This video explains how cost minimisation works when dealing with production, both from the analytical and graphical points of view. We start analysing cost minimisation as the optimisation problem it is, followed by a graphical analysis of the optimum point of production.
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 (usually simplified by using 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.
Learn more by reading the dictionary entry.