Aggregate Long Run Production Functions
Production estimations distinguish between short-run and long-run functions, stating the relationship between inputs, scarce resources, and the outputs that result. Short-run and long-run functions typically refer to the variability of production inputs and have a tenuous association with any real temporal statements of such runs (with the exception that "short-run" will almost occur before "long-run").
Short-run analysis is a production function where one input (usually described as labour) is variable and the other (usually described as capital) is fixed. The application of marginal analysis to short-term production functions indicates that additional units of variable input combined with fixed output will initially significantly increase marginal and average production, slow down at the point of specialisation and, at some point, result in diminishing returns in marginal product and can even result in a fall in production.
In long-run production functions all inputs are assumed to be variable. The firm has enough time to change the amountof all its inputs. As capital and labour increase there are returns to scale which can either be increasing (greater output than the change in labour and capital), constant (equal output gains) or decreasing (less than equal increase to output relative to the change in capital and labour).
(Or, to express as a Cobb-Douglas production function: Q = AL^aK^b, where Q = total quantity of output, L = labour input, K = (k)apital input, a and b are output elasticity and A = total factor productivity)
Now as is well known the number of variables that can be added to a production function are limitless; but the use of L for labour and K for capital inputs are well-established conventions which other variables can be associated with.
My question relates to the question of productivity (a) on an aggregate level and (b) where even long-run production cannot change some inputs, in this case the addition of N (nature) with to use the breakdown of the factors of classical political economy (land (N), labour (L) and capital (K)).
In this case, with one factor constant regardless of the "run", additional contributions to the production function, whether land or capital (or any subcomponent thereof) must eventually reach marginal returns and even cause negative production if too many inputs occur. In other words, production is ultimately governed by the carrying capacity of natural resources.
Can this expansion of the core variables to include economic land (N) be useful in environmental economics? Does it change the way that long run production functions are theoretically established, if only on the aggregate level? Is it now that the case that there is no complete "long run" function, but rather everything is a variety of the short run function?
(As a complete aside this standard, mainstream, economic analysis has an awful lot of Marx in it who described the relationship between 'dead labour' , 'living labour' and tendancy of profit to fall in a similar framework - but with opposite results! Increases in variable capital, instead of being the sole source for the generation of surplus value, actually become a negative to both production and profit.)
Short-run analysis is a production function where one input (usually described as labour) is variable and the other (usually described as capital) is fixed. The application of marginal analysis to short-term production functions indicates that additional units of variable input combined with fixed output will initially significantly increase marginal and average production, slow down at the point of specialisation and, at some point, result in diminishing returns in marginal product and can even result in a fall in production.
In long-run production functions all inputs are assumed to be variable. The firm has enough time to change the amountof all its inputs. As capital and labour increase there are returns to scale which can either be increasing (greater output than the change in labour and capital), constant (equal output gains) or decreasing (less than equal increase to output relative to the change in capital and labour).
(Or, to express as a Cobb-Douglas production function: Q = AL^aK^b, where Q = total quantity of output, L = labour input, K = (k)apital input, a and b are output elasticity and A = total factor productivity)
Now as is well known the number of variables that can be added to a production function are limitless; but the use of L for labour and K for capital inputs are well-established conventions which other variables can be associated with.
My question relates to the question of productivity (a) on an aggregate level and (b) where even long-run production cannot change some inputs, in this case the addition of N (nature) with to use the breakdown of the factors of classical political economy (land (N), labour (L) and capital (K)).
In this case, with one factor constant regardless of the "run", additional contributions to the production function, whether land or capital (or any subcomponent thereof) must eventually reach marginal returns and even cause negative production if too many inputs occur. In other words, production is ultimately governed by the carrying capacity of natural resources.
Can this expansion of the core variables to include economic land (N) be useful in environmental economics? Does it change the way that long run production functions are theoretically established, if only on the aggregate level? Is it now that the case that there is no complete "long run" function, but rather everything is a variety of the short run function?
(As a complete aside this standard, mainstream, economic analysis has an awful lot of Marx in it who described the relationship between 'dead labour' , 'living labour' and tendancy of profit to fall in a similar framework - but with opposite results! Increases in variable capital, instead of being the sole source for the generation of surplus value, actually become a negative to both production and profit.)