so after doing aslm in the first part of the course and where we took prices completely sticky and output was fully determined by aggregate demand uh we said well that minates in the very very short run but but over time at some point the supply side start showing up there are constraints the labor market gets very tight and so on and and so we added a block that started from wage determination and then we look at the impact of wages on prices and then we related inflation rate use that to relate inflation rate to economic activity so output above or below the potential output or or the natural level of output and things of that kind so remember the starting point was a um a wage demand equations so what what workers demand for a wage this period depends on how what's the price level they expect for the period because they set the wage today and they have to leave through the year or to whatever is the Contracting period H with that nominal wage so naturally if if they expect higher price level in the future they're going to demand the higher nominal wage today and then we said that's a funion that is also going to be decreasing in the level of unemployment because the obviously that weakens bargaining for power for workers or makes makes actually becoming unemployed or not having a job H more costly because it's very difficult to exit out of unemployment and then we made us an normalization this function also an increasing function on this variable Z which captures a bunch of Labor Market institutions including wage labor bargaining power so more bargaining power means that for any given level of unemployment workers would tend to demand a higher wage okay so that's what the Z variable was all about then we wanted to go from wages to prices H because the ultimate goal was to bring inflation into the picture and and for that we have to produce a we we introduce a production function H because uh in particular out we made output a function of employment and and that very naturally will connect wage pressure to price pressure because you know you need labor to produce output so the labor market is very tight that means also it's going to be more expensive to produce output and we simplifi this production function a lot we made it output equal to employment and that meant also that one unit of Labor in order to produce one extra unit of output you need one extra unit of label which means you need to pay a wage okay one one one unit of the wage and so then we said suppose that the price setting from the side of the firms simply takes this cost which is the wage and adds a markup to it to pay for a bunch of other things that we haven't introduced in this model okay so the price charged by firms is equal to the wage times one plus some positive numbers 8.2 or something like that so 1.2 H and we can write rewrite this price setting equation as a wage the real wage the firms are willing to offer and it's just equal to that okay so when the markup goes up that means the real wage the firms are willing to offer is lower than otherwise okay that took us to the concept of the natural rate of unemployment and and and what the natural what I said no is there's nothing natural about the natural rate of unemployment it's simply a definition that says that's an employment that results when the price expected price is equal to the actual price that's that's what that's all that that is and if when when we have that condition then we can think of the real wage demanded by work because I can replace expected price for actual price and divide both sides by price so the actual wage demanded by workers is equal to a function of the natural rate of unemployment and I stick the end there precisely because I replace expected price or P for no other reason okay but now we have two equations for the real wage the real wage that firms are willing to pay and the real weight of workers need to demand and we can make them both equal and that determines the natural rate of unemployment okay so remember this from the point of view of the firm this is equal to one over one plus a marup the only endogenous variable the marup is a constant the Z is also a parameter is exogenous and so from the here we can solve the natural rate of unemployment 1 over 1 plus M and we can solve the natural rate of unemployment and if you do the algebra right you you're going to get to a point like that that pins down natural rate of unemployment again there is nothing natural about the natural rate of unemployment it depends on a bunch of parameters okay which for example it clearly depends on the markup it depends on things that we took as constant here as given here all the things that wear in Z those are part of that and so we then we look at things that change and that's just done with equations we look at things that change the natural rate of unemployment that's one example if bargaining Power by workers goes up they're going to demand a higher wage at the initial natural rate of unemployment well that obviously that higher wage is inconsistent with what firms are willing to pay the only way equilibrium can be restor in this model that's the medium run equilibrium is for the natural rate of unemployment to rise to un Prime okay so there you have it nothing natural the natural rate of employ is not constant it depends on institutional parameters such as bargaining power another example is markups it depends on markups as well the degree of competition if you will in the Goods Market if if we are in some equilibrium like this one and now suddenly firms for whatever reason choose or need to charge a higher markup that h means that that at this level of unemploy the wage that workers would demand is higher than the wage that firms are willing to pay the real wage and the only thing that can clear the market in this case here in the medium run is for the natural rate of unemployment to rise okay so here we got two experiments where we move some parameter one the bargaining power of workers and the other one the the markup of the firms and both increase the natural rate of unemployment good The Next Step was to look at things that happen outside the natural rate of unemployment and particular what happens to prices there