#### Summary

Two things determine profits: income, or turnover (the price at which we sell something) and costs (how much we spent making what we sell). Therefore, knowing how much our costs are going to be is essential when planning the viability of a business.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:**