**Description**

This video shows how useful a good understanding of consumption duality can be. Starting with utility maximisation and cost minimisation, this video explores everything you need to understand about consumer theory. We also explain formulas such as Roy’s identity or the Hotelling/Shephard lemma.

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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 our utility function. The first order conditions (which we obtain from the first derivatives) give us Marshallian demand curves.

When dealing with dual demand, that is, cost minimisation, our Lagrangian system is our cost function. The first order conditions give us Hicksian demand curves.

Learn more by reading the dictionary entry.

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