okay we look so what we did is we took the we went back to the model with the expected price here that means an employment that comes out from this equilibrium is not is not going to be necessarily the natural rate of an employment that will be the case only if P happens to be equal to p h then we simplify this function f here for something linear like this very simple but again decreasing in unemployment increasing in this institutional parameters z h we replace this wage here from this expression here and rearrange so we got this here okay and the next step was just to go from here to rate of inflation and we did it through a SE several steps and approximations and we ended up with what is known as the Philips curve okay so this say inflation is increasing an expected inflation on these institutional parameters if the markups go up that will tend to increase inflation H if bargaining Power by workers go up then that's the same but most importantly is negatively related to unemployment and that's the reason that today nowadays you know there's lots of discussion about the tightness in the labor market and and whether that's really necessary do we need to cause a recession a situation where an employment goes up a lot in order to really finally bring down inflation yeah that's was question is alha oh remember that I made up this function we said this function is decreasing unemployment I just uh replace that function for that okay so it's a sensitivity of wage Demand by workers to their employment rate Alpha that is very high means that wage demand is very sensitive very responsive to unemployment y intuition for like an expected price like could you connect that back to like I don't know some sort of like a commodity or something or so what is the intuition for for this yeah like just like a price feels tactile but like an expected price I don't well I mean imagine that workers and firms bargain for a wage that will live through the year you're buying by you're bargaining for the wage nominal wage today you don't set a real wage you set the nominal wage say $100 whatever well the wage demand will depend a lot on on what I expect inflation to be during this period if I expect inflation to be 10% you're very likely to demand a higher nominal wage because you have to leave an average with higher prices so that's that's the role of that is the price I mean I I would prefer and there are countries where that's done to set my wage in real terms so I don't need to worry about that but in practice you in economies with low inflation like the US you don't do that you you get a nominal wage and you have to leave for a year or until the next negotiation for your wage contract with that level of of wages okay with the interest rate or with the the inflation rate whereas the I guess the regular price is defined by the wage is depend on the market no no they're both the same but one is the only thing is that this price here is not sort of the current is what you really expect the price to be during the year is that is this is here just because at the moment in which you set the wage you don't know the price you're going to face as a as a worker but it's it's the price so you don't know the price that you're going to actually face so the only the best you can do is calculate well I think inflation is going to be 10% so give me know what I would have had in mind with inflation equal to zero plus 5% so on average I'm about right that's sort of the logic but this expected price is meant to be your best proxy you have at the moment in which you're bargaining for your wage for what the actual price will be during the life of that particular wage okay um okay so we end up with that that that uh Philips curve here importantly this an decreasing function of unemployment er um and then we' made different assumptions about expectations if expected inflation for example is a constant that's when we say expected infl inflation is very well anchored then you get a Philips curve that looks like this in which inflation it has a constant here and it's decreasing on the rate of unemployment and and during the 60s H that that relationship sort of held fairly well it was a downward slope in relationship it got to be steeper and steeper as we moved into higher and higher inflation levels and then I said but in the 70s the whole thing broke loose you nothing like a downward sloping curve here that happened for two reasons there were some cause push shocks you can think of lots of shocks to M but more interesting H expected inflation became an anchor and then we changed then H the expected inflation mod for rather than being a constant being the some weighted average like this and we said look during the 70s essentially that that Theta was equal to one okay so inflation expected inflation was really whatever was inflation last year people expected that level of inflation to stay the next year rather than going back to that whatever was the constant or inflation Target or historical constant pi and and that meant that the the during that period really the Philips curve looked more like a relationship of the change in the inflation rate as a decrease in function of unemployment so that means that when you increase an employment here you reduce a rate at which unemployment is inflation is rising okay that's the goal of the situation in in a case in which expected inflation is an an anchor and the last step we had there is we replace we notice we said well what happens if we stick in here the natural rate of unemployment then that will give us that will happen only when expected price is equal to actual prices so that means that when inflation is equal to expected inflation from here we can solve the natural rate of unemployment as a function of these structural parameters and once we have that we could go back to our Philips curve and rewrite it in this way okay so you can think of the Philips curve in this way and this is the the the way you typically we typically write it down in which it says H inflation is decreasing in the unemployment Gap so so if the unemployment is above the natural rate of unemployment that means inflation will tend to be below expected inflation if expected inflation happen