#### Summary

This Learning Path is a bit more of a mixed bag than the previous one, finishing off our consumer choice problem, looking at the some useful implications of this in demand theory before moving on to other types of demand theories.There are two ways to solve a consumer’s choice problem. That is, we can either fix a *budget* and obtain the *maximum utility* from it (primal demand) or set a level of *utility* we want to achieve and *minimise cost* (dual demand).

The way to solve either problem is very similar: we look for the Lagrangian function and obtain first order conditions, then solve the system.

When dealing with primal demand, that is, utility maximisation, our Langrangian is as follows:
Subj. to: That is, our Lagrangian is our utility function, which depends on x |

When dealing with dual demand, that is, cost minimisation, our Lagrangian system is as follows:
Subj. to: So that: |

**Video – Consumption duality:**