Chapter 2: Problem 9

Explain why individuals make choices that are directly on the budget constraint, rather than inside the budget constraint or outside it.

Short Answer

Expert verified

Individuals make choices directly on the budget constraint because it allows them to achieve the highest level of utility possible given their income and prices. Choosing inside the budget constraint would result in a lower level of utility, while choices outside of it are not feasible due to income limitations. Therefore, rational individuals seek to make choices directly on the budget constraint to maximize their overall happiness.

Step by step solution

Define budget constraint

The budget constraint represents the combination of goods and services that can be purchased with a given income while considering the prices of these items. It can be expressed as: \( I = P_1 X_1 + P_2 X_2 \) Where: - \(I\) is the individual's total income - \(P_1\) is the price of good 1 - \(X_1\) is the quantity of good 1 - \(P_2\) is the price of good 2 - \(X_2\) is the quantity of good 2 By plotting all the combinations of \(X_1\) and \(X_2\) that satisfy this equation, you can obtain the budget constraint line.

Understand the Optimal Choice

When an individual makes a choice, they typically aim to maximize their utility (happiness) subject to the budget constraint. This implies that the individual will allocate their income to different goods and services in such a way that the marginal utility per dollar spent on each good is the same. Suppose an individual has a utility function \(U(X_1, X_2)\) that depends on the quantity of goods consumed. Utility is always increasing or non-decreasing with quantity, meaning that the more you consume, the happier you are: \( \frac{\partial U}{\partial X_1} > 0 \) and \( \frac{\partial U}{\partial X_2} > 0 \)

Choices on the Budget Constraint

When an individual makes choices directly on the budget constraint, that means they spend all their income on purchasing goods. By doing so, they can achieve the highest level of utility possible given their income and prices. In terms of utility maximization, reaching the highest utility point is the optimal choice and must be on the budget constraint line.

Choices Inside the Budget Constraint

Making a choice inside the budget constraint means the individual is not exhausting their income by purchasing goods. This will result in a lower level of utility because some income remains unspent. The individual could re-allocate their income to consume more of one or both goods, increasing their utility while still obeying their budget constraint. Therefore, choices inside the budget constraint are not optimal.

Choices Outside the Budget Constraint

If an individual chooses to consume outside their budget constraint, this implies that they attempt to spend more money than they have, given the prices of goods and services. This choice is not feasible as it cannot be done without violating the budget constraint.

Conclusion

Individuals make choices directly on the budget constraint because it allows them to achieve the highest level of utility possible given their income and prices. Any choices made inside the budget constraint would not maximize their utility, and choices outside of it are not feasible due to income limitations. Therefore, rational individuals seek to make choices directly on the budget constraint to maximize their overall happiness.

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