Level II Concept: Theories of economic growth

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” s start with the classical model the classical model is also called the malthusian theory theory because it was developed by david malthus malthus came up with this theory in which was more than two centuries ago and at that point economies were primarily farming beasts you can imagine that in a farming based economy. We will have diminishing marginal returns of labor in other words as we keep adding more labour output initially goes up rapidly. But eventually output will increase at a decreasing rate also if we are at a given point. So we have a certain amount of labor and a certain amount of output.

This would tend to be a subsistence level of output. We would have enough output to feed the population now in this situation. What if there is some new technology. So the plow is invented or let s say.

An irrigation system is developed which means that in our farms. The overall output per person goes up so that is possible when we do have some technological innovation. The real gdp per person would rise above the subsistence level. But this would mean there is more output more food with more food.

We could have more people so that would result in a population explosion and that would bring the real gdp per person back to the subsistence level. So the prediction of the classical model is that we can have a growth in real gdp per person. But this growth is temporary in the long run the adoption of new technology results in a larger. But not richer population.

Larger population because we have more output which can feed more people. But the population is not richer. Because the larger output is also spread across more people so you can see that this theory is fairly straightforward. But the predictions don t hold true empirical evidence does not support this theory.

We have seen over the last century that per capita income has increased while population growth has slowed down the other issue is that over the last century. We ve seen rapid technological progress and that technological progress has offset the impact of diminishing marginal returns so this concept of diminishing marginal returns of labour has also not panned out over the last century. So. What we see here is that this model might have explained economic growth two centuries ago.

But it does not work for our current time we therefore need other models the neoclassical model was developed by robert solow in the 1950s. The primary objective of this model is to determine the long run growth rate of output per capita and then to relate this growth rate to three variables. The rate of technological change. The savings to investment rate and population growth.

The neoclassical model is based on the cobb douglas production function. Which we have talked about so. Here. Is the cobb douglas production function.

According to this model as economies develop they eventually reach steady state. Now what a steady state mean in steady state capital per worker and output per worker grow at equal sustainable rates. So there is a constant rate at which capital per worker and output per worker. Grow now in a given economy that sustainable rate might be 3 for example.

But there is a given sustainable rate and then in steady state. According to the neoclassical model this steady state rate. Does not change. This is also called the balanced growth path.

Now there are some important formulas related to the neoclassical model that you need to know the curriculum shows how these formulas are derived. But on the exam. You will not be asked for the derivation. The first key relationship is that the growth rate of output per capita in steady state is given by theta divided by 1 minus alpha.

Here theta is the rate of change of total factor productivity. So if total factor productivity is changing by let s say 3 percent. Then that s what we plug here for theta and then 1 minus alpha. Is the elasticity of labour.

We ve seen this in the past where we ve had alpha. Which is the elasticity associated with capital. We ve also called it the share of national income. That goes to suppliers of capital and 1 minus alpha.

Is the share of overall income or overall output. That goes to labour..

Now example. 10 illustrates this so we are given the labour cost as a percentage of total factor cost so example. 10 actually gives this entire denominator on the exam. You might simply be given alpha.

And then you will have to do 1 minus alpha. So this is the growth rate of output per capita and just to use the numbers from example 10. We are told that for china the total factor productivity. Growth which is.

Theta we are told that that is. 25. Percent and we are told. That.

1 minus. Alpha. Is 465 so when we. Do.

25 percent divided by. 465 we get about 66. Percent. This means that for china in steady.

State the growth rate of output per capita should be about 66. Percent. But the curriculum also says that the actual growth rate in china is about 86. Percent.

So at the time this calculation was done or this data was presented the growth rate in china was. 86. Percent which is higher than 66. Percent so how is this discrepancy.

Explained the explanation is that when this 86. Percent. Growth is happening. China is not in steady state.

So china is at a point. Where additional capital tributing significantly to growth and that s why the growth is higher than the steady state growth rate china at this stage is not at steady state. So anyway. This is the growth rate of output per capita.

The next formula is the growth rate of overall output. So this is the growth in y and not the growth in per capita output. So the growth rate of output is theta over one minus alpha. Which is basically the growth rate of output per capita.

Plus in n. Is the growth rate of the labor force now hopefully this should be familiar. We said earlier that the growth rate of output is equal to the growth in labor productivity. Plus.

The growth rate of the labor force and that s exactly what s happening here this first segment is the growth rate of labor productivity. Which is output per capita and then n represents the growth rate of labor. So this formula should also be easy to remember now the third formula looks a little complicated. But it s not too bad.

What we have here is the output per unit of capital for this relationship. We start out with the growth rate of output. So theta. Over 1 minus alpha plus n.

So we just reuse this expression. And then we add..

The depreciation rate. This is the overall depreciation of equipment in an economy. So we add the depreciation rate and then multiply this whole expression by 1 divided by s s. Is the savings rate.

So i would recommend that you simply memorize this formula. There is a low chance that you will be tested on this particular formula. But in any case to be safe you should learn the formula now let s move on to the implications of the neoclassical model and you need to learn everything on this slide. The first implication is that capital accumulation impacts the level of output.

But not the growth rate in the long run in other words in the long run. We have a certain growth rate. Which is fixed and capital accumulation will not impact the long run a growing economy. We ll move to a point of steady state growth.

So we might have high growth initially but ultimately we will get to a steady state growth rate which we just talked about and again you need to remember that formula. The steady state growth. Rate is going to be theta. Over 1 minus alpha.

Plus. The growth rate of the labor force. So you must remember this formula. The next.

Implication is that in steady state capital. Deepening has no impact on the growth rate or on the marginal product of capital and this goes back to the point that with the cobb douglas function we have diminishing returns. So if we are looking at capital labor. If capital labor is increased eventually the increase in capital labor will cause output labour to go up.

