Introduction
Consumer equilibrium represents a state of maximum satisfaction for a consumer, given their budget constraint. This equilibrium is achieved when the consumer allocates their income in a way that yields the highest possible utility. Indifference curve analysis is a powerful tool used to visualize and analyze these consumer choices. This essay will examine the effects of changes in relative prices on consumer equilibrium, utilizing indifference curve analysis to illustrate the key concepts involved.

The Mechanics of Price Changes and Consumer Equilibrium
A change in the relative price of one good, while holding all other factors constant, leads to a shift in the budget line. Consider the following example: Suppose a consumer consumes two goods, X and Y, and the price of good X increases. This increase in price will cause the budget line to pivot inward, becoming steeper as illustrated in Figure 1. The intercepts of the budget line will change, reflecting the reduced purchasing power of the consumer for good X.


<figure>
<img src="https://i.imgur.com/1VqY01W.png" alt="Budget Line Shift" width="500">
<figcaption>Figure 1: Budget Line Shift after Price Increase of Good X</figcaption>
</figure>


This shift of the budget line triggers two distinct effects: the substitution effect and the income effect. The substitution effect captures the change in consumption of good X due solely to the change in its relative price. As good X becomes relatively more expensive, consumers are encouraged to substitute towards good Y, which is now relatively cheaper. This substitution effect is represented by a movement along the initial indifference curve, as shown in Figure 2.


<figure>
<img src="https://i.imgur.com/7cV8Y12.png" alt="Substitution Effect" width="500">
<figcaption>Figure 2: Substitution Effect</figcaption>
</figure>


The income effect, on the other hand, reflects the impact of the price change on the consumer's real income. A price increase effectively reduces the consumer's purchasing power, similar to a decline in income. This can lead to a shift in the indifference curve, reflecting a change in the level of utility the consumer can attain. The direction of the income effect depends on the nature of the good. For a normal good, an increase in price leads to a decrease in consumption of that good. However, for an inferior good, an increase in price might lead to an increase in consumption, as the consumer substitutes towards the cheaper alternative.


<figure>
<img src="https://i.imgur.com/2Q3L518.png" alt="Income Effect for Normal Good" width="500">
<figcaption>Figure 3: Income Effect for Normal Good</figcaption>
</figure>


<figure>
<img src="https://i.imgur.com/7b7E4sN.png" alt="Income Effect for Inferior Good" width="500">
<figcaption>Figure 4: Income Effect for Inferior Good</figcaption>
</figure>


Combining Substitution and Income Effects
The combined effect of the substitution and income effects determines the overall impact of the price change on consumer equilibrium. The substitution effect always encourages a decrease in consumption of the good whose price has increased. However, the income effect can either reinforce or counteract this substitution effect. For example, if the good is normal, the income effect will also decrease consumption, leading to a larger overall decrease in consumption. However, if the good is inferior, the income effect will increase consumption, potentially offsetting the substitution effect and leading to a smaller overall decrease in consumption or even an increase.

Consider Figure 5, which illustrates the combined effects. The initial equilibrium is at point A. After the price increase of good X, the budget line pivots inward, leading to a new equilibrium at point B. The movement from point A to point B represents the combined effect of the substitution and income effects.


<figure>
<img src="https://i.imgur.com/8520X5L.png" alt="Combined Effect" width="500">
<figcaption>Figure 5: Combined Effect of Substitution and Income Effects</figcaption>
</figure>


The relative magnitudes of the substitution and income effects determine the overall change in consumption. If the substitution effect outweighs the income effect, the consumption of the good whose price increased will decline. Conversely, if the income effect is strong enough to offset the substitution effect, consumption of the good might actually increase or decrease only slightly.


Conclusion
Changes in relative prices significantly impact consumer equilibrium. These changes alter the budget constraint, leading to both substitution and income effects. The substitution effect encourages consumers to shift towards relatively cheaper goods, while the income effect reflects the change in purchasing power due to the price change. Understanding the interplay of these effects is crucial for comprehending consumer behavior and for guiding policy decisions related to taxation and subsidies on specific goods.


Sources:

Mankiw, N. Gregory. Principles of Economics. 8th ed., Cengage Learning, 2021.
Perloff, Jeffrey M. Microeconomics. 9th ed., Pearson Education, 2021.
Varian, Hal R. Intermediate Microeconomics: A Modern Approach. 9th ed., W. W. Norton & Company, 2014.