to be equal to lag inflation that means if an employment is above the natural rate of unemployment then inflation will be falling okay any questions good you need to know this okay how to derive these things I mean not so much yeah you should know how to WR but you need to understand this relationship between the out the unemployment Gap and inflation relative to spected inflation yep unor versus de unored inflation expected inflation it's just a statement about ER what is the model we have H for expected inflation so suppose we have the following model for expected inflation one minus Theta Theta some number between Z and one times a constant inflation plus something that is a function of plus Thea times whatever is previous inflation central banks try to set a target for the inflation rate in the US is around 2% and ideally people will tend to believe they may see an tempor inflation that that is above say 2% but as long as as as people expect that to be undone in the in the in the next period then inflations we say they're very well anchored so that's a case in which very well anchored means th equal to Z here and you always sticking there in the case of the US at 2% and and there's a lot of there's a lot of that's the way the econom is behaving right now inflation today is 5% but if you ask people what do you expect inflation to be two and two years from now people tell you me look around 2% two and a half percent or so unanchor expectation is when when you don't have that anchor that 2% that the FED told you is whatever was the previous inflation that's what people extrapolate will be inflation for Next Period and that's a lot harder when you get into an inflationary episode in that context is very difficult because you at 5% people are still expecting 5% for next year so you need to is much harder to bring inflation down you need to create much more unemployment to bring inflation back to the 2% 2% Target okay that's that's what it means to an so anchor means Theta very close to zero an anchor Theta very close to one that's a a formal definition we then move [Music] to what I think is probably the most important model you'll see in this course which is the islm PC which is just the islm plus the Philips curve and that allow us to talk about the short run which is what we did in the slm and then all the way to the medium Run Okay in medium understood as when you go back to the Natural rate of unemployment natural level of output and so on oh we got a banking crisis there but that's oh this you may find useful here here I was trying to explain the banking crisis and and so and I said we have a model for that already remember we had this x this spreads in the investment function I said well you can think of a negative Financial shock something like a a credit spread shock as an increasing X and that will shift to left okay just saying good uh islm PC model was just going back to the islm model we're going to simplify things by not by just assuming that the Central Bank sets the real interest rate and the real interest rate is that okay ER and uh and to that we added a Philips curve but we didn't like that Philips curve because you know we have everything is a function of output here and interest rate and now we have inflation and then employment rate so yet another variable to carry around so we went from H the output Gap to an employment R an employment gap to an output Gap and and we did that just by noticing that output is equal to the labor force time one minus unemployment rate equivalently similar you can Define potential output or the natural output level as employment Time 1 minus the natural rate of unemployment subtract these two no and I you get that the output Gap is equal to minus L times the unemployment Gap and so we replace this for that expression divided by L and we end up with a Philips curve written in the form of an increasing function of the output Gap so when the output Gap is positive then inflation will exceed expected inflation if expected inflation is an anchor that is expected inflation is equal to lag inflation then that means that a positive output Gap leads to an increase in inflation inflation R okay so we look at an example here H you know this is the type of but now we're going to have the real interest rate here just makes it simpler to think about Central monetary policy in terms of the real interest rate otherwise too many things move at once so this is what we had done for quiz one here you have some particular equilibrium the islm with this real interest rate we got some equilibrium output equal to Y the new part the contribution of this block of the course is that now we need to also check whether this Y is is consistent with potential output or not with natural level of output and that for that we need to uh see whether this level of output H is consider again is above or below the natural rate of output and for that we need to look at the Philips curve okay okay and in this particular case that's not the the case because output is above the natural rate of output you put now given that observation you you put right draw here the the Philips curve you know that because output is above the natural rate of output the natural level of output that means inflation is above expected inflation if expected inflation happens to be an anchor equal to Pi minus one that means that at this output Gap that there's an inflation that is rising okay H now inflation Rising means the central bank will have to react and the way we so you'll have to do something up here you need to bring output down and how can you bring output down so so this economy is is engaging in an inflationary spiral actually given this mod of expectation how do you stop that if you are the fed and you you raise the interest rate no because you need to bring the L back so the equilibrium level of output you need increase the real rate up to a point in which um the level equilibrium level of output is equal to the Natural rate of output um and you may have to do more than that if inflation was an anchor and you find yourself with 5% inflation you may have to temporarily actually to bring inflation back down to 2% you may have to overshoot raise interest rate a lot generate