Transcript for:
Heckscher-Ohlin Model Lecture Notes

[Music] in today's video we're going to discuss the third of the old trade models this one is called the Heckscher Ohlin model heckscher-ohlin model now this model is going to be different and set up from the other two in that once again we'll have two countries and two goods but now we're gonna have two factors of production you recall the Ricardian model we had one factor of production labor which was freely mobile across the two sectors in the specific factors model the second one that we covered we had three factors of production two of which were fixed are specific to one of each one each of a sector and the third one which was mobile and as discussed in that video we consider that specific factors model a short run model because of the fact that that the factors aren't all freely mobile across sectors well here in the heckscher-ohlin model we go back to now that down to two factors and we'll work with capital and labor okay for capital just as before an L for labor and both of these factors will be freely mobile right they can move between our two sectors and just for the sake of this example we're gonna work with s is gonna be for shoes and C represent computers now some important additional assumptions aside from the very important assumption that our two factors are free to move between the two sectors right no no costs of moving from one sector to the other and once again we keep continue to assume that those factors are homogeneous maintaining all those those those assumptions in addition to those we're going to make some other very very important assumptions now the first first assumption or the first were the two assumptions that we're gonna have those are meant just to set up this specific example for us so we're going to assume that computer production is capital intensive and so these this notion of factor intensity this is with the core of understanding the heckscher-ohlin model so what do we mean by computer production being factor intensive well what we're saying is that the ratio of capital to labor that is employed in computer production is higher than the capital to labor ratio in shoe production now of course if if we're saying that computer production is capital intensive relative to shoe production and that's a key thing this is a relative concept right comparing the ratio of capital to labour employed in computers to that same ratio for shoes so if we're saying that computer production is capital intensive we're also saying that shoe production is labour intensive or in other words the labor to capital ratio employed in computers is lower than that for shoes if one of these is true then the other is true so that's one key assumption we're making for the setup of this model we're saying that the production in computers is capital intensive now graphically we can illustrate that with the following and we're going to make use of this graph a little later on when we're showing what happens to the wage to rental rate ratio so we have down here our labor to capital ratio that's employed and our y axis will be the wage to rental rate okay so our is the rental rate for capital W is the wage for labour so if we're saying that shoes are capital intensive flip side of that being that I'm sorry that computers are capital intensive so shoes are labor intensive what does that mean well that means that for any given wage to rental rate the ratio of labor to capital employed in shoes is higher than that for computers this is important to keep in mind when we have this this assumption and when we're saying that the ratio of labor to capital employed in shoes is higher than that for computers we're saying that's at the same wage and rental rate right so the firms are facing the same input prices and for a comparison point and you can see that if you take any wage to rental rate say like W over r0 if you take this one very clear to see that the ratio of labor to capital employed in the xu6 sector is higher than it is in the computer sector okay so this is our basic concept of factor intensity and as I said you know keep this graph in mind we're gonna use this again later on yeah so introduce it here and then you get a chance to see it again hopefully if you're that repetition it'll start to to sink in well can set this one aside for now I'm going to continue with our assumptions and then we're going to show our r2p PFS okay one for the home country one for the foreign country so one key assumption here is for the the set up of this particular example we're assuming that computers are capital intensive now there for shoes our shoe production is labor intensive the other assumption we're going to make here is that the home country is capital abundant and like factor intensity factor abundance is itself a relative concept here what we're doing is we are comparing the capital to labour ratio on the supply side all right so for the home country if we're saying that the home country is capital abundant it has a higher relative supply of capital compared to the foreign country okay so that's our first or second key assumption in terms of the set up specific to this model so we could these two assumptions if we're doing a different model we can change those assumptions around make the shoe sector capital intensive if we wanted to and so the the general insights from the model don't hinge on which fact which sector we make capital intensive or which country we made capital abundant we just need to make some assumptions in order to to work through the example how we are gonna and we're gonna make a couple other simplifying assumptions just to make it easier to work work through this model the one key assumption we have here is that technologies are the same across the two countries home and foreign shoe producers use the same technologies home and foreign computer producers use the same technologies why is that assumption important well this helps to rule out reversals of factor intensity in other words if computer production is capital intensive in the home country it is also capital intensive in the flooring country without that things can get a lot more complicated pretty quickly