Utility Maximization

Utility Maximization is a classical concept in economics that refers to making decisions to achieve the highest level of satisfaction, given the constraints of limited resources. The main objective of this model is to help individuals and firms to make decisions that are in their best interest.

Economists use the concept of utility to model and analyze people’s behavior and decision-making. It is a fundamental concept in the study of microeconomics. This theory also describes the relationship between budget constraints and the demand curve. Furthermore, this theory is subjective, varies from person to person, and is difficult to quantify directly.

• Utility maximization refers to a theory on how an individual can rationally allocate income to derive maximum utility or satisfaction.
• To solve this problem of suitable allocation, there are three solutions per the Marshallian demand: substitution, the point of the indifference curve, and the Lagrangian approach.
• However, the irrational behavior of consumers and ordinal utility can reduce the utility derived from it.
• This theory helps individuals and firms to make choices by providing a way to compare the benefits and costs of different options.

Utility Maximization refers to an economic theory determining how an individual achieves maximum satisfaction (utility) by purchasing certain goods and services. Moreover, this theory is an essential concept in many areas of economics, including consumer theory, producer theory, and welfare economics.

The utility maximization theory dates back to the 18th century, around the classical economists. English philosopher Jeremy Bentham and economist John Stuart Mill were the first to contribute to this theory. In contrast, Mill defined that actions in the right proportion will lead to more satisfaction (utility) and reverse will cause worse. Later, in 1890, economist Alfred Marshall FBA used it as a base for the "law of diminishing utility."

However, while defining this theory, Bentham and Mill faced an issue that became a consumer problem. And they named it a utility maximization problem. So, it stated how consumers should spend their money to gain maximum utility. Since the wrong allocation of income could reduce satisfaction, it was necessary to find a solution. Therefore, Marshallian demand was developed. However, it depends on price, budget constraints, and utility.  The solution assumes that a consumer spends her entire budget and preferences are monotone. Others include linear and exogenous costs, completeness, and continuity.

On this basis, three solutions could solve the problem. Let us look at them:

• The consumer can choose a point on the budget line where they achieve the highest utility.
• Hence, they can use the Lagrangian approach to maximize their utility by using the multiplier.
• And lastly, individuals can use the substitution method by managing the budget constraints.

Furthermore, expected utility is based on the idea that individuals or firms make decisions by weighing different options' potential benefits and costs. Hence, once the decision-maker has specified their preferences, they must identify feasible alternatives, subject to their constraints.

Let us look at the rules or assumptions of the utility maximization function to understand the concept better:

• The principle of diminishing marginal utility:  This rule states that as a person consumes more of a good or service, the additional satisfaction derived from each other unit consumed decreases. Therefore, individuals and firms should allocate their resources to maximize their total utility.
• The rule of equal marginal utility per dollar spent: This principle states that the optimal consumption bundle is achieved where the marginal utility per dollar spent on each good or service is equal.
• Optimization theory at the margin: Individuals and firms should adjust their consumption or production decisions. Therefore, this is done by comparing the marginal utility of the next unit of goods or services with its price or revenue.
• Substitution rule: This principle states that individuals and firms should substitute goods and services with lower marginal utility or higher marginal cost with those with higher marginal utility or lower marginal cost.

Let us look at the conditions of the utility maximization function that helps in deriving satisfaction:

Condition #1

The first condition for this utility maximization model is that the consumer must allocate their entire budget to obtain the highest level of satisfaction.

PxX +PyY= M

 Where Px and Py = Prices of goods, respectively

X and Y = Quantities of goods consumed

M = Consumer’s income or budget

Condition #2

The second condition for this model is that consumers must allocate their budget in such a way that the marginal utility per dollar spent on each good or service is equal.

This condition can be represented as:

MUx / Px = MUy /Py

Where Mux and MUy are marginal utilities of goods

Px and Py are the prices of the goods

Let us look at the formula for calculating the utility maximization of a specific product:

Utility Maximization (or Total Utility) = U₁ + MU₂ + MU₃… MU_N

Where

U1 refers to the utility of a product.

MU2 refers to the marginal utility of two units. Likewise, MU3 is the marginal utility for three units, and so on. MU_N is the marginal utility of the "N" unit of consumption.

However, while calculating this utility, the theory assumes that every additional consumption will reduce the marginal utility.

Let us look at the example of this model based on the formula explained above:

Suppose Xavier goes to a food outlet after successfully achieving his diet goals. However, he needed clarification with chocolates and burgers. The price of one burger is $3, and chocolate is $2. So, he used the utility maximization formula to calculate the product that would give more satisfaction.

Schedule #1 (Chocolates)

So, let us use the formula to calculate the marginal utility for chocolates based on the above schedule.

Utility Maximization = U₁ + MU₂ + MU₃… MU_N

                                                = 20 + 10 + 5 + 0 + (-5) + (-10)

                                      = 20

Schedule #2 (Burgers)

Utility Maximization = U₁ + MU₂ + MU₃… MU_N

                                      = 30 + 5 + 0 + (-5) + (-10)

                                      = 20

However, in both cases, Xavier has achieved almost equal utility from both items. Thus, with a budget of $15, he should allocate income in such a way that he can easily buy burgers and chocolates, attain maximum utility, and still save some money in the end.

This article has been a guide to what is Utility Maximization. Here, we explain its rules, example, conditions, calculation, and formula. You may also find some useful articles here -

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