A budget set represents all possible combinations of goods and services that a consumer can purchase given their income and the prices of those goods. It is constrained by the budget line, which shows the boundary of feasible spending based on income and commodity prices.

When a consumer’s income or the prices of goods change, their budget set may also change. These shifts impact the consumer’s purchasing options, which in turn affects their decision-making process.

What is a Budget Set?

The budget set, also known as a set of opportunities, includes all the feasible bundles of goods that a consumer can afford. Mathematically, it’s defined by the equation of the budget line, which is given by:

Graphically, the budget line forms the upper limit of the budget set, while all points on and below the line represent combinations the consumer can afford.

Factors That Cause Changes in the Budget Set

The budget set is subject to change when there is an adjustment in:

1. Income of the Consumer:

   • If the consumer’s income increases from NNN to N′N’N′, while prices remain constant, the consumer can now afford more goods. This change shifts the budget line outward, expanding the budget set.
   • Conversely, if income decreases, the budget line shifts inward, reducing the number of affordable bundles.

2. Prices of Goods:

   • Decrease in Price of One Good: Suppose the price of one good falls while the income and the price of the other good remain constant. This change will cause the budget line to rotate outward from the axis of the unaffected good, increasing the number of bundles the consumer can purchase.
   • Increase in Price of One Good: If the price of one good rises, the budget line will rotate inward toward the axis of the affected good, reducing the budget set.

Example: Impact of Income Change on the Budget Set

Consider a consumer with initial income NNN, who can buy two goods priced at p1p_1p1 and p2p_2p2. If the income changes to N′N’N′, the equation of the new budget line is as follows:

Notice that the slope of this new budget line, , is the same as the slope of the previous line, indicating that only the purchasing power has changed, not the rate of trade-off between the two goods. This expanded budget line reflects the increase in income, providing access to a broader range of affordable bundles.

Visualizing Changes in the Budget Set

In a graph, the budget set includes all points on or below the budget line. When the budget line shifts due to a change in income or prices, the budget set either expands or contracts. Here’s how the shifts appear:

• Outward Shift: Reflects an increase in purchasing power, either from a higher income or a decrease in prices.
• Inward Shift: Reflects a decrease in purchasing power, either from a reduced income or an increase in prices.

Conclusion

The budget set is an essential concept in economics that highlights the limitations on consumer choices due to income and price constraints. Changes in income or prices directly affect the budget set, influencing the range of options available to consumers and, ultimately, their purchasing decisions.

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