I encourage you to take a really good look at the example of the New Balance Factory that's in there our textbook which is an example of actually a reversal of factor intensity in the real world and we'll discuss that a bit more in class but for now we're just going to set aside the possibility of reversals of factor intensity second key assumption to help simplify things is that consumer tastes or preferences are identical across the two countries and that helps to keep things and it's just a simplifying assumption helps it make it a lot easier working through the model and as I said before it's also important for another reason we're trying to focus in in each of these models we're trying to focus on how one thing by one difference between the country can lead to the basis for trade and predict the patterns of trade all right so in this case in this model we're focusing on the difference in factor endowments right we're gonna focus on the fact that according to our setup the home country is capital abundant and how that will predict the pattern of trade along with the assumption of which industry is capital intensive if we were to add into that very drastically different preferences by consumers in the two countries we wouldn't be able to back out whether the patterns of trade is being determined by the factor abundance the relative factor abundance of home versus foreign or the difference in preferences so by keeping preferences the same across the two countries we can isolate and focus on this key difference between the two countries so if we take all of this information that we have right our assumptions of the fact that computer production is capital intensive and that the home country is capital abundant what would that mean for our pp EPS and what would that mean ultimately for our relative price of computers in the home versus the foreign country in autarky remember autarky means without trade so to be consistent with the way we're setting things up and the way the your textbook looks at things I'm going to put the computer industry on the x-axis so here's the home country and we're going to put the quantity of computers on X and the quantity of shoes on y-axis and then down here we'll have the graph for foreign so quantity of shoes a lot of computers and quantity of shoes computers so we got our two graphs set up now the question is what were the relative shape of the two PPF to look like well given the fact that computers computer computer production is capital intensive in home is capital abundant it makes sense to think that the production possibilities frontier for home is going to be skewed relative to or towards computers so it might look something like this I compared to production in foreign where you think that might be weighted or shifted or skewed more towards shoe production because shoe production is labor intensive and the foreign country's labour abundant and so I've tried to draw these so that you could really see the distinction and when you're working through examples it really helps to just make the TPP F's very very different from each other so you go ahead and exaggerate that difference just that it's a lot easier to see what's happening here so those two assumptions show us that you know the PPF sar gonna have a very very different shape well why why is that important well if you were to look at either of these two PPS and let's take some amount of computer production well what would we see if you look at the PPF for home you've got a fairly fairly flat slope there right the PPF is relatively flat whereas if I had a similar level of computer production in foreign somewhere like out here that would be really really steep and remember the relative right the price the relative price of the good on the x-axis is equal to the slope of the PPF and we saw this with the Ricardian model and with the specific factors model right the slope of the PPF in equilibrium at least right will be equal to the negative of the price of the good on the x-axis relative to the good on the y-axis right so in our in our case that would be PC over PS my price of computers over the price of shoes so the question of course is well where is that equilibrium going to be what will be equal the equilibrium relative price of computers being and this is where that that last assumption that I just mentioned comes in handy makes it easy for us say look if preferences household or consumer preferences are identical across the two countries but they're faced with these different trade-offs on the production side in equilibrium we might expect something like this so go ahead and just pick equilibrium point for the home country first and here's our indifference curve and so what do we see here well if we that dotted line right there that's the relative price line let's compare that to what we might expect to see for or foreign well we might expect to see and the foreign country that given how a relatively difficult it is for them to produce computers we might expect that the relative price of computers is going to be higher so perhaps we end up with something like like this and if we draw our line right our price line which again is reflecting the slope of both the PPF and the indifference curve in equilibrium you can very clearly see that the relative autarky price for the foreign country is higher at the relative price of computers so in equilibrium and when you combine the assumption that computer production is capital intensive in the home country is capital abundant and then add in homogeneous or identical preferences across home and foreign this leads us to the prediction that we would expect the relative price of computers in the home country to be lower than for the foreign country ok why is that important well remember and think back to both of our previous models right specific factors and Ricardian the country that has the lower relative price for a good has the comparative advantage in that good because the relative price is also giving you the opportunity cost of producing that good so ultimately our assumptions add up to saying that the home country has its comparative advantage in producing computers and so just as we showed