a negative output gap for a while and then once you reach the level of inflation you like the 2% then you can go back uh to the Natural level of output okay so that's the reason central banks worry a lot about unanchor expectations because then they know that they find themselves an inflation above their target is not going to be enough to bring the output Gap to zero they're going to have to overshoot in the way down in order to re re-anchor expect well in order to bring inflation back down to the Target of 2% but in any event even if inflation are expect well anchor you still have to bring output down because at the very least you need to close this pos positive output Gap and that if you're the FED in the US or any Central Bank you do it by increasing the real interest rate now in practice central banks really don't control the real interest they control the nominal interest ratees so there's a little fight there between inflation and and what they do to the nominal interest rate but let's ignore that complication for now okay now H suppose that the FED is is is in vacation and and and so and and somebody someone else you know decides in the government decides that no we cannot have this very high level of inflation so what else could you do and you're not the FED fed in vacation who else can make policy the government the central government the treasury and so on no what is the instrument they have what do they need to do the problem they have is output is too high and that's what is leading to lots of inflation so what do you think they should do c govern expend raise taxes something of that kind okay but they need a fiscal contraction because that will bring the yes down and so equilibrium output will be lower okay so that's an alternative you have you should know this and here I just did what we just discussed just in in a steps these things happen slowly the F doesn't hike interest rate in one shot and so on it takes a while before you get to the final equilibrium oh I I show you the deflationary spiral said sometimes things can get very complicated ER because you may hit the zero lower bound the FED can bring the nominal interest R to zero but if inflation is already low that may not give you the real interest that you need in order to get output equal to the Natural rate of output I me here was one example in which you need a negative real interest rate to get output to be equal to Natural rate of output but that may not happen because you you you hit the zero lower bound H and so at that point the problem you have is that and that's was the trag tragedy of Japan for so long is that not only you cannot bring the interest rate the nominal interest rate below zero but you start getting into deflationary inflation below expectation and expectation goes to number very close to zero because of an anchor deflation expectations then you start getting negative expected inflation and when you get Negative expected inflation even if you're at the zero lower Bound in the nominal interest rate that means a positive real interest rate so effectively you're increasing interest rate at the same time and that can be a very complicated thing to get out of again that's what happened to Japan for a long time what would you do if as a government if you fall into a situation like that and Japan did a lot of that well you can do lots of things but but in particular of the kind of things you know what what would you do if you are in a situation like this in which the zero lower bound is binding and and inflation is actually falling here I had a benign case in which inflation expectation was well anchor that's not what happened to Japan after they experienced a long period of deflationary forces the then the people began to expect more deflation more deflation and so on so what else can you do let me give you a hint Japan is one of the countries has the highest levels of public debt how do you accumulate public debt yeah you you need to borrow a lot you have big fiscal deficit so that's the way you can fight this you know you can shift the yes to the right by having an expansionary fiscal policy that's the only tool really you have you lose the power of monetary policy against the zero lower bound but you still have fiscal policy and they did a lot of fiscal policy not interesting this is this is interesting ER that's a different kind of shock suppose you are at your medium run equilibrium and then all of a sudden markups go up perhaps for example because the price of oil went up a lot and something like that so then what you then that's a different kind of shock from the previous one from from any fiscal sh or anything like that that's an aggregate demand this is an agre supply problem because the first thing I know of a permanent at least change in m is that the natural rate of unemployment has to rise if the natural rate of unemployment has to rise that mean my Philips Curve will shift now okay in that particular case I know the Philips Curve will shift to the left how do I know that well because I know that that the natural rate of unemployment went up which means the natural rate of natural level of output has to come down and the natural level of output coming down means simply that that the level at which is expected inflation and inflation are equal happens at a lower level of output so the Philips can move to the left so suppose you were in this equilibrium here I'm doing for the case of an anchor expectations but the same logic goes for the case of anchor expectation ER so suppose you were at some equilibrium like this it was your medium run equilibrium but now the price of energy goes up a lot and and and you expect that to last for a while that means the Philips curve moves up so that means that if output with output at this level now you get you have a problem because you start getting inflation out of this okay because this this level of output is too high relative to the new level of the natural the new level of natural level of output so you have a positive output Gap positive output Gap means inflation above expected inflation if you have an anchor expectations means inflation starts rising up so that means the FED now needs to react to that and needs to