Consumer Theory: Consumption Sets

We make decisions every single day and most of these decisions involve spending our money. The study of spending behavior based on preferences and money is called Consumer Theory. Every decision and preference of customers are mathematically modeled to provide an overview of the current economy as well as giving producers/vendors/sellers insight on consumer behavior. The model of consumer choice consists of four main aspects: consumption set, feasible set, preference relation, and behavioral assumption.

Consumption Set are set of items or services bundles conceivable for the consumers (unnecessary affordable) and consumption bundles are described by a vector containing a number of different commodities. For instance, we let 𝑋 represent the consumption set and 𝑥𝑖 ∈ ℝ represent a number of items 𝑖; thus, 𝑥 is a consumption bundle consist of (𝑥1, 𝑥2, … , 𝑥𝑛 ). Moreover, the consumption sets must at least have the following characteristics:

1. Consumption set must be non-negative.

2. Consumption set is a closed set (all limit points are included).

3. Consumption set is convex.

4. Empty Set is part of the consumption set (not buying anything is also an option for consumers)

Feasible set is sets part from consumption plan that are affordable for the consumers and, in general, represented as 𝐵 ⊂ 𝑋. Feasible set aims to capture the achievable alternatives given the economic circumstances of the consumers. Preference relation specifies the characteristics of consumers’ behavior regarding their choices under certain circumstances. In other words, it describes consumers’ limitation to perceive their situations and information regarding their own choices.

Lastly, behavioral assumption defines the principles of how consumers make their final decisions. According to Advanced Microeconomic Theory by Jehle and Reny (2011) regarding behavioral assumption: “the consumer seeks to identify and select an available alternative that is most preferred in the light of his personal tastes.”. This concept of consumption set is considered as one important foundation of describing consumers’ preference relation and its more common term: utility.