Constrained choice occurs when an economic agent must determine the optimal combination of choice variables (given some relationship between combinations of those variables and payoffs) in the face of a constraint limiting the set of feasible combinations for those variables available to the agent. For instance, a consumer seeks to choose the combination within his or her means of consumption goods and services that maximizes welfare. More specifically, if C1 and C2 are the goods for which the consumer must choose the optimal combination, the consumer’s problem is to maximize utility (U(C1,C2)) given a budget constraint: p*C1 + p2*C2 < M, where p1 and p2 are the prices of the two goods and M is the consumer’s overall income or purchasing power.
The concept of constrained choice has been extended both theoretically and empirically to more elaborate settings. It arises naturally when agents must make forward-looking decisions or when agents are uncertain. For instance, life cycle models of saving and consumption focus on the challenge presented to agents who must maximize discounted lifetime utility given the constraints imposed by current and future income, and prices and opportunities to save or borrow. Agents may face uncertainty in terms of future income and prices, as well as the returns to savings. The simple budget constraint posed must then be recast in intertemporal terms in a fashion that reflects the impact of per period saving or borrowing, as well as uncertainty regarding future income flows, returns to saving, and prices. A common way of approaching this is the value function method, which essentially reduces the rather complex intertemporal problem to a series of two-period problems.
The concept of constrained choice has also been extended to other behavioral settings, such as joint decision-making. For example, household bargaining models attempt to capture a household’s members’ efforts to maximize their personal utility from the consumption of goods and services, given a limit to overall household purchasing power. The household bargaining example also speaks to alternative approaches to choice. For instance, much of game theory studies interactive decision-making. This approach focuses on the constraints placed on an agent’s decision-making by other agents’ likely responses to his or her decisions. Thus the agent does not necessarily face a static, internal (to him- or herself) constraint as in the examples previously presented, but other agents’ likely reactions to the agent’s behavior, and their responses’ implications for the agent’s own payoff function, effectively constrain his or her behavior.
