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 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-- let me give ourselves some real estate on the right-- 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 if you want more rabbits, if you want 1 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. 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 at 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, that's all good. All of these five 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. 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 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 let's write the scenarios, scenario for short, scene for short. And then let's think about the marginal cost of 1 incremental rabbit. I'll just draw a rabbit here. 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 1 extra rabbit, we are going to have to give up 20 berries. In Scenario E, if we're sitting in Scenario E, and we want even 1 more rabbit we now have to give up 40 berries. So the marginal cost at that point of 1 more, I keep wanting to say squirrel, 1 more rabbit is 40 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 1 extra rabbit is now 60 berries. You go to Scenario C. The cost is now 80 berries. So in Scenario C the cost is now 80 berries. Finally you got to Scenario B and the cost of, sitting in Scenario B, of getting 1 extra rabbit-- 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. 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 call this the different scenarios. So this-- let me do in the same order. Let's call this Scenario F, Scenario E. I'll just do it in one color right now. Scenario E, Scenario D, Scenario C and Scenario B. Actually, let me-- 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 0 rabbits. Scenario F you have 0 rabbits. So let's say 0, 1, 2, 3, 4, and 5. And so this is the number of rabbits, not squirrels, the number of rabbits that you right now are able to catch, on average, each day. And then in the vertical axis, right now, I want to put the marginal cost in berries. And let's see, it goes from 20 up to 100. So let's say that this is 20, 40, 60, 80, and 100. So Scenario F, that's when we had 0 rabbits. And 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 E, that's one where we had 1, where we already had 1 rabbit and we are thinking about the marginal cost of getting another one. So that's scenario E, is right over there. This is scenario D. Marginal cost is 60. We already have 2 rabbits and we are thinking about getting a third. That's Scenario D. And then Scenario C, we already have 3 rabbits, thinking about getting a fourth. That's Scenario C. And then finally, we have Scenario B where we already have 4 rabbits and we're 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've just done is plotted the marginal cost along-- these are points on, 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 then this scenario just happened to be a line. 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 we have. And actually, I should probably draw this axis, I should probably draw-- let me copy and paste this. So let me cut this. Let me cut that and then let me paste it, because it really should sit on the 0 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. 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 paid 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 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 in Scenario F right here, we have no rabbits and we have 300 berries. If we have no rabbits and a lot of berries, let's say, we'll say, we have a lot of berries. We might be in the mood for a rabbit. We would be willing to pay a lot in berries for a rabbit. So let's say we would pay 100. We would pay 100 berries to 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 1 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 2 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 hunter-gatherer's preferences. Scenario C, well, they already have more rabbits, 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 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, 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 it's 40 berries. And then in Scenario B it is 20 berries. So in Scenario B it is 20 various, 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. And this 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's 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 Situation F, I have no rabbits. I already know that it would cost me 20 rabbits to try to get an incremental one. But I've already said that I'd be willing to pay 100. Sorry, it would cost me 20 berries to get an incremental rabbit. But I've already said that I'm 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 that I'm willing to pay 100 berries for a rabbit and it would only cost me 20 berries for a rabbit. So I'm saying that 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 in Scenario E. 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 more rabbits. I still want to move along the production possibilities frontier in this general direction. Now what happens as I get closer to D? So if I'm in this scenario right over here, and 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. In 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 would 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 2 and 1/2 rabbits a day, would I-- does this make sense for me to try to get any more rabbits? Well, at that point 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 than the cost associated with it. So I definitely don't want to move past D. So 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 allocated efficiency over there. The marginal cost as a function of our rabbits and the marginal benefit of our function of rabbits is equal.