Production I: Cost minimisation

Summary

In 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 and cost:

Production duality:

Cost minimisation tries to answer the fundamental question of how to select inputs in order to produce a given output at a minimum cost.

A firm’s isocost line shows the cost of hiring factor inputs. This line gives us all possible combinations of inputs (here labour and capital) that can be purchased at a given cost.

Assuming that a certain amount of output wants to be achieved, we have several possible combinations to achieve it, but only one that minimises costs. The isocost line tangent to the isoquant, which represents the amount of output targeted, will reveal the input combination that results in the lowest cost, for that given output.

We can also use the method of Lagrangian systems to analytically solve a constrained minimisation problem. The first derivatives determine a system of equations that can be resolved by submitting our sought output to the restriction presented by the minimisation of costs:

Video – Cost minimisation:

And now, let’s put both of these scenarios together in our last entry in this LP, with production duality.

Cost I: Production maximisation

Production I: Production duality