tighten interest rate in order to to go to a new level of H natural level of output okay and that's the response but if the F that's not react and a little bit of this is what happened we had some Supply shocks and so on that were considered to be temporary well they weren't as temporary so there was no reaction but it turns out that that they lasted a lot longer than the fair expected and so so so now they had to catch up okay that was part of the reason we got into a high inflation episode that was the main reason in Europe the US is a mixture of aggregate demand lots of fiscal policy and so on and ER and supply side in Europe was very much a story of this kind well a financial Panic you need to upset it with a decline in in in real interest rate and a little bit of that has been happening it's not the FED that has cut their rates but but the markets have anticipated the FED will not raise interest rate as much as they expected before we got we got into this banking mess so we had already sort of studied the short run the medium run and now we want to look at the long run okay and that's what economic growth is about economic growth Theory and facts and so on let me go to so one of the things I I highlighted is that we tend to see among countries that are fairly similar along education and variables like that systems economic systems and political systems and so on you tend to find relationship like this that is countries with a lower per capita income at the beginning of the sample tend to grow faster in the sample and that captures very much the idea that there's a convergence there's a force towards convergence of H income per capita if you will okay that's another illustration of that phenomenon lots of dispersion here ER 70 years later a lot less dispersion but we also said that some countries that do not match that and but we focus most of what we did in growth on understanding this process the process of convergence and how it happened with without technological progress and so on and then we spent a little bit of a lecture say at most 10 10 points worth in a quiz or seven points talking about sort of anomalies and things like that no five points or something so the key ER object here one of the key objects there there are a couple but but one of them was well now we need to be a little bit more serious about the production function we said because for the short it's okay to take Capital as given and just worry about most of the fluctuation in output will come from fluctuations in employment that's not so over long periods of time capital accumulation plays a huge role and so we need to be explicit about the fact that Capital matters a lot for production okay and so we postulated a production function like this output as increas increasing function of cap and of capital and labor and now we said for this part of the course we're not going to worry about unemployment and so on employment labor force population they're all the same for us here for this part of the course and then said this production function has some important properties one is it has constant returns to scale things change quite a bit if you don't have constant return to scale so we have constant return to scale which means you should know this that if you scale all output all input all the factors of Productions by the same factor output Also Rises by the same factor okay so a production function we use a lot was aob Douglas you know output equal square root of K * the square root of n well the sum of those exponents is one so that's a a production function with constant return to scale okay so anything that has the exponents add up to one then you're that's a constant return to scale technology but importantly and it also has decreasing returns with each of its factor of production that means as you rather than moving both factors of production up you move only one well you're going to increase output but as just keep increasing that factor alone you're going to increase output by less and less and less and less because essentially has fewer and fewer of the other factor of production to work with okay and so that's decreasing returns to Capital or labor I mean if you fix the other factor of production you move up it's going to increase at a decreasing rate so one normalization that we start with was well a scaling Factor could be a population one over population okay that's a scaling factor and if I do that I multiply both everything by one / n would go into output per person is an increasing function of a increasing function but at a increasing rate of capital per person okay we plot that function here and and this conc is increasing but it's concave that shows the decreasing returns of capital no h and we got that function there then the SEC uh and we talk well we said H so so so when you move in this you can increase output per person per per person by simply increasing Capital per person and the more you increase Capital per person output will increase more and more but but but at a decreasing rate you can see that moving a the distance between A and B is the same as the distance between C and D however the increasing output when you go from A to B is enormous compar when compare with the increasing output that you get from the increasing capitals over per per person from C to D okay decreasing returns this there is another way of of increasing output per person which is with technological progress when the function f shifting up over time and we split the two main lectures in grow both into one part one in which we just we shut down the second Channel and then the second important lecture here had we focus on this channel so that's a that's what we have so let's go to when I shut down this channel for now and focus on on the case without technological progress first okay so so we put things together we said this is comes from the previous lecture we can write a output per uh per person as an increasing function of um Capital per person second key equation is well this is a proper it has to be if you in a closed economy no over expenditure or anything like we could add that but it's not important for the message then investment has to be equal so investment is going to be very important