
- How much would we pay to them in berries
- for an extra rabbit?
- And let's not even look at this thing right over here.
- So we're sitting in scenario F -
- and you remember scenario F is right over here -
- We have no rabbits -
- how much would we be willing to pay?
- We have no rabbits, and we actually have a ton of berries.
- So in scenario F, we have no rabbits,
- and we have 300 berries.
- If we have no rabbits and a lot of berries,
- so let's say - we have a lot of berries,
- we might be in the mood for a rabbit -
- We'd be willing to pay a lot in berries for a rabbit.
- So let's say we would pay 100 berries
- to that hypothetical convenience store for a rabbit.
- Now, let's say that we're in scenario E,
- how much would we pay to that
- hypothetical convenience store?
- Well in scenario E, we already have one rabbit
- and we have fewer berries,
- so we need a rabbit less,
- and we have fewer berries to give.
- So we're not willing to give
- quite as many berries for another rabbit.
- So maybe we'll only give 80 berries.
- Then you go to scenario D,
- we already have two rabbits,
- and we have even fewer berries.
- So we're willing to give even fewer berries for another rabbit.
- This is what we would pay to a convenience store,
- based on our current preferences.
- Then we can go all the way to scenario C -
- and it is subjective. It's not like a measurable thing.
- It's based on this person's preferences,
- this hunter-gatherer's preferences.
- Scenario C - well, even more -
- they already have more rabbits, even fewer berries.
- So they will pay even less.
- Then finally scenario B they have a good number of rabbits
- and even fewer berries.
- They'd be willing to pay very little for an incremental rabbit.
- So let's plot the marginal benefit
- as a function of the number of rabbits that they already have.
- So if we go to scenario F, the marginal benefit,
- doing that little thought experiment, is 100.
- In scenario E, the marginal benefit -
- how much you would hypothetically be willing to pay in berries?
- It's now 80 berries.
- In scenario D, it is 60 berries.
- In scenario C, it is 40 berries.
- So scenario C is right over here, and scenario C is 40 berries.
- In scenario B it is 20 berries, just like that.
- Now we are not just plotting the marginal cost,
- we are plotting the marginal cost
- and the marginal benefit in berries.
- The marginal benefit curve is really a line here,
- once again for simplicity, looks like that.
- Now given this, this is the marginal benefit curve.
- Marginal benefit is a function of the number of rabbits
- that we already have.
- And, this is the marginal cost
- as a function of the number of rabbits we already have.
- So when I say E, this is the situation E.
- That's situation D.
- This is also situation C.
- This is the marginal benefit at situation B.
- Given this, what would I rationally do?
- These are really my preferences.
- What would I rationally do?
- If I am sitting here in situation F.
- I have no rabbits.
- I already know that it'd cost me 20 rabbits
- to try to get an incremental one.
- But I've already said I am willing to pay 100.
- Sorry it costs me 20 berries to get an incremental rabbit.
- But I already said I am willing to pay 100 berries
- to get an incremental rabbit.
- So I would want to move along the curve.
- So I would definitely want to get more rabbits.
- I said I am willing to pay 100 berries for a rabbit.
- It would only cost me 20 berries for a rabbit.
- So I definitely...I am saying I want to get more rabbits.
- And another way to look at this visually,
- marginal benefit is much higher than marginal cost here.
- So I am will to go forth and try to get more rabbits.
- That's even true in scenario E.
- The marginal benefit of an incremental rabbit
- is worth much more to me than marginal cost.
- So I am willing to get more rabbits.
- So scenario E, I am still trying to get more rabbits.
- I still want to move along the production possibilities frontier
- in this general direction.
- Now what happens when I am in...
- What happens as I get closer to D?
- So if I am in this scenario right over here
- This isn't one of my label scenarios.
- But if I am right over there,
- still my marginal cost is lower than my marginal benefit.
- I will still want to get more rabbits,
- all the way to scenario D.
- In scenario D I am a little bit neutral.
- I am willing to pay 60 berries for a rabbit.
- But that's exactly how much I'd have to give up
- to get that extra rabbit.
- Let's just think about scenario D for a little bit.
- I just circle it right over here.
- It looks kind of interesting.
- Now let's go ... now we want to do anything beyond scenario D.
- So if I am at this point right over here,
- if I am working enough on average to get 2.5 rabbits a day,
- would I...
- does this make sense for me to try to get any more rabbits?
- At that point, the benefit to get an incremental rabbit
- is smaller than the cost of getting a rabbit.
- At that point, if I try to get another rabbit,
- I am getting less benefit from it than the cost associated with it.
- So I definitely don't want move past D.
- I achieve allocative efficiency
- where my marginal cost and my marginal benefit is equal.
- So based on the way that I've rigged the numbers
- in this example right over here,
- you want to settle on scenario D.
- We have achieved allocative efficiency over there.
- The marginal cost as a function of our rabbits and
- the marginal benefit of our function of rabbits is equal.
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