Comparative Advantage & Ricardian Model: Trade Gains Explained with Farmer & Rancher Example

in this video we're going to talk about what's known as the labor productivity model um another term that we'll use is

the ricardian model because David Ricardo um first developed this model of trade this is something that you've

actually already done and I'm going to start by going through um an example that's very similar to what you have

already seen so at the beginning this will hopefully feel very familiar to you um

it's the basic model where we think about why people trade or why two countries would trade and it boils down

to comparative advantage and understanding the difference between comparative advantage and absolute

Advantage um so let's get started I'm going to use an example where we have two people okay

and we can think about this as two countries but let's start by thinking about just two two people that at first

aren't going to trade with each other then we're going to allow them to trade and see what happens so we're going to

have what I'm going to refer to as a farmer and a Rancher um the farmer and the Rancher

each can produce two goods we're going to have them produce meat and potatoes I'm going to give you some

information about how much meat and potatoes they can produce and then we'll use those numbers throughout the uh

example that we go through so let's start by thinking about the number of minutes needed to make 1 o so this is

going to be minutes needed

for 1 oce and we're going to be thinking about them making meat and

potatoes let's start by thinking about our farmer then we'll do the

Rancher let's suppose that the farmer needs 60 Minutes to produce an ounce of meat so this is going to be 60

minutes so it takes the farmer a full hour to produce an ounce of meat let's suppose it takes the farmer 15 minutes

to produce an ounce of potatoes and I don't want you to worry about what that looks like we just think

about um make it as simple as if the farmer simply thinks about making meat for an

hour and then at the end of that process there's an ounce of meat okay we don't need to worry about uh you know any

tools or inputs or anything it's just time is going to be the input labor is going to be the input here now let's

think about how much time the Rancher needs to make meat and potatoes let's suppose that the Rancher needs 20

minutes to make an ounce of meat so the Rancher here clearly is is quicker at making meat than the farmer is okay

let's suppose the Rancher needs 10 minutes to make an ounce of potatoes so in terms of

both meat and potatoes the Rancher can make meat and potatoes faster than the farmer and and you might think about

that as the Rancher being more productive now hopefully you know that what this tells us is that the Rancher

has the absolute advantage over the farmer in production of both meat and potatoes but hopefully you also remember

and we'll review this that that doesn't really matter okay now what I'm going to do is I'm going to convert that into a a

day's work okay so let's think about the amount produced in eight hours amount

produced in eight hours now the choice of how many hours that doesn't matter okay we're

going to uh think about that as just being some arbitrary number what we'll see is that these are the numbers that

really matter but this helps us kind of think about the the example and make it more concrete so let's have meat here

potatoes if the farmer needs 60 Minutes to produce an ounce of meat and spends all eight hours producing meat then at

the end of the day the farmer would have 8 ounces of meat if the farmer spends or needs 15

minutes to produce an ounce of potatoes that means that in each hour can produce 4 ounces and if the farmer Works 8 hours

can produce 32 ounces the Rancher needs 20 minutes to produce

an ounce of meat that means the Rancher can produce 3 ounces of meat every hour and in8 hours could produce 24

ounces the Rancher needs 10 minutes to produce an ounce of potatoes that means the Rancher can produce 6 ounces every

hour and if the Rancher spends eight hours producing potatoes that would be 48 ounces

so that table gives us the amount of time or the amount of meat and potatoes that the farmer and the Rancher could

produce if they spent all of their time making meat or making potatoes now again the choice of eight hours is completely

arbitrary we could make that a 40-hour work week we could make it one hour it it doesn't matter we'll see that that's

not really that important now let's start about start start by thinking about what happens if

the farmer and the Rancher do not trade with each other and in international economics that situation where there's

no trade that's referred to as autarchy so we're going to start by thinking about the autarchy situation the farmer

whatever the farmer wants to consume the farmer is going to have to produce themselves same with the Rancher once

they start trading then they're able to consume a bundle of meat and potatoes is not the same bundle that they produced

so we'll start by thinking about them not trading and the way that we're going to do that is we're going to think about

what the ppf the production possibilities Frontier looks like for both the farmer and the Rancher and

you've drawn a production possibilities Frontier before let's start by drawing the farmer production possibilities