here because it's what will make the Capital stock grow but there has to be funed fing for that and the funding come from saving okay and we simplify things by assuming that the saving function is just proportional to the level of output which is reasonable when you think about long run all these things scale up when you're thinking about very shortterm no we have some constants and so on floating around but but but over the long run things do scale up and so we can write investment in equilibrium investment has to be equal to saving saving is proportional to Output so we get that investment in this economy is increasing in output this is an constant somewhere between zero and one okay and the last key equation here is the capital accumulation equation the capital accumulation equation says that Capital t+ One is equal to Capital today minus the depreciation some a fraction of the machines break down in every period but plus the new investment plus I okay and we rote things and replace the saving function and so on and we end up in in in qu an expression like this that says Capital per person here grows with investment which is funded by savings which is an increasing function of output which in turn is an increasing function of capital per person minus whatever is the depreciation and what we did then the the start diagram in in in the solo model is is we plot this function and that function we know that the state state is when these two things are equal that pins down the K star of over n k Over N start of this economy but we also know that to the left of that point in in capital space this term is greater than that and therefore H the Capital stock is rising to the right we get that this term is greater than that and therefore the Capital stock is falling okay and that's what we have in this diagram so that's the state of the economy when when the depreciation per worker which is the require in the minimum in you need to keep the Capital stock constant is whatever is depreciation per worker no anything else you do it will grow the stock of capital anything less you do you're not maintaining enough of your Capital stock is declining and that's exactly what happens here that's State you have Capital below that then then uh Capital stock will be rising because you have lots of saving and therefore lots of investment relative to what you need in order to maintain the stock of the small stock of capital you have until you reach a c state and the and you know the this model alone can explain really the that pattern we have that that you know that the poorer economies tended to grow faster than the Richer economies if you think of poorer economies as economies that are otherwise similar but that have low a low stock of capital to start with well those economies are going to be to the left of the stady state and therefore they're going to tend to grow at whatever is the steady state rate of growth plus this catching up growth okay and so this is a very powerful little model it can explain a lot of that those convergence the convergence that we saw in in the data okay do you understand this this is important okay then we did some experiments what happens if you increase the saving rate at the time when solo was writing this model many people said that what was behind growth was saving well in this model we show that indeed if a saving rate Rises then you at any given level of capital suppose that was the oldest state if now the saving rate Rises that will increase H increase investment above what you need to maintain that level of the stock of capital so the stock stock of capital going to start growing when that happens output per capita will grow faster than in a state state because you're going to go be going from here to there but eventually you'll converge to the same whole rate of growth so the point here is that the saving rate cannot change per se does not change the rate of growth in the long run but it gives you transitional growth and a lot of the the Asian Miracle of the very fast rates of growth from the 60s and 70s and 80s has to do with this kind of thing very sudden increasing saving rates plus other institutional changes and so on but High increase in the saving rate that also Le led to very fast growth okay so again this little model can explain a lot as well it can explain when you see those growth Miracles often is associated to some for some reason varies a lot across different scenarios the saving rate went up quite a bit but point is so that gives you very fast growth in the short term but eventually pets out okay so the the the next thing we all that we did for a fixed population it said well so suppose now the population is growing H I said the diagram we had before would be very unpleasant because all these curves would be shifting so what we need well what we need to do is divide not by a constant we need to divide by whatever is the population at that point in time and that will give us the same diagram we had with one little twist so I went through sort of a little algebra here to arrive to a capital accumulation equation Capital per person equ an equation for the change in the capital per person which is very similar to what we had the only difference is that the required capital investment required to maintain the stock of capital per person has an extra term here GM and I said that GM so let's think about this term so Delta so think of this as the required investment in order to maintain the stock of capital where it was ER if if h this Delta comes from the fact that well you have a stock of capital you lose a fraction of that well you need an investment equal to that fraction that you lost in order to maintain the stock of capital the same that's that's that's that's clear but that's not enough to maintain the capital per person constant if if per person is rising population is rising because even if you maintain the stock of capital constant the denominator is rising at the rate of population growth so in order to maintain the capital per person constant you need to deal with the growth of denominator as well and that means you need a little you need also investment to match the increase in population so they can keep the capital per