But at a decreasing rate. So we have this diminishing returns concept there might be some rapid growth initially so when countries like china or india. Start with a relatively low amount of capital. Initially as capital labour.

Is added the growth can be rapid. But eventually we will get to steady state increasing the supply of some input such as capital relative to others. Such as labour will lead to diminishing marginal returns. We ve talked about that in the long run the only way to sustain growth in potential gdp per capita is through technology.

The third point has to do with convergence. According to the neoclassical model. There will be a convergence of per capita income in developing and developed countries in other words developing countries will eventually catch up with developed countries. The reason is that we have high marginal productivity of capital in developing countries.

So developing countries are over here initially because the capital to labour ratio is low and at this stage. The marginal productivity of capital is high so at least in the short run. The growth rate of developing countries should. Exceed the growth rates of developed countries.

And that should cause developing countries to catch up with developed countries. Now. This is what the neoclassical model is saying and we ve talked about convergence here at a very basic level later in this lecture. We will talk about convergence in a lot more detail.

The fourth implication of the neoclassical model has to do with the effect of savings on growth. A higher savings or a higher investment rate leads to a temporary increase in growth rate during this transition period. Where we have a temporary increase in growth rate. There is a higher level of per capita output and productivity in steady state.

However. The growth rate does not depend on income saved or invested a higher savings rate. Does lead to a higher per capita output. Higher capital per labor and higher labor productivity.

Now this is not to be confused with what we said earlier earlier. We said that there is a temporary increase in growth rate..

So here we are talking about the economic growth rate. Whereas here we are talking about per capita output capital per labor and productivity. So a higher saving rate will lead to a richer population. But it does not lead to an increase in the growth rate and again.

I emphasize this is what the neoclassical model is saying now i want you to work through example tin with example 11. I warn you that this is fairly complicated if you have the time you can try and work through it. But an easier solution would be to simply watch my video. Where i highlight the key points related to example.

11 in fact. I have videos for all the examples and i would say that if you have time you work through the examples on your own and then also watch the videos to make sure that you get the key concepts that are being communicated in each of these examples. Now let s look at some limitations of the neoclassical model. According to the neoclassical model.

The technology impact is a residual this means that when we talk about the percentage change in output or the economic growth rate. We say that this depends on capital it depends on labor and then the impact of technology is a plug so it s a residual we can figure out the overall change in output. We can figure out the impact of capital and labor and whatever can t be explained using changes in capital and labor are attributed to technology. If we look at the growth of developed countries in the last several decades.

Most of the growth has been attributed to total factor productivity or technology. So we have a model which basically does not really deal with a factor. That is the primary contributor to growth. So that means that there is something missing in the neoclassical model.

Another issue is that according to the neoclassical model steady state growth rate is unrelated to saving and investment rate. However empirical evidence does show a positive correlation between savings rate and growth rate. So. This is another issue.

The third issue is that according to the neoclassical model. If capital stock rises. Faster than labor productivity. Then return on investment will decline.

So we will have diminishing returns. But evidence suggests that for advanced countries. The impact is actually the opposite so rising stock has actually resulted in higher productivity. Given the limitations associated with the neoclassical model efforts have been made to improve the model.

So what economists have tried to do is reduce the portion of growth attributed to total factor productivity. So we ve said that in the model total factor productivity is essentially the residual. What economists have tried to do is extend the model by adding inputs like human capital r. D.

And public infrastructure. So as to reduce the contribution of total factor productivity. But this still does not solve the larger problem. Which is that technology is an exogenous variable.

It is still something that is outside the neoclassical model and therefore we need another model or theory. Where technology plays a more central role this brings us to the endogenous growth theory. Which is actually a series of models. The focus is on explaining technological progress rather than treating it as exogenous and the way.

This is generally done is by including research and development and human capital as factors of production so in the neoclassical model. We have capital and labor. Which are typically the factors of production here with the endogenous growth theory. We are also including r d.

And human capital as factors of production. But we should keep in mind. That there is something different about r. D.

Research and development has high externalities. If a given entity is doing r d..

This. Research and development is going to help the particular entity. But it will also help other organizations and because of this we might have a free rider problem. Where several entities will not do sufficient r.

D. Because they know they can benefit from the r. D. Of other organizations.

And for this reason in advanced countries. A significant amount of r d. Happens. Under the government but in any case.

The larger point is that now research and development essentially technology development is included as part of the model with the endogenous growth theory. Output per worker is proportional to capital per worker. So if we have capital per worker on the x axis and output per worker on the y axis. We have a relationship like this the slope of this line is c.

And we can therefore. Say that output per worker is equal to c. Times capital per worker. Here.

We have a proportional relationship. Which is important because in the neoclassical model. We had diminishing returns. But here there are no diminishing returns with this theory.

The growth rate of output per worker is equal to the growth rate of capital per worker. And that is equal to s. Times. C.

Minus. The depreciation rate. Minus the growth rate of labor. Now s.

Is the saving rate c. Is this ratio over here so c is equal to y over k. It s the output per worker. Divided by capital per worker.

Now there are two major implications of the endogenous growth theory. One is that a higher saving rate will lead to a permanently higher growth rate. And that s clear over here. If we have a high s or if s goes up then this overall expression goes up we don t really have a short term or temporary effect.

When s increases. The entire expression goes up the other key implication. Is that there is no reason. Why incomes of developed and developing countries should converge.

So with this theory. As capital per worker goes up the output per worker also keeps increasing. I now want you to work through example. 12.

Which highlights the difference between the neoclassical theory and the endogenous growth theory. ” ..

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