with our previous models if you open up to trade what's what's going to have to be true in order to get both countries to be willing to engage in trade the world price is gonna have to be somewhere in between the two autarky prices so from the home country perspective that's going to be seen as an increase in the relative price of computers so if we add that world price in here and look for our tangency with the PPF so maybe it'll be at a point this what would we see well we would see an increase in the production of computers and a decrease in the production of shoes we have specialization in computer production of course unlike the Ricardian model this production isn't specializations not complete all right we don't move in the home country to producing computers and only computers and completely give up shoe production we still continue to produce shoes we just don't make as many of them as we did before opening up to trade and if we look at look for our equilibrium in terms of consumption right so we produce here we consume upon right on that trade line so in that case I end up with say a point like here and we can call that and I'll actually call that for I'll call that D for the demand or the consumption and what do we see well we see that we're producing up here right QC 1 but we're only consuming at QC d in the home country so what's that difference well QC 1 minus QC d alright we're producing more than we're consuming of computers in the home country so those are our exports of computers likewise we're consuming qsd shoes but only producing qs1 so that difference is our imports of shoes and likewise we could go in and do the same thing for the foreign country we would notice that from their perspective the relative price of computers is lower so that price line is flatter than it is without trade so their production would shift to a point like up here and we'll put put them on a indifference curve here right so what do we notice well we notice that production shifts from QC 0 Q s 0 for them up to a point like here Q s 1 and Q C 1 alright so there their direction of specialization is the opposite from what we have for for the home country right shoe production is labor-intensive in the foreign country is labour abundant so what happens in general and we open up the trade what do we notice we notice that foreign which is labour abundant is going to increase its production of the labour intensive good and decrease its production of the capital intensive good the home country which is capital abundant when it opens up to trade will see an expansion of the capital intensive sector an increase in production and computers and a decrease in production or a shrinking of the labor intensive sector in this case shoes so this is the first basic insight that we have from the heckscher-ohlin model a country will specialize in producing the good that intensively uses the factor of production it possesses in abundance repeat that again because it's a kind of a mouthful and and can be quite a bit to try to absorb in one go a country will specialize in the production of the good that intensively uses the factor of product production it possesses in abundance in other words the home country is capital abundant in computer production is capital intensive so home is going to specialize in computer production export computers and then import shoes that's very bits the first basic insight from the heckscher-ohlin model now the next thing we want to do is take what we've shown here and ask well what are the implications then for the returns to our factors of production what are the implications for the wage to rental rate and because in addition to predicting patterns of trade patterns of specialization we want to know what does this mean for the welfare of the different groups in in our society here and we'll pick that up in the next segment [Music] you right now that we've shown how to predict the patterns of specialization and trade based on the initial assumptions of which industries capital-intensive in which country is capital abundant we'd like to take a next step in show well what does that mean for the returns to our two factors labor and capital and so we start of course by by thinking about what happens to production as we showed earlier when we open up the trade we go from producing at a point like a to a point like B so we in the home country would see an increase in computer production and a decrease in Shu production so what will that mean right that shift of production well that's going to entail a shift of resources across the sector's as well so now we're going to go back to that other graph that I introduced the beginning of the video when we were talking about factor intensity and so we're going to write up on our y-axis that's going to give us the relative prices of the two inputs right so the wage to rental rate ratio on our x-axis we're going to have the labor to capital ratio and if you recall what we said was the fact that shoe production is labor intensive well that means that at every wage - rental rate shoe production employs a higher ratio of labor to capital compared to computers and you can see that visually by the fact that the relative demand for labor or the relative usage of labor in the shoe sector is shifted over to the right compared to that for computers now in addition to that also got our relative supply right yeah this is a supply and demand model and so our relative supply of labor to capital is fixed I'm gonna take that as being fixed and that L bar over K bar now what we need to add in here is our economy wide relative demand for labor right do you think of each of these curves is representing the sector or industry relative demand for labor right so this is the relative demand for labor in computers this curve is the relative demand curve for labor in the shoe sector well how do you get the economy wide or the aggregate relative demand curve well that's going to be a weighted average of these these two relative demands how can we see that well we start with our equilibrium a recognition that in equilibrium the relative supply of Labor has to be equal to the relative demand for labor right so the