SummaryIn this first LP on production, we examine the decisions that lead to optimal levels of production. This is crucial, as it mirrors the same decisions that we saw consumers making: assigning our limited (and expensive!) resources in the best way possible in order to maintain optimal levels of production.
Production maximisation must be seen as an optimisation problem regarding the production function, represented by isoquants, and a constraint regarding production costs, represented by an isocost line.
Producers are therefore faced with the following problem: faced with a set of possible production levels and a fixed budget, how to choose the level which maximises their production?
If we know the production function of a certain producer, and we know their budget, we have the two restrictions necessary to maximise their production. This can be done graphically, with the point where isocost and isoquant meet defining an optimum, as shown in the adjacent figure.
It can be also done mathematically, through a Lagrangian, where the first derivatives determine a system of equations that can be resolved by submitting our production function to the restriction presented by the budget:
Video – Production maximisation: