This video explains how cost minimisation works, 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 consumption.
Cost minimisation is a way of solving the optimisation problem regarding the utility function and the budget constraint, even though the most common way of doing this is by means of utility maximisation.
If we think about it, we don’t normally have a fixed budget for most purchases. We have a certain utility we expect to derive from them and we hope to spend as little as possible on them (but we don’t have a maximum budget).
In this case, it is utility that is fixed as a restriction, and cost that we can play around with. It’s like solving the consumer’s choice problem in a mirror image way to utility maximisation, and is associated with Hicksian demand curves.
The way we resolve this minimisation problem is very similar to utility maximisation, and is also done with a Lagrangian system, since there is a duality in consumption.
Learn more by reading the dictionary entry.