Thursday, February 27, 2014

The Production Function

Inputs and Outputs: The Production Function

The central feature of any economy is that economic agents take factor inputs---labor, capital, and raw materials---and convert them into useful products. Not quite alchemy, but useful nonetheless. We call this relation between factor inputs and output a production function. Thus we might write

Y = A F(K,N),

where Y is output (real GNP), K is the stock of physical capital (plant and equipment), and N is labor (the number and hours of people working). The letter A measures what we will call productivity. A higher value of A means that the same inputs lead to more output, as clear a definition of productivity as I can think of. [Despite this, the word productivity is used in many different ways. When you run across it in other contexts, your first order of business is to find out exactly what it means.] For future reference, we'll refer to A sometimes as total factor productivity, to distinguish it from, say, average labor productivity, Y/N.
As we'll see shortly, we owe a lot of the growth in the US economy (and other economies, too) to increases in A. For now, let's think of things that might affect A.

(i) Technological progress can be thought of as increases in A: invention of the diesel engine, the transistor, the microchip, penicillin, and so on.

(ii) The skill level of the labor force is another thing that might be incorporated in A. One of the big differences between rich and poor countries is that the former have better educated and more highly skill workers. For this reason, we would not expect NAFTA (the North American Free Trade Agreement with Mexico and Canada) to result in American wages falling to the level of Mexican wages. (I'm afraid Ross Perot was out to lunch on this one.)

(iii) Oil prices. We've seen that an increase in the price of imported oil may leave us with lower GNP, other things equal, since a greater fraction of gross output goes to oil, less to capital and labor (hence less value-added). We can think of this as a downward movement in A (and, in fact, that's what we see in the data).

(iv) Weather. A drought or extreme cold snap might lead to lower output for given inputs. Droughts aren't a big deal in the US economy, since agriculture is a small part of the economy, but it gives you the idea that lots of things might affect A.

(v) The economic and legal environment might also play a role in aggregate productivity. Most economists think that competitive markets play an important role in allocating resources in an efficient manner, and this kind of thinking is behind many of the changes in the former Soviet Union and Central Europe. Conversely, corruption and red tape are often given much of the credit for India's lethargic performance.