Gossen's 2nd law

What Is Gossen's 2nd Law?

Gossen's 2nd Law, also known as the Law of Equi-Marginal Utility, is a fundamental principle within microeconomics that describes how consumers distribute their limited income among various goods and services to achieve the maximum possible satisfaction or utility. The law posits that a consumer maximizes total utility when the last unit of currency spent on each good or service yields the same level of marginal utility²⁴. This economic principle is central to understanding consumer behavior and efficient resource allocation in a market economy.

History and Origin

Gossen's 2nd Law is attributed to Hermann Heinrich Gossen (1810–1858), a German economist who is recognized for developing a comprehensive theory of marginal utility prior to the "Marginal Revolution" of the 1870s. ²³Gossen's seminal work, Entwickelung der Gesetze des menschlichen Verkehrs, und der daraus fließenden Regeln für menschliches Handeln (Development of the Laws of Human Relations, and the Rules of Human Action Derived Therefrom), was published in 1854.

H²²is book, written in a dense and mathematical style, was initially poorly received and largely ignored during his lifetime, contrasting with the prevailing Historical School of thought in Germany at the time. Go²⁰, ²¹ssen, disappointed by the lack of recognition, even ordered the destruction of unsold copies of his work shortly before his death. It¹⁸, ¹⁹ wasn't until the 1870s, when economists like William Stanley Jevons, Carl Menger, and Léon Walras independently rediscovered similar ideas, that Gossen's contributions were finally acknowledged, largely due to Robert Adamson discovering a copy in the British Museum in 1878.

##¹⁷ Key Takeaways

• Gossen's 2nd Law states that to maximize total utility, consumers will allocate their spending so that the marginal utility per dollar spent is equal across all goods and services.
• It serves as a core principle in understanding rational consumer choice and how individuals make optimal purchasing decisions given their budget constraints.
• The law implies a process of continuous adjustment by consumers, shifting spending from goods with lower marginal utility per dollar to those with higher marginal utility per dollar until equilibrium is reached.
• While foundational, its applicability in real-world scenarios is subject to criticisms regarding the measurability of utility and the assumption of perfect rationality.
• The law extends beyond monetary transactions, applying to the allocation of any scarce resource, such as time.

Formula and Calculation

Gossen's 2nd Law can be formally expressed using the following formula, which illustrates the condition for an economic agent to maximize utility subject to their budget constraints:

$\frac{MU_A}{P_A} = \frac{MU_B}{P_B} = \dots = \frac{MU_N}{P_N}$

Where:

• (MU_A), (MU_B), (MU_N) represent the marginal utility derived from consuming the last unit of good A, good B, and good N, respectively.
• (P_A), (P_B), (P_N) represent the prices of good A, good B, and good N, respectively.

This equation signifies that for total utility to be maximized, the ratio of marginal utility to price must be identical for all goods and services consumed. If this condition is not met, an individual could increase their total satisfaction by reallocating spending from a good with a lower ratio to one with a higher ratio.

Interpreting Gossen's 2nd Law

Gossen's 2nd Law provides a framework for understanding how individuals make optimal choices when faced with scarcity and unlimited wants. In essence, it suggests that consumers are constantly evaluating the "bang for their buck" for every purchasing decision. If a consumer finds that spending an additional dollar on one good provides more satisfaction than spending that same dollar on another good, they will shift their spending until the satisfaction per dollar is equalized across all goods. This optimization process leads to the most efficient use of their available funds, ensuring that no further increase in overall satisfaction can be achieved by reallocating their expenditures. The¹⁶ law implicitly incorporates the concept of opportunity cost, as choosing to spend on one good means foregoing the utility that could have been gained from another.

Hypothetical Example

Consider Sarah, who has a fixed weekly entertainment budget of $50. She enjoys watching movies and reading books.

Following Gossen's 2nd Law, Sarah would aim to equalize the marginal utility per dollar for movies and books.

1. First $10: Sarah buys one movie (MU/P = 8). Remaining budget: $40.
2. Next $5: Sarah considers buying a book (MU/P = 8). She buys the book. Remaining budget: $35.
   • At this point, MU/P for movies (80/10=8) equals MU/P for books (40/5=8).
3. Next $10: Sarah considers buying a second movie (MU/P = 6). She buys the movie. Remaining budget: $25.
4. Next $5: Sarah considers buying a second book (MU/P = 6). She buys the book. Remaining budget: $20.
   • Now, MU/P for the second movie (60/10=6) equals MU/P for the second book (30/5=6).
5. Next $10: Sarah considers a third movie (MU/P = 4). She buys it. Remaining budget: $10.
6. Next $5: Sarah considers a third book (MU/P = 4). She buys it. Remaining budget: $5.
   • MU/P for the third movie (40/10=4) equals MU/P for the third book (20/5=4).
7. Final $5: Sarah can only afford one more item. She sees that a fourth book (MU/P=2) provides the same utility per dollar as if she could afford a fourth movie (MU/P=2). She buys the book. Remaining budget: $0.

Sarah's optimal consumption bundle, maximizing her total utility within her $50 budget, is 3 movies ($30) and 4 books ($20). This step-by-step approach demonstrates how individuals implicitly apply the principles of Gossen's 2nd Law in their financial planning and spending habits.