L bar K bar represent the supply side in the L bar of the L over K without the bars on them those are gonna represent the demand side relative demand for labor well you can take take that now and split it up into LC all right which is the amount of labor employed in computers plus a last night that's just an accounting identity all right we've taken L and said well what is ll is the total labor used well that's equal to the amount of labor employed and computers plus the amount used in shoes right and so if you look at this well that's what can we do here I'm saying this is LC over K you can split that up and it's two pieces plus LS over K that we split those up we have that now what can we do with what we have here how can we how can we show that the overall labor demand is I'm an average right a weighted average of these two individual labor demands well when you look over here what do we have we have LC over KC right that's the relative demand for labor and computers so we'd like this first term to have that same ratio in it so how would we get that well to get that you can take that LC over K and divided by KC right so now we have LC over KC but of course the fact that we've divided by KC if we want to maintain that we also will multiply it by KC all right so in an essence when you multiply and divide by the same variable you're just multiplying by one right so mathematically legitimate operation we've not changed this equation okay and then the second part of it was the LS over K I want to do the same thing right we want to divide by KS and then we'll multiply by KS so that's actually that's really all we had to do here is where we do basically did things in two steps first recognize that total demand for labor is equal to the demand for labor the amount of labor used in each sector and then recognize that we want to be able to write this equation in terms of the relative demand or relative employment of labor within each sector and now we can just rearrange these terms and so if you think about what we actually have here is LC over KC which is the relative demand for labor in computers times Casey over K which is what well that's the share of capital that's employed in computers + LS / KS which is the relative demand for labor and shoes times KS / K which is the share of capital that's employed in the shoe sector so when I say that the aggregate relative demand for labor is a weighted average of the two industry relative demand curves those weights are given by KC / K and KS / K and of course one thing you can see is that what is KS well KS is just equal to 1 minus KC all right so if I increase K see if I put more weight into the computer sector then I'm putting less weight and KS will go down putting less weight in the shoe sector so if we go we can go ahead and say draw our economy-wide relative demand curve and let's say that's just l / k0 it's be our initial relative demand for labor and of course simple supply and demand a little more complicated than the basic supply and demand graphs that you see in principles but basic concepts are the same right it really is just at its heart supply and demand graph just we're looking at relative supplies right relative quantities and relative prices so the intersection of the relative supply curve with our relative demand curve gives us the equilibrium wage to rental rate so this is so far without right before we've even opened up to trade this would be our autarky equilibrium right our no trade equilibrium well what happens when we open up to trade we'll go back to our p PF what we saw here was that our production shifted from a to b increase in computer program decrease in shoe production so what does that mean well in terms of our our weights in order to increase computer production we're gonna have to pull both labor and capital out of shoes and into computers in order to expand computer production so in other words this KC over K like the share of capital that's employed in computers is going to increase at the same time KS over K is going to decrease because we're taking labor and taking capital out of shoe production in order to put them into computer production so what does that mean well that means that our aggregate economy-wide relative demand curve we're gonna put more weight on the computer sector sector so that means that the aggregate curve is going to shift down it's going to putting more weight so it's going to be closer to the relative labor demand curve for the computer sector so what does that mean in the end well our wage to rental rate will go down now up to this point we've said simply that the wage to rental rate that ratio goes down but we want to know what in in absolute terms not just relative terms but in absolute terms what happens to these two different prices right the wage rate and the rental rate the returns to these two factors now in order to to think about that we can make use of conceptually something we talked about in the specific factors when we discuss specific factors model and we're going to go back and think about the marginal productivity of capital and the marginal productivity of labour within each sector and again this graph here is going to come in very and be very useful for us so now that the wage to rental rate has gone down what is that going to mean for relative employment of Labor within each sector okay and this is this is the key step Tunder in terms of understanding what happens to the wage and rental rate in absolute terms not just the wage to rental rate ratio now let's focus on the computer sector first initially when we had W over r0 if you take that wage to rental rate you could take that and see where it intersects the relative demand curve for labor for computers and that happens at this point here well that tells us that Elsie KC 0 which is the relative demand of the relative employment of labor and computers is initially here what happens when the wage to rental rate Falls well when that Falls labour is becoming relatively cheaper right relative to what well relative to capital all right we're lowering the price of labour relative to capital so logically producers are going to shift their input mix away from labor