The Law Of Substitution (With Diagram)

GP Chudal
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Understanding the Law of Substitution

The Law of Substitution, also known as the second law of Gossen, is a fundamental economic principle that deals with the relationship between the satisfaction derived from the consumption of various goods and the allocation of resources to achieve maximum satisfaction. This law is also known as the law of equi-marginal utility, the law of maximum satisfaction, the law of apathy, or the proportionate rule.


According to the Law of Substitution, when a consumer seeks to maximize total satisfaction, the marginal utility of one good divided by its price must equal the marginal utility of another good divided by its price. This means that a rational consumer will allocate resources so that the last dollar spent on each good produces the same marginal utility.


In the mid-nineteenth century, H.H. Gossen, a German economist, proposed this law. Professor Alfred Marshall, a well-known British economist, refined and gave it its current form. The Law of Substitution, according to Marshall, is one of the most important economic principles and a critical tool for understanding consumer behavior.


According to the law of substitution, when a consumer seeks to maximize total satisfaction, the marginal utility of one good divided by its price must equal the marginal utility of another good divided by its price. This means that a rational consumer will allocate resources so that the last dollar spent on each good results in the same marginal utility, resulting in maximum satisfaction.


The Law of Substitution can be stated algebraically as follows:

MUx / Px = MUy / Py = MUm

Where,

MUx is the marginal utility of good X,

Px is the price of good X,

MUy is the marginal utility of good Y

Py is the price of good Y, and

MUm is the marginal utility of Money.


This equation states that the consumer will allocate their resources between the two goods such that the marginal utility per dollar spent is equal for both goods.


In the case of multiple goods, the Law of Substitution can be stated algebraically as follows:

MU1 / P1 = MU2 / P2 = … = MUn / Pn = MUm


Where,

MU1 is the marginal utility of good 1,

P1 is the price of good 1,

MU2 is the marginal utility of good 2,

P2 is the price of good 2, and so on, up to MUn and Pn for the nth good.

MUm is the marginal utility of Money.


This equation states that the consumer will allocate their resources among all goods such that the marginal utility per dollar spent is equal for all goods.


The Law of Substitution is also known as the Law of Equi-marginal Utility because it involves balancing the marginal utility of one good with the marginal utility of another. The term “equi-marginal” means “equal marginal,” emphasizing the significance of balancing the marginal utility of various goods.


The Law of Maximum Satisfaction refers to the fact that the Law of Substitution is concerned with maximizing the satisfaction or utility that a consumer can derive from the consumption of goods. The consumer can achieve maximum satisfaction by allocating resources in a way that maximizes total utility.


The Law of Apathy is another name for the Law of Substitution. However, the Law of Substitution is not commonly referred to by this name. In some cases, however, it describes the idea that consumers are apathetic to certain goods if they provide the same level of satisfaction as other goods. This means that if two goods provide the same level of utility, consumers may substitute one for the other.


Similarly, the law of substitution is known as the Proportionate Rule because it emphasizes the importance of allocating resources in a proportionate manner. This means that the last dollar spent on each good should produce the same marginal utility, resulting in a proportionate allocation of resources among various goods.


Assumptions of the Law of Substitution

The law of substitution is based on the following assumptions:

  1. Rationality: According to the Law of Substitution, consumers are rational and seek to maximize their total satisfaction or utility. This means that consumers will make decisions based on their preferences and will always try to allocate their resources in such a way that their satisfaction is maximized.
  2. Fixed Income: Consumers have a fixed income, which means they have a limited amount of money to spend on goods and services, according to the Law of Substitution. This assumption is required because consumers must choose how to allocate their limited resources among various goods.
  3. Prices remain constant: The Law of Substitution assumes that the prices of goods remain constant. This assumption is necessary because if the prices of goods change, the marginal utility of each good changes, making the application of the law difficult.
  4. Applicability of the Law of Diminishing Marginal Utility: The Law of Substitution assumes that as a consumer consumes more of a good, the marginal utility of each additional unit of that good will eventually decrease. This is due to the fact that the consumer will eventually become satiated with the product, and the additional units will provide less and less utility.
  5. Interchangeability of goods: Goods interchangeability is assumed by the Law of Substitution, which means that the consumer can substitute one good for another to achieve the same level of satisfaction. This assumption is significant because it allows consumers to choose between various goods based on their relative prices and marginal utilities.
  6. Perfect knowledge: The Law of Substitution assumes that consumers have complete knowledge of the prices and qualities of goods. This means that customers are aware of all of their options and can make informed decisions based on their preferences.
  7. Independence of goods: The Law of Substitution presumes that the marginal utility of one good is unaffected by the consumption of another good. This means that the consumer can divide their resources among various goods without having to worry about how the consumption of one good affects the marginal utility of another.

