When there aren't gains from trade

so let's say we're in a very simplified world where we have two countries country a and Country B and they're each capable of producing apples or bananas or some combination of them and what this chart tells us if country a put all of their energy behind apples in a day they could produce three apples and if they put all of their energy behind bananas in a day they could produce six bananas similarly country B if they put all of the energy behind apples in a day they could produce two apples and country B if they put all of the energy behind bananas in a day they could produce four bananas so given this who has the comparative advantage in apples and who has a comparative advantage in bananas and how should they trade pause this video and try to figure it out on your own alright so when we're thinking about comparative advantage we really want to think about well what is the opportunity cost of producing an apple in each country and what is the opportunity cost of producing a banana in each country and so let me make another little sub column right over here opportunity cost and so what is the opportunity cost of an apple and country a and pause the video at any point if you get inspired well to produce three apples they would have to portrayed off six bananas and so that means per apple they are not producing two bananas so this is two bananas - bananas I'll just write bana bananas per Apple and their opportunity cost for bananas is just going to be the reciprocal of that so one over two apples apples per banana and then for country B we can do a similar calculation and you might be noticing something interesting is about to happen what's country B's opportunity cost of apples well one way to think about it if they produce two apples that means they're giving up four bananas or they're giving up two bananas per Apple so two bananas bananas per Apple and once again if we want to think in terms the opportunity cost of a banana well to produce four bananas there give up to apples so this is one half of an apple / banana / I was right banana right over there so this one is a little bit interesting they have the same opportunity cost it for for it that had the same opportunity cost for apples in terms of bananas and they say have the same opportunity cost for bananas in terms of apples and so they because they have the same opportunity costs let me write this down same opportunity opportunity costs costs there is no comparative advantage so no comparative advantage in either advantage advantage in either and so based on our very simple model here there are no gains from no gains from trade another way we could visualize this that maybe makes it maybe hopefully a little bit more clear so let's let me make one axes here I'm trying to draw a straight line alright and then this is my other axes right over here and let's make this one right over here this horizontal one let's make this the Apple's axis and let's make the vertical one the bananas axis bananas and we're saying per day per day and this of course is Apple's per day and so if we look at country a let me do country a in a new color so country a let's say orange and they put all of their energy behind apples they could produce one two maybe spread this out a little bit they could produce one two three apples in a day and they put all of the energy behind bananas they could produce let's just say this is two four six so that's 6 this is 4 this is 2 this is 3 right over here let me put markers in between to make this clear so if they put all of the energy into bananas to produce six in a day and so their production possibilities if we assume it is a linear trade off would look something like this and the slope right over here this would be the opportunity cost this would be so the slope right over here every time we increase apples by one we decrease bananas by two so in this situation we would have a so the slope slope here is equal to well it's actually a negative slope it's equal to negative two bananas bananas per Apple so this right over here this slope based on how I picked the axes this is giving me the opportunity cost for Apple's in terms of bananas every time I increase an Apple how many bananas am I actually giving up so that is my opportunity cost there and now if we think about country B and let me do this in a new color I'm running out of colors country B right over here they can either produce four bananas or two apples or things in between but notice it has the exact same slope the slope is the opportunity cost and if we switch these axes right over here then the slope would be the opportunity cost for bananas in terms of apples but the big takeaway here if you see the production possibilities of two countries and the head and we're talking about two Goods and they have the same slope then that means our opportunity cost are going to be the same and there's not going to be a gain from trade remember the whole point of comparative advantage and trading is that both countries will benefit that's really the big takeaway here but there are situations where both countries wouldn't benefit because they have the same opportunity cost and this was an example of one of them now the other case sometimes they will have one will have a comparative advantage over the other and they do have different opportunity costs and then you might have no gains from trade maybe there's some way that they can't know each other's opportunity cost there's some way that they don't trade maybe irrespective of what the models tell us about comparative advantage some country says hey I don't want to produce bananas i apples are the future that's a higher skilled industry whatever else so there's definitely scenarios especially even in our model in our very simplified model where there might not be gains from trade and the classic one of course is when there's no comparative advantage and both countries have the same opportunity costs in the goods