Frontier so we're going to put on our vertical axis for this example we're going to put put

meat and on our horizontal axis we're going to put potatoes and the numbers that we have

here in our table are going to give us the end points of the farmers production possibilities Frontier so remember that

a ppf tells us all of the possible combinations of our two goods meat and potatoes that the farmer is able to

produce if the farmer spends all of their time making meat they can make 8 ounces so we'll put that right here

there's 8 ounces of meat that's going to be a point on the farmers's production possibilities Frontier now if the farmer

spends all eight hours making meat that means there's no hours left over to make potatoes so this point has uh

coordinates 8 ounces of meat 0er ounces of potatoes on the other hand and the

farmer could spend all of their time making potatoes and in that case would have 32 o so here's another point on the

farmer's production possibilities Frontier and if we connect those we get the full production possibilities

Frontier so this is the farmer's ppf the farmer could produce spend all of their time making meat and be at this

point or spend all of their time making potatoes and be at that point or they could spend any combination of eight

hours making meat and potatoes and be at any other point on this production possibilities Frontier they're also

capable of producing any point inside the ppf but that would be inefficient they've got eight hours to work they

want to consume the largest bundle of meat and potatoes that they can and so they're going to be on that production

possibilities Frontier let's just arbitrarily pick a point for them to start with and let's

suppose that the farmer spends half of their day making meat the other half making potatoes in that case they would

have 4 ounces of meat and 16 ounces of potatoes that would be a point right here in the middle of the production

possibilities Frontier so that point has coordinates 4 oz of meat 16 o of potatoes let's label

that point a now that's just an AR arbitary choice and it doesn't really matter which point

we start with we just need a starting point and that's a convenient one so we're going to think about that as being

the starting point for our um farmer now let's draw the ranchers production possibilities Frontier and it's going to

be similar except clearly the endpoints are going to be different let's put that one right over here let's put

it so that we can compare we're going to also put

meat on the vertical axis potatoes on the horizontal axis the choice of which good you put on

the vertical and horizontal axis is purely up to you it doesn't matter if the Rancher let's label this

one farmer and this one will be our Rancher

if we look at how much meat the Rancher can produce if the Rancher spends all of their time making meat they can produce

24 ounces so that's going to be some point up here I'm not worried about the comparison of this vertical distance

with that vertical distance I I know it's not to scale but that does not matter the other end point of the

ranchers production possibilities Frontier is going to be 48 ounces of potatoes so we're going to stick that

that one somewhere out here so there's the ranchers production possibilities

Frontier um let's also do the same thing for the Rancher that we did for the farmer let's

suppose that the Rancher spends half of their time making meat half of their time making potatoes that will put them

right here at the midpoint of that production possibilities Frontier where at the end of the

day they have 12 O of meat and 24 o of potatoes will'll label that point a and so now we've got a place that we

can start from now we can see the situation that the farmer and the Rancher are in if they do not trade

with each other we'll be able to allow them to trade and then see what situation that that puts them in let's

start by thinking about the fact that if they do not trade then whatever they want to consume they have to be able to

produce the production possibility Frontier tells us what they're capable of producing and so in this autarchy

situation this production possibilities Frontier is also their consumption possibilities Frontier so if we think

about the Rancher the Rancher is going to be able to consume any point on this ppf they could consume all meat one day

and no potatoes or all potatoes and no meat or 12 ounces of meat and 24 ounces of potatoes or any point on that

production possibilities Frontier but they're not going to be able to get outside of that production possibilities

Frontier there's no possible way for them to achieve a point say out here okay same for the farmer we also see

that the ranchers production possibilities Frontier is farther out in this direction it's farther away from

the origin than the farmers is and you already probably know that that just represents the fact that the Rancher has

the absolute advantage over the farmer in terms of producing both meat and potatoes so we can see absolute

Advantage from that table over there where we've got 8 ounces of meat versus 24 o of meat or 32 o of potatoes versus

48 o of potatoes or we can see absolute Advantage from the fact that the end point for the farmer here is higher or

excuse me for the Rancher is higher than the farmer's endpoint also in that direction the ranchers end point is

farther out than the farmers what we want to do now is we want to think

about what happens when they're allowed to trade and what we'll see what you've already you know we're going to see is

that trade is going to allow them to achieve a consumption Point outside of their um production possibilities