hours towards labor and away from capital right if labor is getting cheaper we want to use a higher ratio of labor to capital I'm going to see that right here the labor to capital ratio in the computer sector goes up from 0 to 1 now we see that increase same thing we can see the same thing for the shoe sector all right they're gonna go from here down to here alright so they're gonna also increase their labor to capital ratio okay so that's one one important insight here is that in order to maintain equilibrium between relative supply and demand for factors right when they open up the trade because the relative price of computers goes up we shift more production into computers away from shoes but in order to get that to happen in order to keep all of our factors of production employed it has to be that the wage to run rate will drop in order to get producers within both sectors to use a higher ratio of labor to capital it's so within both sectors the ratio of labor to capital employed goes up as the wage to rental rate Falls and this is what allows us to make to continue to fully employ laboring capital otherwise it's not possible right so think about it this way as I'm releasing labor and capital from the shoe sector I'm going to I need to get all those workers and all of that capital employed in the computer sector well how can that be so click here just we make up a quick example this might help to see why this all has to work this way so let's say that initially in order to produce a unit of computers I'm using one worker and four units of capital all right and then let's say in the shoe sector I'm using two and two I this is to make one one unit so if I want to make one more unit of computers what do I need I need to take four units of capital out of shoes so that means I've got to take four right well if I take four four pieces of units of capital out of shoe production that means I'm also no longer using those four workers that were going along with that capital to make those make those shoes right so okay what's going on here so I take those four units of capital and I put them into from shoes into computer production but the computer industry only wants to use one of those four workers I've now got three workers who are unemployed because we're shifting resources from the labor to the capital intensive industry so what would that do think about Eve all these workers who and the workers they're homogeneous and they're equally able to work in in either sector but these workers are no longer employed so what's going to happen you have these unemployed workers you can imagine that they'll start right you've got this excess supply of labour well that'll start beating the wage down and as their search for for work bids the wage rate down that's what's going to cause ultimately employers producers in computers and the shoe sector to start hiring more workers right to reabsorb those freed up resources so a little miracle example like that helps us to see what's going on and why this all has to be the case well so what does all of this mean then for our for our returns to capital and labor well remember the marginal product of capital is equal to what the the gonna be at least a function of the labor to capital ratio and likewise the marginal product of labor will be a function of the capital deliberation I'll write it the other way around just because right the marginal product of capital increases as the labor to capital ratio increases whereas the reverse is going to be true for labour right the marginal product of labor will increase as the capital to labour ratio increases this is nothing new we've already discussed this in terms of both the I would be discussing that we discusses in terms of specific factors right couldn't discuss that in terms of the Ricardian model because it was only one factor of production so this is conceptually and this isn't new and again I go back to what I said earlier in a previous video that you should it one thing it helps is sometimes if you recognize we're using the same core concepts basic techniques as we move from one model to the next right and you can see how some of these basic ideas can be used when we're working through each of these different models so ultimately what what does this mean for us well in terms of in terms of how is this useful if we're looking at the real returns well what is the rental rate on capital well the rental rate on capital is equal to the you know I'll focus on the computer sector first right the price of computers times the marginal product of capital and computers it also has to be equal in equilibrium all right because we're using capital in both sectors equal to the price of shoes times the marginal product of capital in shoes and we can write both of these in real terms by dividing through by the prices because as stated before what we care about is care about the real rental rate in the real wage all right we care about the purchasing power of the wage and of the rental rate and likewise we can also write that the wage in real terms would be equal to the marginal product of labor in computers and the wage in real terms in terms of the price of shoes equal to the marginal product of labor and shoes well what's happening to these real prices the key is what's happening to the marginal products all right so think about it because the price of computers when we open up the trade the price of computers is going up at the price of shoes is going down and moving in opposite directions so even if nominally the rental rates going up it doesn't guarantee at least what we said so far that the RK right the rental rate to ratio / / the price of computers is going up right they're both moving in the same direction but focus on the marginal product of capital and what did we see happening as the wage - rental rate falls within each industry the ratio of labor to capital employed goes up which means that the marginal product of capital will go up that means the real return to capital the rental rate divided by the prices of the goods will go up the flip side of that right as L / K is going up that's saying that K over L is going down which means that the marginal productivity