The law of substitution can be explained with the help of the following table and diagram:

Let us assume that a consumer has $40 to spend on commodities X and Y, whose prices are $5 and $10, respectively. The Marginal utilities of both the goods are as follows:

UnitsMUX (in Utils)MUY (in Utils)MUX /PX (in Utils)MUY /PY (in Utils)
15080108
2457097
3406086
4355075
5304064
6253053

For two goods, X and Y, the above table shows the marginal utility and marginal utility per unit of money spent. According to the Law of Substitution, a consumer will allocate resources among various goods so that the marginal utility per unit of money spent is equal for all goods. We assume in this table that the prices of goods X and Y are constant and equal to $5 and $10 per unit, respectively.


The table’s first column represents the various units of goods X and Y that the consumer may consume. The marginal utility of goods X and Y are represented in the second and third columns, respectively. The marginal utility of a good is the additional utility or satisfaction gained by consuming one more unit of the good. For example, if a consumer increases their consumption of good X from one to two units, their marginal utility for good X falls from 50 to 45.


The marginal utility per unit of money spent for goods X and Y is represented in the fourth and fifth columns, respectively. This is calculated by dividing the good’s marginal utility by its price. For example, at the first unit of consumption, good X’s marginal utility is 50 utils, and its price is $5. As a result, the marginal utility per dollar spent on good X is 50/5 = 10 utils per dollar. Similarly, at the first unit of consumption, the marginal utility per unit of money spent for good Y is 80/10 = 8 utils per dollar.


According to the Law of Substitution, the consumer will allocate their resources between goods X and Y so that the marginal utility per dollar spent is equal for both goods. Looking at the table, we can see that the marginal utility per dollar spent for good X is higher (10 utils per dollar) than for good Y at the first unit of consumption (8 utils per dollar). As a result, the consumer will devote more resources to consuming good X until the marginal utility per dollar spent for both goods is equal.


We can see that as we move down the table, the marginal utility per dollar spent on good X decreases while the marginal utility per dollar spent on good Y increases. To determine the consumer’s equilibrium point given the prices and budget constraint, we need to find the combination of units of goods X and Y that maximizes the consumer’s total utility or satisfaction while spending $40.


From the table, we can calculate the marginal utility per dollar spent for both goods X and Y at each unit of consumption. The marginal utility per dollar spent for good X (MUX /PX) decreases from 10 utils/dollar to 5 utils/dollar as the consumer purchases more units of X, while the marginal utility per dollar spent for good Y (MUY /PY) decreases from 8 utils per dollar to 3 utils per dollar as the consumer purchases more units of Y.


Using this information, we can identify the combination of units of X and Y that will give the consumer the maximum satisfaction or total utility while staying within their budget of $40.


One approach is to compare the marginal utility per dollar spent on each good and allocate the budget such that MUX /PX = MUY /PY. This means the consumer should purchase units of X and Y such that the additional satisfaction gained from each good per dollar spent is equal. Using the table, we can see that this occurs in the sixth unit of consumption, where both goods provide 3 utils per dollar spent.


Since the price of X is $5, and the price of Y is $10, the consumer can spend $40 on a combination of X and Y such that:

5X + 10Y = 40


Simplifying the equation, we get the following:

X + 2Y = 8


Using trial and error or substitution, we can find that combining 4 units of X and 2 units of Y satisfies the budget constraint and the condition of equi-marginal utility. Therefore, the consumer will be in equilibrium at 4 units of X and 2 units of Y. This can also be depicted in the following diagram:

law-of-substitution-diagram

The MU curves in the first and second panel show the change in marginal utility per unit of dollar spent on Commodity X and Y, respectively. Because the marginal utility of each good diminishes, these curves slope downward. The graph shows that when a consumer buys four units of Commodity X and two units of Commodity Y, the ratio of MU per unit price of X and Y (i.e. MUx/Px = MUy/Py) equals seven utils. The dotted line represents the equal marginal utility of seven utils derived from the most recently spent unit of dollar on both commodities.

