Production functions: short and long run

Key Questions

  • Producers need both capital (K) and labor (L) in order to produce the output of "q" quantities.
    In the short run, the producer can only change one input, L. In a graph, you can plot the input L in the lower axis and the quantity (q) in the vertical axis, so you can analyse how production changes when only the labor varies. First, it grows with growing rates, then with diminishing rates until it finally becomes negative.
    In the long run, the producer can vary both L and K inputs. That way, he will seek all possible combinations of L and K that result in the same output, which are is the isoquants . In a graph, you put K in the vertical axis and L in the horizontal axis, like this: graph{10(x^0.5y^0.5)=100 [-10.27, 54.66, -2.25, 30.22]}
    The blue line is the isoquant for 100 quantities of output. Other isoquants can be added to the graph to identify how the inputs react to the increase of q, that is, the returns to scale.