Allocative efficiency and marginal benefit

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 it 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 any point on that curve productive productive let me give ourselves some real estate on the right productive efficiency productive efficiency let me write productive efficiency efficiency which means or one another way to think about it is that it want 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 if you want more rabbits if you want one more rabbit you're going to have to give up you're going to have to give up some berries or if you're at Point C and you want more berries you want more berries you're going to have to give up some rabbits so any and 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 this point right over here you have not achieved productive efficiency here because you can get more rabbits 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 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 in efficient now all of these that's all good all of these five sand or six scenarios we've achieved productive efficiency but which of these do we pick how do we decide to allocate our time so what I want to talk about in this video is allocative efficiency allocative 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 or we said the opportunity cost of each 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 let's write the scenarios scenario for short scene for short and then let's think about the marginal cost of one incremental rabbit of I'll just draw a rabbit here of one incremental rabbit and it's going to be given in berries so in berries in berries in berries alright let's start with scenario F and this is all review from the last video sitting in Scenario F if we want if we want to get one extra rabbit we are going to have to give up we are going to have to give up 20 berries in scenario e if we're sitting in Scenario e and we want even one more rabbit we now have to give up we now have to give up 40 berries so the marginal cost of that the marginal cost at that point of one more one more I ski pointing say squirrel one more rabbit is 40 berries now let's go to scenario D 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 is now 60 berries is now 60 berries you go to scenario C the cost is now the cost is now 80 berries so in Serie C the cost is now 80 berries finally go to scenario B and the cost of seating in scenario B of getting one extra rabbit you're going to have to give up 100 you're going to have 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 and you have no more berries to give up so these are all the possible scenarios and the marginal costs of them and we can actually plot them on a line and so let me do that right over here this will be useful so let me draw one axis right over here one axis over here and this is let's let's call this the different scenarios so this the same order let's call this scenario F scenario f scenario e I'll just do in one color right now scenario e scenario D scenario C and scenario and scenario B actually let me let instead of doing it that way let me just talk about it in terms of the number of squirrels I have so the number of squirrels that I have so in Scenario F if you remember in Scenario F oh not squirrels rabbits in Scenario F you have zero rabbits scenario F you have zero rabbits so let's say 0 1 2 3 4 & 5 and so this is the number of rabbits not squirrels the number of rabbits that you that you right now are able to catch on average each day and then in the vertical axis in the vertical axis right now I want to put the marginal cost the marginal cost in berries in berries and let's see it goes from 20 up to 100 so let's say that this is so this is 20 40 60 80 and 100 so scenario F 1 that's when we had zero rabbits and the marginal cost of getting the marginal cost of trying to get another rabbit you would have to give up 20 berries so that is scenario F right over there scenario scenario e that's one where we had one where we already had one rabbit and we are thinking about the marginal cost of getting another one so that scenario E is right over there this is scenario D marginal cost is 60 we already have two rabbits and we're thinking about getting a third that's scenario D and then scenario C scenario C we already have three rabbits thinking about getting a fourth that's scenario C and then finally we have scenario B where we already have four rabbits and we think we're we're thinking about getting a fifth and we would have to give up a hundred berries to get that fifth to get that fifth rabbit so that scenario be right over there so what I have just done is plotted the marginal cost along these are points on our essentially our marginal cost curve our marginal cost as a function of the number of rabbits we have so let me connect all the dots and in this scenario just happened to be aligned doesn't always have to be aligned it but in many introductory economics courses it's often aligned for simplicity so let me make this let me just make this a line right over here this is our marginal cost as a function of the number of rabbits we have and actually I should probably draw this axis I should probably draw let me let me copy and paste this so let me cut this so let me cut that and then let me paste it because I really should sit on the zero point right over there right over there and ignore that little that little 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 so the marginal benefit the marginal and I'll write it is Mb the marginal benefit of the marginal benefit of an incremental rabbit and once again we're going to write it in varies and the way to think about the marginal 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 can be store only sells only sells bunnies and they only accept berries how much would we pay to them in berries for an extra rabbit so and let's not even look at this thing right over here so if we're sitting in Scenario F 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 the scenario F right here we have no rabbits and we have 300 berries if we have no rabbits in a lot of berries let's say we'll say what we have a lot of berries we were it 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 a hundred we would pay we would pay a did a hundred varies to that that that hypothetical convenience store for a rabbit now let's say that we're in scenario e 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 C 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 just based on thinking about it 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 just based on this person's preferences this is hunter-gatherers preferences scenario C well even more they already have more rabbits even if you were buddy even fewer berries so they'll pay even less and then finally scenario B they have a good number of rabbits and even fewer berries they would be willing to pay they'd be very willing to pay very little for an incremental 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 a hundred in scenario e the marginal benefit how much you would hypothetically be willing to pay in berries is now 80 berries in scenario D it is 60 berries in scenario C it is 40 berries so scenario C is right over here so in scenario C is 40 berries and then in scenario B it is 20 berries it is 20 berries so in Scenario B it is 20 berries just like that so now we're not just plotting the marginal cost we're plotting the marginal cost and the marginal benefit in berries and the marginal benefit curve and it's really a line here once again for simplicity looks like that now given this so this is the marginal benefit curve marginal benefit is a function of the number of rabbits that we already have is the marginal cost as a function of the number of rabbits we already have and so when I say e this is actually situation e that situation D this is also situation C and this is also this is the marginal benefit at situation B so given this what would I rationally do if these really are my preferences what would I rationally do so if I'm sitting here in in situation F I have no rabbits I I already know that it would cost me 20 rabbits to try to get to try to get an incremental one but I've already said that I'd be willing to pay a hundred I'm sorry it would cost me 20 berries to get an incremental rabbit but I've already said that I'm willing to pay a hundred berries to get an incremental rabbit so I would want to move so I would want to move along the curve so I would definitely want I would definitely want to get more rabbits I said that I'm willing to pay a hundred berries for a rabbit it would only cost me 20 berries for a rabbit so I definitely am saying that I'm 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'm willing to go forth and try to get more rabbits that's even true and scenario II the marginal the marginal benefit of an incremental rabbit is worth much more to me than the marginal cost so I'm willing to try to get more rabbits so in scenario E I'm still trying to get I'm still trying to get more rabbits I still want to move along the production possibilities frontier in this in this general direction now what happens what happens when I'm in what happens as I get closer to D so if I'm in this scenario right over here this isn't one of our labeled scenarios but if I'm right over there still my marginal cost is lower than my marginal benefit so I'll still want to get more rabbits all the way until I'm scenario D and scenario D I'm a little bit neutral I'm 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 so let's just think about scenario D for a little bit I'll just circle it right over here because it looks kind of interesting now let's go now what we want to do anything beyond scenario D so if I'm at this point right over here if I'm working enough on average to say get two and a half rabbits a day would I would I does this make sense for me to try to get any more rabbits well at that point the the benefit of getting an incremental rabbit is smaller than the cost of getting a rabbit at that point if I try to get another rabbit I'm getting less benefit from it I'm getting less benefit than the cost associated with it so I definitely don't want to move past D so the I achieve allocative efficiency where my marginal cost and my marginal benefit is equal so the based on the way that I've rigged the numbers in this example right over here you want to settle 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