Frontier what I need to do is take a break and and kind of redraw this and and organize it over there so I'll do

that and then be back in a second so now we've got our production possibility Frontiers for

the Rancher and the farmer kind of redrawn there I'm going to create another table right

down here where we summarize the production and consumption for both the farmer and the Rancher um so let's start

by putting I'm going to put my Farmer on the left and my Rancher

here we're going to think about the amount of meat and potatoes that each of them both produces and consum consumes

so we're going to have meat potatoes for each of

them and we're going to start with this autarchy situation so let's put up here the amount of meat and potatoes

that they each produce when there's no trade now those points are represented by

point a in each of our pictures so for our farmer The Farmer at the end of each day

has 4 ounces of meat and 16 ounces of potatoes our Rancher has 12 ounces of meat and 24 ounces of

potatoes so that's the situation with no trade and and remember that when they're not trading their production and

consumption points have to be the same once they start trading that's no longer going to be true so I'm going to

draw a little line here just to represent this no trade situation from what happens when we allow them to trade

with each other so now let's suppose that the Rancher goes to the farmer and proposes a uh a a way that

they can cooperate with each other change what they produce and then engage in a trade and the Rancher tells the

farmer that this is going to allow both of them to be better off um and probably if you're the farmer at first you would

be skeptical that that that's true because again a lot of people believe that the world is a zero some game so

the farmer might be worried at first that the Rancher is going to take advantage of them but let's suppose that

they sit down and they listen to the um ranchers plan and what the ranchers plan involves is each of them changing their

production point and then engaging in a trade so let's suppose that we think about first the production

points let's suppose that the farmer is going to specialize completely in producing potatoes so instead of

producing at Point a the farmer is going to move down here to this point we'll call it point

B and that's going to be the farmer's new production point the Rancher on the other hand so

so the farmer each day is going to produce 32 ounces of potatoes no meat now that obviously at the end of

the day is going to leave the farmer with a bunch of potatoes and no meat but we're going to see that the second part

of of the Rancher's plan is that they engage in a trade so the Rancher is going to move to

this point point B the Rancher is not going to specialize completely in meat but

they're going to move in that direction so if the Rancher moves to point B let's suppose

point B is a point where the Rancher produces say 18 ounces of meat and 12 O of

potatoes so those are our new production points so the farmer is going to move towards production of potatoes the

ranchers is going to move towards production of meat then they're going to trade and the

trade let's put our trade up here the trade is going to be the farmer is going to give the Rancher 15

ounces of of potatoes in return for 5 O of meat so it's going to be 15 o of potatoes

four five ounces of meat now we can think about that trade from either person's perspective

essentially the farmer because the farmer is only producing potatoes the farmer is going to pay for five ounces

of meat with 15 ounces of potatoes the Rancher is going to be producing mostly meat and very little potatoes so the

Rancher is going to be paying 5 five ounces of meat for 15 ounces of potatoes okay so it depends on Whose perspective

you're looking at they're just mirror images of each other now let's think about what that

looks like in our table here so now we're going to put the situation with trade so let's start by thinking about

production and we're going to put points B up here so in terms of the farmer the farmer is now going to be producing zero

ounces of meat and 32 ounces of potatoes our Rancher is going to be producing um 18 ounces of

meat and 12 oz of potatoes so that's what production looks like so now let's add to our table the

the trade that we've got up here so the farmer is producing no meat zero ounces of meat but is going to get 5 ounces of

meat in the trade so here's here's the trade the farmer is going to get 5 ounces of

meat in terms of potatoes the farmer is going to be producing 32 ounces of potatoes but is going to trade 15 ounces

of the of them away so this is going to be minus5 o okay from the Rancher's perspective it's

going to be the opposite here the Rancher is going to be producing 18 ounces of meat but is going to trade

five of them away so this is losing 5 ounces but what they're going to get for the 5 ounces of meat is

15 o of potatoes so this is plus 15 so there's our trade now let's think

about how that trade leaves them at the end of the day let's think about their consumption

point so our farmer produces zero ounces of meat but gets 5 ounces of meat in the trade so at

the end of the day the farmer has five ounces of meat that's one more ounce of meat than they had when they were

producing and consuming at Point a the farmer is producing 32 ounces of

potatoes but trading 15 o away that leaves them with 17 o of potatoes at the end of the day so

now let's put this consumption point on the farmers production possibilities Frontier this consumption point is 5

ounces of meat and seven o of potatoes so 5 O of meat 17 ooun of potatoes that's a point right out here outside of

the production possibilities Frontier for the farmer we'll call that point C that's their consumption point so we can

see that by engaging in this trade with the Rancher the farmer is able to reach a consumption Point that's better than

what they could have produce themselves but now that's probably not surprising because the farmer is the least

productive person out of the two what we need to do is see where this trade leaves the

Rancher so let's think about meat production the Rancher produces 18 ounces of meat trades away five of them

that leaves the Rancher with 13 ounces of meat at the end of the day the Rancher produces 12 ounces of

potatoes and gets another 15 in the trade so that leaves the Rancher with 27 o

of potatoes at the end of the day so in terms of the ranchers consumption Point that's 13 O of meat 27 o of potatoes so

that's a point right out here there's the Rancher's consumption point and we can see here that the

