Demand Set
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A Demand Set is a model of the most-preferred bundle of goods an agent can afford. The set is a function of the preference relation for this agent, the prices of goods, and the agent's endowment.
Assuming the agent cannot have a negative quantity of any good, the demand set can be characterized this way:
Define L as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space R + l; that is, the space of nonnegative real vectors of dimension L.
Define > p as a weak preference relation over goods; that is, x > px' states that the allocation vector x is weakly preferred to x'.
Let e be a vector representing the quantities of the agent's endowment of each possible good, and p be a vector of prices for those goods. Let D( > p,p,e) denote the demand set. Then: D(>p,p,e) = {x: px <= pe and x >p x' for all affordable bundles x'.
