factors of production (and their relative contribution)

Question

I am reading mankiw's intermediate economics text. what i find is that when he writes a production function for how much will be produced in an economy. he says it is dependent upon quantity of inputs (capital, labour) and technology (defined by the production function itself).

Now my question why he ignored raw materials, energy and land? When you need to produce more cars. you will need more energy, more raw material (steel or whatever) and more land (after a certain threshold).

Secondly, the idea of technology is kind of tricky. Like usually technology does not hang in thin air. It is usually embedded in the capital itself. pentium 3 as compared to pentium 4 computer, for instance. Also labour. every hour of labour is not equal. Highly skilled labor may be more productive.

So, how do you actually go about disentangling what is the contribution of "technology", capital and labour to output, in a real world data. Like some growth accounting exercises do. It may be very hard to say what is capital and what is technology. every dollar of investment in capital is not same, and it is not independent of technology.

Answer 1

People aren't ignoring things like raw material, energy, and land, they're abstracting them. They're saying, "We don't want to keep track of each of these separately, so we'll say that for our purposes, as an input to production, they're all really the same thing: capital." Whether that level of abstraction is appropriate for a specific problem can be questioned, and it is, and people come up with other models that refine the abstraction. For an example of this, which goes to your second question, rather than shovel all "technology" into either the production function itself or an investment which is reflected in capital, you can claim there is "labor augmenting technology", and that appears as a coefficient of the labor input- instead of y = f(K, L), you have y = f(K, AL).

When you talk about "disentangling" the parts of a production function, you have to be careful not to put something back into the problem that wasn't there when the abstraction was made, otherwise, you've changed your problem. To take your Pentium example, if you've made a model that includes a labor augmenting coefficient, you might want to put it there, otherwise, you might want to put that in capital, as an investment the firm has made. Although the production function represents "technology", the worker is still using the same basic production process, so it doesn't seem to belong there. But what you can't do is put it directly in labor, if you haven't allowed labor to be directly affected by technology.

The point is, however you claim it affects output, you have to make sure the abstractions you've made support it as an input.