Rancher gets even farther outside of their production possibilities Frontier than the farmer did which for a lot of

people is counterintuitive because the Rancher is the more productive person and the Rancher is trading with a less

productive person so for a lot of people that makes them feel as if the Rancher is not going to be able to be better off

by trading with a less productive person but we can see that clearly they are better off they're even better off than

the farmer is let's look now at the gains from trade so if we think about the

gains and we're going to be comparing this consumption line with the no trade the autarchy consumption line which is

right up here so in terms of the gains from trade we can see that here there's one extra ounce of meat that the farmer

is consuming there's also an extra ounce of potatoes in terms of the raner we see

that there's an extra ounce of meat and in terms of potatoes there's three extra ounces of

potatoes so if we look at at total meat and potato production in the world here our simple world that includes only the

farmer and the Rancher we can see that at the end of this process of changing how they produce and then engaging in

this trade there's two extra ounces of meat and four extra ounces of potatoes in the world the the economic Pie has

gotten bigger there's more meat and potatoes to go around and consequently both the farmer and the Rancher are able

to consume at a point that they could not have reached by themselves so this represents the gains from

trade if we want to understand where these gains from trade come from remember that it's important to keep in

mind the difference between absolute advantage and comparative advantage so what you hopefully already know is that

the Rancher has the absolute advantage in production of both meat and potatoes over the

farmer what has happened here though is that that's not what's important what's happened is that by engaging in a trade

with each other both the Rancher and the farmer are able to specialize in the good for which they have the comparative

advantage so comparative advantage has to do with opportunity cost absolute Advantage the definition of absolute

Advantage is that a producer has an absolute Advantage if they require less of the input to produce a unit of the

good another way to think about that definition is that a producer has an absolute Advantage if using the same

amount of input they can produce more of the good so clearly the Rancher has the absolute advantage in production of both

meat and potatoes in an 8 hour day the Rancher could produce more meat or more potatoes than the

farmer but what really matters is not the amount of time needed to make meat or the amount of time needed to make

potatoes what matters is the actual opportunity cost because any minute spent making potatoes is a minute that

can't be spent making meat and that's when you get the opportunity cost remember the number of minutes is just

an intermediate step what really matters when you make an ounce of potatoes is how much less meat can you produce not

how many minutes it takes you but what's the actual cost in terms of the other good now hopefully you remember that the

opportunity cost is represented by the slope of this production possibilities Frontier so we can easily get the

opportunity cost of producing potatoes and producing meat for each of the two people we've got here so let's put

together a little table here that represents the opportunity cost of producing meat and potatoes for both the

farmer and the Rancher so let's talk about the opportunity cost of we'll start here with um 1 ounce

of meat and then we'll do 1 oce of potatoes

we'll do it for the farmer and the Rancher so let's start with our

farmer and I'm actually going to start with the opportunity cost of an ounce of potatoes because remember that the

opportunity cost of the good on the horizontal axis is represented by the slope of that production possibilities

Frontier so the slope of this ppf is 1/4 you can think about that as this vertical distance divided by that

horizontal distance it's going to be 8 over 32 which is 1/4 so for the farmer the opportunity cost of the good on the

horizontal axis potatoes is going to be 1/4 ounce of meat the opportunity cost of the good on

the vertical axis in this case meat is going to be the reciprocal of the slope so all we have to do is take this number

take the reciprocal of it which would be four so now we get the opportunity cost of an ounce of meat is 4 ounces of

potatoes so there's our opportunity cost for the farmer let's talk about the Rancher now so if we want the

opportunity cost for an ounce of potatoes for the Rancher it's going to be equal to the slope of this production

possibilities Frontier 24 over 48 is 1/2 and so we see that for the Rancher the opportunity cost of an ounce of potatoes

is going to be 1/2 ounce of meat the opportunity cost for the Rancher for meat is the reciprocal of

the this slope of the ppf so it's going to be 2 O of potatoes so now we know the actual cost

in terms of the other good not in terms of minutes in terms of the other good we can see what producing an ounce of meat

costs each of these people the farmer only has to give up a quarter ounce of meat to produce a a single ounce of

potatoes the Rancher has to produ or give up a full 1/ half ounce of meat so in terms of who has the smaller

opportunity cost for producing potatoes it's the farmer in terms of meat

production for the farmer to produce an ounce of meat they have to give up 4 ounces of potatoes the Rancher only has

to give up 2 ounces of potatoes so the Rancher has the smaller opportunity cost for production of an ounce of meat so

now we see that in terms of the actual cost of production the farmer has a lower cost of production for potatoes

than the Rancher does and in terms of production of meat the Rancher has a smaller opportunity cost and that's why

this trade that the Rancher proposed involved the farmer moving to this point where they produce the good for which

they have the lower opportunity cost in other words they produce the good for which they have the comparative

advantage and the Rancher moving towards meat prod production because they have the comparative advantage in the

production of meat so we can see here that trade has allowed each of them to specialize in

the good for which they have the comparative advantage in other words they're specializing in the good that

they're most efficient at producing now one thing that we have to keep in mind that that you know from

your principal class is that it's impossible for one of these people to have the comparative advantage both

