Modern textbook presentations of production economics, from
Samuelson's innovative Foundations of Economic Analysis to the
present day, treat producers as successful optimizers. They produce
maximum outputs allowable by the technology in place and the
resources at their disposal. They minimize the cost of producing
whatever outputs they choose to produce, given the technology in
place and the input prices they face. Cost-minimizing input demands
are derived from the resulting minimum cost function by means of
Shephard's lemma. They also maximize profit, given the technology
in place and the output and input prices they face. Profit-maximizing
output supplies and input demands are derived from the resulting
profit function by means of Hotelling's lemma.
Conventional econometric practice, beginning with the pioneering
work of Cobb and Douglas, has generally followed this theoretical
paradigm. Thus least squares-based regression techniques are used
to estimate the parameters of production, cost, and profit functions.
In such a framework departures from maximum output, from
minimum cost and cost-minimizing input demands, and from
maximum profit and profit-maximizing output supplies and input
demands, are attributed exclusively to random statistical noise.