of labour is falling and as the marginal productivity of labour Falls that means that the real wage rate in terms of either good is also falling so not only is the wage - rental rate going down but we're actually seeing is that the wage rate in real terms is falling and the rental rate in real terms is increasing right and this is what gives us Stolper Samuelson theorem all right we get our very very important theorem here and this is that again this is kind of like the the heckscher-ohlin theorem stated earlier this is a bit of a mouthful and it can be much to take in at once so I'm gonna give you the general theorem and then step back and just state it again in the context of this example so when we open up to trade what do we see we see that the factor of a the factor of production which a country possesses in abundance the real return to that factor will increase and the real return to the other factor will decrease in other words the way we set up this example was a home country is capital abundant so when we open up to trade capital like the abundant factor sees its return the rental rate increase in real terms labor which is the relatively scarce factor sees its return right the real wage rate decrease now of course everything we say for the home country the reverse holds true for the trading partner for the foreign country so when we open up the trade in this example the home country sees a relative price of computers fall or right or go up rather so we increase computer production decrease shoe production that causes the relative demand for labor economy-wide to shift down causes the wage to rental rate to fall increases the labor to capital ratio employed within each sector and then ultimately that leads to a fall in the wage rate in real terms and an increase in the wage rate in the rental rate in in real terms the opposite patterns will happen for foreign right when we open up the trade foreign is going to decrease computer production and increase shoe production causing relative demand for labour to increase in the foreign country and then ultimately the wage rate to go up in real terms and the rental rate to fall in real terms everything that happens in this model goes back to the change in relative prices when we open up the train everything falls down from the response to seeing those change in relative prices and that's the key in economics is think you know one of the keys is recognizing that prices are signals and that economic agents respond to changes in those prices to help reinforce everything next we're going to do a numerical example showing the changes in the wage to rental rate in real terms [Music] okay so just as we did for the specific factors model I'm gonna work on a numerical example to help reinforce these ideas of what's happening to the real returns to our factors of production one major difference is here with heckscher-ohlin we only have two factors of production we have two industries two factors of production than both freely mobile so we only have to solve for two prices I had a change in the wage rate and the change in the rental rate and so we can do that with a tweak wage and model I couldn't do that with specific factors we had three input prices to solve for so what we did was we just assumed a change in the wage rate and then solved for the changes in the rental rate for capital and for land so similar conceptually but some differences given that we're working with a different number of factors compared to what we did for specific factors model but we start from the same the same starting point here and recognize that the rental rate for capital times the amount of capital and actually I'll just use C's here the subscript because only one rental rate so our CKC what is that so that's total payments to capital in the computer sector remember that's equal to revenue in computers - wages paid to workers employed in computers right so similar to what we did in the previous looking at the previous model with our numerical example and we took a few steps to show that if you divide through then by KC and what what do we want to do well we want to convert this into the percent changes and so he said well you take this as the change in the rental rate and computers is equal to the change the price times that quantity - change revery - changes for all of our all of our dollar values right our prices and divided that through by by K and there's a next step we said what we want to do is we want to convert these into percentage changes right so how do you how do you do that well you got to divide through by K KC that we had change in our time sorry times are in rental rate and computers so our C KC so what's our c kc total payments to capital in the computer sector and now what are we going to have to do is we divided through on both sides so that was fine what I want to convert this into a percentage change as well so we'd like to divide through by the price and computers but then we have to multiply all right so divide and multiply by the price of computers and that turns that first term into the percentage change and the price of computers times pcqc - percent change in the wage times WLC because likewise we're going to divide by W and multiply by W dividing by W here turns this into the percentage change in the wage and multiplying by W makes this WL see all over RC Casey well same thing to work through the same steps and you'd have same expression or similar expression for the shoe sector all right the percent change in the price of shoes times revenue in the shoe sector minus the percent change in the wage rate times wages paid to labor in the shoe sector all divided by rsks now of course which should recognize is that these two rental rates right they're the same right so you can get rid of these subscripts here I had our SKS but you don't really need them right in equilibrium the rental rates got to be the same across the two sectors just as the wage rate has to be the same across the two sectors because our fact our factors are freely mobile between Xu and capital production right across the two sectors so what does that mean well now we've got two equations and we've got right the