Optimal Consumer Choice

The optimal consumer choice occurs when the marginal rate of substitution equals the price ratio of the goods, while adhering to the consumer’s budget constraint. In a Cartesian diagram, this is illustrated at the point where the indifference curve (reflecting the consumer's preferences) is tangent to the budget constraint line. The graphical representation is shown below:

Following the principle of rationality, consumers aim to maximize their utility by reaching the highest possible indifference curve. In the example above, indifference curve C lies beyond the consumer's feasible consumption possibilities, making it unattainable. Meanwhile, curves A and B are within reach, with curve B being the highest achievable curve, and thus the optimal choice.

MRS_x1,x2 = P_x1/P_x2

Mathematically, the tangency between the indifference curve and the budget line implies that they have the same slope at the point of optimal choice. The slope of the budget line is defined by the price ratio of the goods, -p₂/p₁. Since prices are set by the market, this ratio represents the rate at which the market trades the two goods. In contrast, the slope along the indifference curve changes from point to point and is given by dx₁/dx₂ = - U'₂/U'₁. This rate reflects how willing the consumer is to trade one good for another and is known as the marginal rate of substitution (MRS). Analytically, the optimal consumer choice can be described by a system of two equations: one defines the optimal condition, while the other establishes the budget constraint.

Corner Solutions. In certain scenarios, the optimal choice does not occur at the point of tangency between the indifference curve and the budget line. Instead, the consumer's choice may fall on one of the two intercepts of the budget line.

The theory of optimal choice rests on somewhat unrealistic assumptions, such as perfect information and complete consumer rationality (perfect rationality). In reality, consumers often lack the information needed to fully assess a product’s quality or price. Moreover, their decisions may follow imperfect logic (imperfect rationality) or, as behavioral economics suggests, may even be entirely irrational.