Impact of Price Changes on Budget Lines: An Economic Analysis

In economic theory, the budget line represents all possible combinations of two goods that a person can afford given their income and the prices of these goods. This article will explore how the budget line shifts when the price of one good changes, specifically focusing on the example of goods X and Y with respective prices of $3 and $5, and a budget of $100.

Initial Budget Line Analysis

When the budget line is established for goods X and Y with prices of $3 and $5 respectively and a total budget of $100, the resulting budget line is given by the equation:

3x 5y 100

This equation can be graphed by finding the x and y intercepts:

Setting x to zero and solving for y, we find the y-intercept: y 20 Setting y to zero and solving for x, we find the x-intercept: x 33.33

The initial budget line shows that if the person spends all their budget on good X, they can buy up to approximately 33.33 units of X. Conversely, if they spend all their budget on good Y, they can buy up to 20 units of Y.

Effect of Doubling the Price of Good X

When the price of good X doubles from $3 to $6, the budget line shifts inward. This is because the same budget of $100 can now only buy a smaller quantity of good X. The new budget line equation becomes:

6x 5y 100

To determine the new x-intercept, set y to zero and solve for x:

Setting y to zero, we find the new x-intercept: x 16.67

The y-intercept remains the same at 20, meaning that if the person spends all their budget on good Y, they can still buy 20 units of Y, but the amount they can buy of good X has decreased to about 16.67 units.

Graphical Representation

The table below summarizes the various combinations of goods X and Y that can be purchased with a budget of $100, given the price of good X changing from $3 to $6:

Combination of Goods Quantity of X Quantity of Y $3x 5y 100 30, 2 $3x 5y 100 25, 5 $3x 5y 100 20, 8 $3x 5y 100 15, 11 $3x 5y 100 10, 14 $3x 5y 100 5, 17 $6x 5y 100 16.67, 15.33

Mathematical Representation and Equations

The initial budget line can be expressed in slope-intercept form as:

y -frac{3}{5}x 20

When the price of good X doubles, the new budget line is:

y -frac{6}{5}x 20

Graphically, the line is steeper, reflecting the higher price of good X.

Conclusion

The example of doubling the price of good X from $3 to $6 demonstrates how changes in prices affect the budget line and, consequently, the possible combinations of goods that can be purchased with a given budget. This analysis is fundamental in understanding price elasticity, budget constraints, and consumer behavior in economics.