Practical Applications

Gossen's 2nd Law has broad practical applications in understanding various economic phenomena:

• Consumer Spending Patterns: It explains why consumers adjust their purchasing habits when prices change or their income fluctuates. If the price of one good falls, its marginal utility per dollar rises, encouraging consumers to buy more of it until the ratios are re-equalized across all goods.
• Pricing Strategies: Businesses can use insights from this law to inform their pricing strategies. By understanding how consumers perceive the utility of goods, firms can set prices that align with consumer value, potentially influencing demand elasticity.
• Government Policy and Taxation: Policymakers can consider Gossen's 2nd Law when designing tax policies or welfare programs. Policies that disproportionately affect the marginal utility per dollar of certain goods can alter consumer choices and overall welfare.
• Market Equilibrium: The aggregate behavior of individuals striving to satisfy Gossen's 2nd Law contributes to the overall demand curves in an economy, which, in turn, helps determine market prices and quantities, moving markets towards equilibrium.
• Beyond Consumption: The principle of equalizing marginal benefit per unit of cost extends beyond consumer spending. For instance, in production theory, firms aim to allocate resources among various inputs to equalize the marginal product per dollar spent on each input, thereby minimizing production costs. Sim¹⁵ilarly, individuals allocate time between work and leisure based on the marginal utility derived from each.

##¹⁴ Limitations and Criticisms

While Gossen's 2nd Law provides a foundational theoretical framework, it faces several limitations and criticisms in its real-world applicability:

• Measurability of Utility: One of the primary criticisms is that utility is a subjective and psychological concept that is difficult, if not impossible, to quantify or measure numerically. The¹², ¹³ law assumes cardinal utility (that utility can be measured in specific units like "utils"), which is often not realistic.
• ¹¹ Assumption of Rationality: The law assumes that consumers are perfectly rational and possess complete information, always making decisions to maximize their utility. In ⁹, ¹⁰reality, human behavior is influenced by emotions, cognitive biases, social factors, and incomplete information, leading to deviations from purely rational choices. Thi⁷, ⁸s is a core critique from rational choice theory and behavioral economics.
• ⁶ Constant Marginal Utility of Money: The law often assumes that the marginal utility of money remains constant. However, for many individuals, the value of an additional dollar might increase as their money supply decreases, especially for those with very limited income.
• ⁵ Divisibility of Goods: The law assumes that goods are infinitely divisible, allowing for precise adjustments in consumption to equalize marginal utility per dollar. Many goods are not divisible (e.g., cars, houses), limiting the exact application of the formula.
• Interdependence of Goods: The law typically assumes that the utility derived from one good is independent of others. In reality, goods can be substitutes or complements, meaning the utility of one affects the utility of another. Cri⁴tics like Joan Robinson highlighted how the entire framework of marginal utility theory can collapse if preferences are not stable and independent, making it difficult to discern the cause of behavioral changes.

##³ Gossen's 2nd Law vs. Consumer Equilibrium

Gossen's 2nd Law is, in essence, the condition for achieving consumer equilibrium. The confusion often arises because the terms are closely related, with one describing the state and the other the means to achieve it.

• Gossen's 2nd Law describes the rule or principle that a rational consumer follows to maximize their satisfaction: equalize the marginal utility per unit of currency across all goods and services. It is the underlying mechanism that guides consumer choice.
• Consumer Equilibrium refers to the state where a consumer has allocated their limited income in such a way that they cannot increase their total satisfaction by reallocating their spending. At this point, the condition specified by Gossen's 2nd Law is met, and the consumer is in a state of balance.

Thus, Gossen's 2nd Law provides the necessary condition for a consumer to reach consumer equilibrium, given their preferences, income, and the prices of goods. It builds upon Gossen's First Law, also known as the law of diminishing marginal utility, which states that as a consumer consumes more units of a good, the additional satisfaction derived from each successive unit decreases. The Second Law then extends this concept to multiple goods, explaining how consumers balance these diminishing returns across their entire consumption basket.

FAQs

How does Gossen's 2nd Law relate to everyday spending?

Gossen's 2nd Law suggests that in your daily spending, you implicitly try to get the most satisfaction for every dollar. For example, if you're deciding between buying an extra coffee or a snack, you weigh which purchase would give you more "value" or satisfaction for the money spent at that moment. You adjust your spending until you feel you're getting the most out of your budget across all items you buy.

Can Gossen's 2nd Law be applied to non-monetary decisions?

Yes, the principle of Gossen's 2nd Law can be applied to any decision involving the allocation of scarce resources, not just money. For² instance, you could apply it to how you allocate your time: you try to spend your time on different activities (work, leisure, exercise) in a way that the last unit of time spent on each activity provides you with equal marginal satisfaction.

What happens if the prices of goods change?

If the price of a good changes, the ratio of its marginal utility to its price will also change. According to Gossen's 2nd Law, a rational consumer will then reallocate their spending. For example, if the price of a good decreases, its marginal utility per dollar increases, making it relatively more attractive. The consumer would then buy more of that good and less of others until the new equilibrium of equal marginal utility per dollar is restored across all goods. Thi¹s adjustment reflects the underlying principles of consumer behavior in response to market dynamics.