Goods because there's no possible way that the slope could be smaller in both directions for the farmer or for the

Rancher so if the Rancher has the comparative advantage in one good the farmer is going to have the comparative

advantage in the other good and vice versa so it's impossible to have the comparative advantage in both the other

side of that coin is that it's impossible to have the comparative advantage in neither you have to have a

comparative advantage in something so let's think about um the price that's implied by this

trade and why that trade works but in order to do that what we're going to need to do is erase the board one more

time and kind of reorganize some material so let me let me do that okay so let's think

about the trade that the Rancher proposed and think about the price that's implied by that trade and we're

going to use this table that we've got of the opportunity costs of each of the good for each person to help us

understand why that uh that trade created the gains so let's think about starting with our farmer so let's take

the farmer's perspective and let's um look at the price that the farmer is pay paying for the meat that they're

getting so the farmer Got 5 O of meat that was what they received and

they paid 15 o of potatoes so they got 5 O of meat for 15 oz of potatoes now let's think

about the price that they would have paid for 1 ounce of meat so they got 5 O of meat for 15 o of potatoes that means

they got each ounce of meat for 3 o of potatoes so they got 1 o of meat for 3 oz of

potatoes and if you're not sure how I did that I've got five here if I want to convert that to a one I need to divide

it by five five divided by five is one but if I'm going to divide that by five I also have to divide that by five and

15 divid by five is three so for the from the farmers perspective they got each ounce of meat for 3 ounces of

potatoes and let's think about why that is a good deal from their perspective if the farmer would have produced an ounce

of meat it would have cost the farmer four ounces of potatoes to produce it they're able to get each ounce of meat

for three ounces of potatoes okay let's also think about that trade from the ranchers perspective why does the

Rancher like this price of three ounces of of potatoes for each ounce of meat well

the Rancher is the one selling the meat the Rancher is able to produce each ounce of meat for 2 ounces of potatoes

and then sell it for three ounces of potatoes they gain from that transaction so both of them like this trade because

it implies a price that falls right in between their opport Unity costs okay the buyer is able to buy it for a price

that's less than what they would had to pay if they produced it themselves and the seller is able to sell it for a

price that's higher than what it costs them to produce let's think about it from the Rancher's perspective so the

Rancher the Rancher's perspective is that they got 15

ounces of potatoes for 5 ounces of

meat we want to put that in terms of how much each ounce of potatoes cost the Rancher so that we can rewrite that is

they got each ounce of meat got one ounce of meat or excuse me one ounce of potatoes for

1/3 oun of meat and I did the same thing there I've got a 15 but I I want to turn that into a one so I need to divide it

by 15 but I also have to divide that by 15 and 5 divided by 15 is 1/3 so the ran Rancher got each ounce of

potatoes and paid a price of 1/3 ounce of meat now let's think about why the Rancher likes that well the Rancher

likes that because if they would have produced that ounce of potatoes themselves they would have had have paid

a full half ounce of meat all they had to pay was a third ounce of meat the farmer also likes that because the

farmer is the one selling the potatoes and they're able to produce them for a half ounce of or excuse me for a quarter

ounce of meat and then sell it for a third ounce so they're able to gain both of them are um made better off by that

transaction and clearly any trade that implies a price that falls in this range is is also going to fall in that range

because these are reciprocals of each other so now we have a good sense hopefully of of that farmer Rancher

twers trade model we've seen that that trade allows each of them to specialize in the good for which they

have the comparative advantage we see that when they do that they're able to achieve a point outside

of their production possibilities Frontier which represents the gains that they get from Trading with each other

what we want to do now is we want to talk about this model in more general terms this is a model known as the

ricardian model and so what I'm going to do now is develop this model more generally I'm I'm going to give you a a

a symbolic representation of this model but I want you to keep in mind that all we're doing is exactly what we did here

once I get the model developed and we think about how it works how it looks symbolically then we'll go through a

numerical example that's similar to this one and we'll see that it's actually very simple so we'll do that in our next

video