Gossens 2nd law

What Is Gossen's Second Law?

Gossen's Second Law, also known as the Law of Equi-Marginal Utility, is a fundamental principle in microeconomics that describes how consumers allocate their limited income across various goods and services to achieve maximum total utility maximization. This law asserts that to maximize satisfaction, a consumer will distribute their spending so that the last unit of currency spent on each good or service yields the same level of satisfaction or marginal utility. It is a core component of consumer behavior theory, explaining how individuals make optimal choices given their budget constraint.⁴⁰

History and Origin

Gossen's Second Law is named after Hermann Heinrich Gossen (1810–1858), a German economist who is recognized for developing a comprehensive theory of marginal utility. His seminal work, Entwickelung der Gesetze des menschlichen Verkehrs und der daraus fließenden Regeln für menschliches Handeln (The Development of the Laws of Human Intercourse and the Rules of Human Action Derived Therefrom), published in 1854, laid the groundwork for this principle. Although his ideas were revolutionary at the time, Gossen's work received little recognition during his lifetime and he died a disappointed man. His³⁹ contributions were largely overlooked until the late 1870s when prominent economists such as William Stanley Jevons, Carl Menger, and Léon Walras independently developed similar marginalist theories and subsequently recognized Gossen's pioneering insights.

³⁸Key Takeaways

• Gossen's Second Law explains how consumers optimize their spending to achieve the highest possible satisfaction.
• It posits that total utility is maximized when the marginal utility per unit of currency spent is equal across all goods.
• The law is often referred to as the Law of Equi-Marginal Utility or the Law of Substitution.
• ³⁷It assumes that consumers are rational economic individuals aiming for maximum satisfaction from their limited resources.
• ³⁶This principle is a foundational concept in rational choice theory and resource allocation.

Formula and Calculation

Gossen's Second Law can be formally expressed using a mathematical formula. For a consumer to achieve maximum utility from a bundle of goods, the ratio of the marginal utility of each good to its price must be equal for all goods consumed.

Consider two goods, A and B, with marginal utilities (MU_A) and (MU_B), and prices (P_A) and (P_B), respectively. The law states:

where:

• (MU_A, MU_B, \dots, MU_n) represent the marginal utilities derived from consuming the last unit of goods A, B, ..., n.
• (P_A, P_B, \dots, P_n) represent the prices of goods A, B, ..., n.

This equation signifies that the satisfaction gained from the last dollar (or unit of currency) spent on any good is the same as the satisfaction gained from the last dollar spent on any other good. If this condition is not met, the consumer could reallocate spending to increase total satisfaction.

Interpreting Gossen's Second Law

Interpreting Gossen's Second Law involves understanding that consumers continuously adjust their spending until they reach a point of economic equilibrium. If, for instance, the marginal utility per dollar spent on good X is higher than for good Y, a rational consumer would shift some spending from Y to X. This reallocation would increase total utility until the ratios of marginal utility to price become equal for both goods. This implies that consumers are always striving to get the most "bang for their buck" across all purchases. The concept underscores the idea that individuals seek to balance the satisfaction gained from various products against their respective costs, reflecting a core aspect of scarcity in economics.

Hypothetical Example

Imagine Sarah has a budget of $50 to spend on two items: coffee and pastries. Each cup of coffee costs $5, and each pastry costs $2. Sarah wants to maximize her satisfaction.

Let's assume the marginal utility (MU) Sarah gets from coffee and pastries changes as she consumes more:

Sarah starts by comparing the MU/Price for each item.
Initially, both the first coffee and first pastry yield a MU/Price of 4.
If she buys a second coffee, MU/Price drops to 3. If she buys a second pastry, MU/Price drops to 3.
Sarah will continue to allocate her $50. She'll buy quantities where the marginal utility per dollar is equal. In this simplified example, if she buys 2 coffees ($10 spent, total MU/P for coffee is 3 for the second unit) and 2 pastries ($4 spent, total MU/P for pastry is 3 for the second unit), she's at an equilibrium for those units. She would continue this process until her budget is exhausted, ensuring that the last dollar spent on each good provides the same marginal utility. This continuous adjustment demonstrates the principle of substitution effect in action as she switches consumption based on changing marginal utilities.

Practical Applications

Gossen's Second Law has several practical applications in economics and consumer decision-making. It helps in understanding the formation of a demand curve, as consumers' willingness to pay for additional units of a good declines in accordance with diminishing marginal utility, influencing overall market demand. Busi³⁵nesses can use the principle of marginal utility to inform their pricing strategies, potentially offering discounts for bulk purchases to encourage more consumption even as the marginal utility of additional units decreases. For ³⁴instance, a cell phone company might offer a lower per-gigabyte price for larger data plans, recognizing that the marginal utility of additional data may decrease for a user after a certain point. The ³³law also sheds light on consumer surplus, which is the difference between what consumers are willing to pay for a good and what they actually pay. The concept of marginal utility is also considered in public policy, such as progressive taxation, where the argument is that the marginal utility of money is lower for higher-income individuals.

Limitations and Criticisms

Despite its foundational role in economic theory, Gossen's Second Law, like other marginal utility concepts, faces several limitations and criticisms. A primary challenge is the assumption that utility is quantitatively measurable, often referred to as "cardinal utility." In r³²eality, individuals' satisfaction is subjective and difficult to quantify or compare across different people. Pref³¹erences are not always stable and can change over time, further complicating the measurement of utility.

Ano³⁰ther critique points to the assumption of a "rational economic individual." Human decision-making is often influenced by psychological factors, biases, and market imperfections, leading to deviations from purely rational utility maximization. For ²⁹example, people may not meticulously calculate marginal utility ratios for every purchase but instead rely on habits or simple rules of thumb. The ²⁸law also assumes perfect information about prices and available goods, which is rarely the case in real-world markets. The complexity of modern economies, with numerous goods and services, makes the practical application of precisely equalizing marginal utility per dollar across all expenditures a significant challenge. Mode²⁷rn behavioral economics provides various insights into how actual consumer choices diverge from purely rational models.

²⁶Gossen's Second Law vs. Gossen's First Law

Gossen's Second Law is distinct from, but closely related to, Gossen's First Law, also known as the Law of Diminishing Marginal Utility.

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