person constant okay so that's a that's a modification so in terms of our diagram all that happened here I have technological progress as well set it to zero for now all that happened relative to the previous diagram is that now this I rotated this curve up upward a little bit okay GN but then you conduct analysis exactly in the same way the only thing that is different now is that in the previous model we had that the rate of growth the stady state rate of growth was equal to zero and the state state rate of growth of output per person was also equal to zero population was not growing output was not growing the ratio wasn't growing either here is still the case that in a steady state output per person is is not growing okay but that also means since population is growing at the rate GN or N I don't know how I call it here H that means output must be also growing at the rate GN that's what will keep output per person not growing okay so so for the output itself a very important factor in in in in in the in growth is population growth and if you look at rates of growth in general in the world s certainly in the developed World H they're falling for a variety of reasons and one of them is because population growth is falling okay but per person that doesn't make a difference but but but for the level the rate of growth it does and then we we added technological progress which we model as a effective as enhancing labor so having a better technology means is as you had more workers so for any given level of workers having a better technology we model it as having more workers okay and you can model it exactly that way you can use exactly the same diagram we had before but now we will divide our scaling Factor rather than being one over population is going to be one over effective population effective workers one over again and you conduct exactly the same analysis you do exactly the same approximations I did before H but the difference now is that ER is that here you have a rather than GN you have G why is that well because if I want to maintain the capital per effective worker constant then I need to First make up for the depreciation of the stock of capital that's I have to stabilize the numerator but then I have to take into account that the denominator is growing for two reasons because population is growing and because technology is growing and in order to maintain the ratio constant I'm going to have to investment so so to maintain that ratio constant and that's the reason now we have this this line here rotates even further and we get Delta plus GA plus GN okay and you should play with these things what happen in this diagram if I you know if I increase GA or stuff like that and notice that here now still you have a steady state but it's a steady state in the space of output per effective worker in capital per effective worker that means for example that so that means that these quantities are not growing in the stady state but output will be growing at which rate in the stady state in any state state here what is the rate of growth of output if output Over N is constant in in the today State how can that happen output has to be growing at which rate at the same rate as the denominator so it's GA plus GN what about that's a tricker question what happens to Output per person in this stady state what rate is it growing at output per person sorry somebody said the right thing but ga exactly I want to keep this ratio constant I'm asking the question at which Pace does this need to rise in order to maintain this constant well at the same rate as a is growing good here we also did we asked the question well could it be that here if we change the saving rate we get some extra kick in the long run and the answer is no for the same logic as we had before you're going to get transitional growth but you're eventually you're going to convert to a stady state and the rate of growth in the long run is not going to be a function of the saving rate is going to be equal to GA plus GN okay good do here measuring technological progress blah blah told you the story of China good oh we run out of time so let me just say the the the last thing uh that I want to say so the last thing we discussed you say well what happen if you add education to this and and try to no I make what am I doing yeah I expanded the model a little bit I had education and said does this change conclusions a lot I said no not really I mean it it doesn't change the conclusion with respect to the long run it affects the level of output per capita if you have more education but it want a che affect the rate of growth in the long run and the last point I made is that look H in this model if you expand it and you try to assume the technology the technology is the same and the rate of technological progress is the same across the world you stick those parameters in the mod population growth education levels and all that then you don't explain the amount of inequality we see in the world the world will look a lot flatter if if it was just H differences in population growth depreciation education level and things like that but with the same technology so if you want to account for so this model the mod doesn't produce enough inequality in the world you need to add something else that explains that we have some countries in Africa that are not growing that they're growing at a very low levels rate and we said that something else technology for whatever reason it happens that there's a pocket of countries that that seem to have a lower sort of permanently lower level of technology and both level and growth rate and that's what explains sort of a subset of countries that are sort of seem stack they are not consistent with this convergence type thing so that's the reason it's called conditional convergence those countries themselves are converging to something but they're converging to something much lower and with much lower rate of growth than most of the rest of the world but for the final lesson is for the average country on average it's clear that poorer countries grow faster than richer countries that's a that's that's a dominant Force but you need a little more if you want to explain certain pockets of the world okay