# How private Households maximize Utility

Did you understand how private households maximize utility in your microeconomics lecture or tutorial? Here is a revisit of the household maximization problem described in many microeconomic and economics textbooks. But with a clear outline of a better understanding of how households set goals, their opportunity cost optimization process, and the interpretation of outcomes.

## Two areas of a decision within a private household

The private household is the smallest unit of decision-making in an economy. The key concept you want to understand is how consumers reach their optimal consumption decision. There are two areas of decision-making within a private household, and these are as follows:

• Which bundle of goods does the household prefer over another? Using utility functions and indifference curves, we capture the resulting preferences of the individuals. The utility describes the satisfaction that the goods contribute to a household on an ordinal or cardinal scale.
•  Which resources can the household spend and how? The budget restriction limits the choice of bundles of goods that a private individual can afford.

Any decision-making problem you want to resolve will rotate around these two general questions.

## Household Maximization Problem

In a utility maximization problem, the first question will be the goal, and the latter will be your restriction. But why? In a maximization problem, you will prefer to increase the utility if your resources are limited.

## Household Minimization Problem

If your optimization problem is an expenditure minimization problem, you will take the second question as the goal, while the former will be your restriction. The reason is simple. In such a care, your maximum attainable utility is a fixed level of utility, but the expenditure is your choice.

## Indifference Curve and the Marginal Rate of Substitution (MRS)

An indifference curve demarcates all bundles of goods that contribute the same level of utility to the household. On the other hand, the Marginal Rate of Substitution (MRS) describes the slope of the indifference curve. MRS is, therefore, the measure of opportunity costs of choosing a bundle of goods over all other alternatives. The MRS influences which bundle of goods the household will prefer over another (the first area of decision-making).

## Budget Restriction and the relative Prices of Goods

The budget restriction demarcates all bundles of goods that are affordable to the household. To construct the budget restriction, you will need the market prices of the goods in the bundle. You will then compare the value of all goods with the income level of the household. You will only consider those bundles of goods that incur costs lower or equivalent to income level (affordable bundles of goods). Lastly, among those achievable bundles of goods, some efficient bundles utilize the whole income of the household.

So why have we described the budget restriction in such detail? Because we want to tap into the second area of decision-making. To reach our second goal, we have to explain the role of the slope of the budget restriction. The second area of decision-making relies on the steepness of the budget restriction, which we measure using the relative price of goods.

## How private households maximize utility and miminize expenditure.

Both the utility maximization problem and expenditure minimization problem will lead to the same outcome. The outcome is that the household must choose an optimal bundle among the affordable bundles in a utility maximization problem. That is the bundle that keeps the cost constant. In an expenditure minimization problem, they will select the optimal bundle among the preferred bundle of goods. That is the bundle of goods that keeps the utility constant. In either case, the outcome is that the chosen bundles have to fulfill an optimality condition.

The optimality condition connects both areas of decision-making by setting the Marginal Rate of Substitution equal to the relative price of goods. This statement reveals the concept of opportunity costs in economics and is the most fundamental statement for all economic decisions. In mathematical terms, the slope of the indifference curve should be equivalent to the marginal change (slope) of the budget restriction. In terms of economics, the narrative means that the opportunity costs of choosing a bundle (MRT) should be equivalent to the relative prices of goods in the markets (cost of buying or selling the goods in the market). That is how private households maximize utility.

## Literature

Varian, H. R. (2016). Grundzüge der Mikroökonomik (9., aktualisierte und erweiterte Auflage). De Gruyter Oldenbourg. Cite
Pindyck, R. S., & Rubinfeld, D. L. (2018). Mikroökonomie (9., aktualisierte Auflage). Pearson. Cite
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