change in the rental rate and the change in the wage rate to solve for right and this all comes from at our other two prices the goods prices those are changing as a result of opening up the trade right those are exotic sahjhan us to this to this little model so here's our setup similar to what we saw before now we'll have total revenue and computers is a hundred total revenue out of that hundred fifty dollars is paid to work to labor 52 capital keep things easy total revenue the shoe sector is also a hundred but here $60 is paid out in wages and $40 in terms it was paid out to in rental rentals to capital just stay consistent with the example that we worked through graphically we'll have the price of computers go up by 10 percent and just as we did when thinking about the specific factors model in reality we say well you know we expect that the price of shoes is falling but it's just simpler in terms of working through the problem just to keep keep that that price just that this is you know no change right so the relative price of computers is going up in this example because the price of computers is going up while the price of shoes is staying constant we could also have the price of shoes falling it won't change any of the qualitatively any of the predictions that we get here everything will still still hold it's just a lot more complicated to work through so if we start and start plugging in here all right the percent change in the rental rate is equal to a 10% increase in the price of computers times 100 minus the percent change in the wage times 50 all over 50 and the percent change in the rental rate our second equation which is equal to the percent change in the price of shoes which was zero times 100 minus percent change in W times 60 all over 40 so what does that simplify down to simplifies down to so 10% of 100 is 10 so that's 1/5 or 0.2 minus 50 over 50 cancel and we just have the percent change in W zero percent times 100 zero so the first term pops to 0 minus percent change in the wage times 60 over 40 which is 1.5 that's equal to a minus 1.5 percent change in the wage again since these two rental rates are equal to each other we can just set equation 1 equal to equation 2 and what does that give us that says then that the minus 1.5 percent change and the wage is equal to 0.2 minus percent change in the wage right and will bring bring I'll bring the percent changes at the wage over the right hand side to make it positive and what does that give us it says and then so bring the point two over thee the other side minus 0.2 equals 0.5 percent change in the wage I multiply by by 2 both sides by 2 to get rid of the point five and you get that the scent change in the wage is minus 0.4 right or in other words minus forty percent so what do we go to who has the next step well we can now take that minus forty percent and plug that into either one of our equations so if I take that and plug it into one what does that tell us well then the percent change in R is equal to 0.2 minus 0.4 or minus 0.6 which is minus 6 or minus a minus which becomes a plus right 60 percent right because we're plugging in a minus 0.4 into the so the two negatives turn into a positive or I could plug it into equation 2 instead I plug that into equation 2 and we see the percent change in R is equal to negative 1.5 times the negative 0.4 which once again gives us plus 0.6 or plus 60 percent all right if you did everything correctly you should get the same answer by plugging into either equation so what are we seeing here we're seeing that the wage rate fell and it fell by quite a bit fell by 40 percent and the rental rate increased by 60% let's compare those changes to the changes in our prices so when you look at this the percent change in the wage rate which was minus 40 percent is less than the fall in the percentage change and I'd fall in the price of shoes which was zero which is less than the price of computers which was plus 10% and then lastly here the percentage change in the rental rate which was plus 60 percent so when he putted all this together what do we see right we say look we started with a fairly modest increase in the price of computers right price of computers only went up by 10 percent and that gives us these out size changes to the rental rate in the wage right price of computers went up only by 10 percent but in this example that causes the rental rate to go up by 60 percent and the wage rate to fall by 40 percent this is what we call the factor price magnification effect and this is a feature prediction of the of the heckscher-ohlin model it why is this important because this tells us look you only need relatively small price changes as a result of opening up to trade to generate relatively large changes in factor prices and of course what most people are concerned with you know think about the media if you think about politicians everyone focuses on of course the wage rate I know everyone's always concerned with what's happening to wages and in particular you can rethink the setup of this entire model so that instead of talking about labor and capital we could have been talking about skilled workers versus less skilled workers and seeing how if you think that the United States is skill abundant which by pretty much any metric we are then when we open up to trade the wages for skilled workers should go up whereas the wages for less skilled workers should go down which is something that we've been debating and discussing as society you think about any any election presidential election Senate races anything about how much these topics come up well is saying that you know the the the stagnation of real wages for less skilled workers that we saw for a couple of decades that might actually be possibly caused by rising imports and falling prices for those Goods even though we're only observing relatively modest decreases in the prices of the goods that those workers are producing so empirically this factor price magnification effect has the potential to really to you know to say the hay trade can play a big role here and we'll discuss the empirical evidence surrounding a lot of these predictions of the heckscher-ohlin model in class