[MUSIC PLAYING] An important economic concept relevant to agriculture is the idea of a production function. So a production function is the relationship between the level of an input that's used and the level of the output that's generated. So an example in agriculture is the relationship between the level of a fertilizer that's used and the yield of a crop that's generated. So in this diagram, you can see a typical shape, a common shape for such a relationship. On the bottom axis, we've got the level of nitrogen fertilizer applied to the crop, and on the vertical axis, we've got the wheat yield. And that's a very classic shape for a production function. It increases up to a certain level and then flattens off. But production functions can also be different shapes. Here's one where it increases for a while, flattens off, and then eventually decreases. That can also be realistic for a crop's yield response to different fertilizer levels. So for example, in a non-irrigated farming system, if a farmer applies a lot of nitrogen fertilizer, and then towards the end of the season, there's no rain, it's very dry, then applying excessive amount of fertilizer can actually, in some circumstances, reduce yields. So as I said, production functions describe the relationship between inputs, which in mathematical terms are often denoted by x, and outputs, or y. And so a simple mathematical term, we'd have y is a function of x. Now, there are a variety of different agricultural inputs, each of which would have its own production function. So there'd be a production function for the relationship between water application and crop yield, between pesticide application and crop yield, between the level of feed supply and livestock production, and between the level, as we said, of fertilizer application and crop yield. Now one very common, almost ubiquitous, characteristic that productions functions have is that they usually almost always have diminishing marginal returns. Now, a diminishing marginal returns production function means that the level of output increases, but it increases at a decreasing rate. In other words, it flattens out, or it could even start to tilt downward eventually. So that means that as you apply more and more of an input, you get less bang for your buck. And at some point, you can reach the point where it's not worth applying more of the input, even if it would actually increase yields. Because the cost of that input is higher than the benefit of the additional yield that you would get. So economists recognize that usually the optimal level of an input isn't at the very highest level of output that's possible. Because for the last bit of inputs that you've applied, the rate of increase of output wasn't that high. It wasn't high enough to justify it. So economists are interested in the shape of the production function, because it determines the optimal level of inputs, so the level of input that results in the maximum profit. And it can also influence the riskiness of production. So we'll talk about those issues more in a later segment. So to summarize this segment, production functions describe the relationships between inputs and outputs of the production process. Production functions can take different shapes, and they usually, almost always, have diminishing marginal returns.