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Exceptions or limitations of the Law of substitution

Unrealistic Assumptions: Several unrealistic assumptions underpin the Law of Substitution, including the assumption of rational behavior, perfect information, homogeneous goods, constant marginal utility, and ceteris paribus. These assumptions may not always hold true in practice, limiting the Law of Substitution’s applicability.


Inability to Take Income Effects into Account: The Law of Substitution focuses on substituting two goods based on their relative prices and marginal utilities. It does not consider the impact of changes in income or prices of other goods on consumer behavior. In other words, the Law of Substitution ignores income effects, which can influence consumer choices.


Ignoring Consumer Preferences: The Law of Substitution assumes that all consumers have the same preferences and will always choose the best combination of goods. However, consumer preferences can vary depending on age, gender, income, culture, and personal preferences. Because the Law of Substitution does not account for individual preferences, it may not accurately predict consumer behavior.


Inability to Account for Dynamic Changes: The Law of Substitution assumes that the marginal utility of each good remains constant as the quantity consumed increases or decreases. The marginal utility of goods, on the other hand, can vary depending on various factors, such as changes in production, technology, and consumer tastes. As a result, in dynamic market environments, the Law of Substitution may not accurately predict consumer behavior.


Imperfect Market Applicability: The Law of Substitution assumes perfect competition and perfect information, which may not be true in imperfect markets. Consumers may not have perfect information in imperfect markets, and producers may have some market power to set prices. In such cases, the Law of Substitution may not apply or need to be modified to account for market imperfections.


Non-monetary Factors Are Ignored: The Law of Substitution focuses solely on monetary aspects of consumer behavior, such as prices and income. It does not consider non-monetary factors such as social norms, cultural influences, and ethical concerns, all of which can influence consumer behavior. As a result, the Law of Substitution may not provide an exhaustive understanding of consumer behavior in all circumstances.


Lack of Universality: The Law of Substitution is based solely on the assumption of two goods. In the real world, however, consumers may choose between multiple goods with varying prices and marginal utilities. In such cases, the Law of Substitution may not be directly applicable, and alternative theories or approaches to analyzing consumer behavior may be required.


Significance or Importance of the Law of Substitution

  1. Helps in decision-making: The Law of Substitution is a useful tool for individuals and businesses in making optimal choices among various goods or services. By comparing the marginal utility per dollar spent for each option, we can determine the most efficient allocation of resources to maximize satisfaction or profits.
  2. Explains consumer behavior: The law of substitution helps to explain how consumers make choices when faced with limited resources and multiple options. Consumers tend to allocate their resources in such a way that they achieve the maximum satisfaction or utility for their spending.
  3. A basis for demand analysis: The Law of Substitution is a crucial concept in economics that underlies demand analysis. It explains how changes in prices or incomes affect the quantity demanded of a good or service and how consumers adjust their consumption patterns in response.
  4. Efficient resource allocation: The Law of Substitution encourages individuals and firms to allocate their resources efficiently. By choosing the combination of goods that provides the most satisfaction per dollar spent, resources are allocated in a way that maximizes overall welfare and utility.
  5. Helps in price determination: The Law of Substitution helps in determining the prices of goods and services. Suppose a good is priced too high relative to its marginal utility. In that case, consumers will substitute it with a similar good that provides a higher marginal utility per dollar spent, leading to a decrease in demand and price.
  6. Useful in production decisions: The Law of Substitution is not only relevant for consumption decisions but also for production decisions. Producers can use the law to determine the most efficient combination of inputs that will produce the maximum output per dollar spent.
  7. Assumption of rationality: The Law of Substitution is based on the assumption of rationality, which assumes that consumers make choices that maximize their satisfaction or utility. This assumption is critical for predicting consumer behavior and the effects of price changes on demand. However, it may not hold true in all cases, as consumers may not always have complete information or may be influenced by other factors such as social norms or peer pressure.

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