Production includes any activity, and the provision of any service, which satisfies and is expected to satisfy a want

Production, growth, and elasticities

Take the aggregate production function given above, and see what it implies not just about real GDP, but about how real GDP grows. To do this, use the mathematical tools developed before to take logs and growth rates of that production function.
lnYt=αlnKt+(1−α)lnAt+(1−α)lnLtln⁡��=�ln⁡��+(1−�)ln⁡��+(1−�)ln⁡��
and therefore
gY=αgK+(1−α)gA+(1−α)gL.��=���+(1−�)��+(1−�)��.
This tells us that growth in real GDP depends on growth in capital, growth in productivity, and growth in labor. Not surprising. Notice that the effect of growth in capital, gK��, on growth in real GDP depends on the size of α�. If capital grows at 10%, then real GDP grows at α� times 10%. If α=0.3�=0.3, then real GDP would only grow 3% when capital grows 10%. A similar story holds for productivity and labor and the parameter (1−α)(1−�).
If you recall from earlier economics classes, and elasticity measures the percent change of one thing with respect to the percent change in another. The values α� and 1−α1−� are elasticities. 
Because α+(1−α)=1�+(1−�)=1, the aggregate production function has constant returns to scale with respect to capital and labor.
What does this mean? Think of what happens if both capital and labor grow by 10% (but productivity doesn’t grow at all). Then gY=α10��=�10. Constant returns to scale means that if you scale up both inputs by the same percent, output goes up by that percent as well. This is different than increasing returns to scale, which would imply that output went up by 20%, say, if you increased capital and labor by 10%.
Now why am I ignoring productivity in all this? That’s because productivity is really a different animal than the inputs capital and labor. The guide is going to spend a lot of time talking about why productivity is so different, so hang on to that question for the time being. The quick version is that capital and labor are tangible things that can only be used in one place at one time, but productivity is something less tangible that applies everywhere at once.
Okay, one last thing about these elasticities. I set them up as parameters that appear to be fixed over time. That is, α� doesn’t have a subscript t�, implying that the elasticity of real GDP with respect to capital (and therefore with respect to labor) is the same in 1970, 1980, 1990, … and 2020. Does that make sense?
It does to some degree. The reason is that these elasticities should be roughly equal to the cost shares of their respective inputs. In other words, α=ϕK=RK/(wL+RK)�=��=��/(��+��) and 1−α=ϕL=wL/(wL+RK)1−�=��=��/(��+��). Recall that one of the four facts about a BGP was that labor’s cost share (and hence capital’s) was constant. If those cost shares are constant, then the parameters α� and 1−α1−� are constant.
I’m going to punt the explanation for why elasticities should equal cost shares to a sub-page, as that gets us into the weeds a little. But it will be worth reading through that explanation to understand why I’m not just making this up.
This says that GDP depends on the K/AL�/�� ratio, or capital relative to the size of productivity and labor. This is sometimes called the “capital per efficiency unit of labor” ratio. But we will stick with K/AL�/��.
Why do we use this? It turns out the ratio K/AL�/�� is relatively easy to analyze, and that it will end up becoming stable (e.g. unchanging) in the long-run. Economically, the reason is that capital K� is itself going to be built using GDP, and so it evolves over time based on how big GDP gets. Productivity and labor, AL, are determinants of GDP, and so they help determine the size of the capital stock. The capital stock will have to grow in proportion to productivity and labor because of this, and hence their ratio is relevant to us.
In practice, this form of the production function can be used to write GDP per capita.
yt=(KtAtLt)αAt.��=(������)���.
And using this, we can write the growth rate of GDP per capita using the logs-derivatives method as
gy=α(gK−gA−gL)+gA.��=�(��−��−��)+��.
This is identical to what we have above, just re-arranged a little again. This separates the growth rate of GDP per capita into two parts. The first, α(gK−gA−gL)�(��−��−��), is the growth rate of the K/AL�/�� ratio itself, and depends on how fast capital grows relative to productivity and labor. The second, gA��, is just straight productivity growth. Note that productivity growth has two effects: one on the K/AL�/�� ratio and one directly on GDP per captia. This will turn out to be important when we look at the long-run growth rate.
The last thing to do here is to talk about another way to refer to the K/AL�/�� ratio. Start with the capital-output ratio, K/Y�/�,
KY=KKα(AL)1−α=K1−α(AL)1−α=(KAL)1−α.��=���(��)1−�=�1−�(��)1−�=(���)1−�.
In other words, the capital-output ratio is just the K/AL�/�� ratio raised to a power. The K/AL�/�� ratio and K/Y�/� are basically capturing the same thing, just with some slight variation. What this means is that sometimes we’ll slip in a mention of the capital/output ratio to save some time, rather than writing out or talking about the K/AL�/�� ratio.
Why do we care about the K/Y�/� ratio? It is useful in finding the rate of return on capital, for one.
Economic Growth Economic growth is a long-term expansion of the productive potential of the economy. Growth is not the same as development! Growth can support development but the two are distinct. M. Todaro defines economic development as an increase in living standards, improvement in self-esteem needs and freedom from oppression as well as a greater choice. Economic development is Concerned with structural changes in the economy, but economic growth is concerned only with increase in the economy’s output. Economic growth is a necessary but not sufficient condition of economic development. Economic growth brings quantitative changes in the economy; where as economic development deals with quantitative and qualitative changes in the economy.
Rostow’s Five-Stage Model of Development Rostow's Stages of Growth model is one of the most influential development theories of the twentieth century. In 1960, Rostow presented five steps through which all countries must pass to become developed. Traditional Society: This stage is characterized by a subsistent, agricultural based economy, with intensive labor and low levels of trading, and a population that does not have a scientific perspective on the world and technology. Preconditions to Take-off: In this stage, the rates of investment are getting higher and a society begins to develop manufacturing. Take-off: Rostow describes this stage as a short period of intensive growth, in which industrialization begins to occur, and workers and institutions become concentrated around a new industry. Drive to Maturity: This stage takes place over a long period of time, as standards of living rise, use of technology increases, and the national economy grows and diversifies. Age of High Mass Consumption: Here, a country's economy flourishes in a capitalist system, characterized by mass production and consumerism. Now we look at the processes by which economies grow like living things. Economic growth is “the process whereby the real per capita income of a country increases over a long period of time.” We enumerate the factors which lead to the growth of an economy.
Growth of population, particularly working population, is the first cause of growth. A rapidly growing population in relation to the growth of the national product keeps the output per head at a low level. This has been the case with developing countries like India. On the other hand, the increase in the output per head of developed economies like the United States has been much higher because of their low rates of population growth in relation to the growth rates of their national product.
Technical knowledge and progress are the twin factors in increasing output per head. Technical knowledge and progress are interdependent. It is technical knowledge which brings about new methods of production, leads to inventions, and development of new equipment. Similarly, changes in equipment require new technical knowledge for producing and training personnel in their manufacture and use. Thus for an increase in output per head, an economy requires physical capital in the form of improved capital equipment, and human capital in the form of highly qualified and trained personnel.
The rates of growth of technical knowledge and capital depend on the percentages of national income spent on R & D (research and development), of modern technology, and on imparting general and technical education to the people. One of the principal causes of the high growth rates of developed countries has been the spending of higher percentages of their national income on R & D, and on education.