A Numerical Derivation of a Demand Function

We can easily verify the complicated behavior of prices seen above, and a basic example of optimal household demand when we observe the barter exchange economy illustrated by an Edgeworth Box Diagram of two commodities, goods {1,2} and two agents.

Fig. 2.6 Demand law

By applying the Lagrangian method^[33] to this, we can reach the solution:

It immediately follows that the demand for any good depends not only on its own price but also the price of alternatives and the initial asset holdings. It seems quite obvious that demand is always affected by price variations as well as the agent’s asset variations. The total differentiation will then give:

2.2.4