Introduction
Consumer equilibrium represents a state where a consumer maximizes their utility, or satisfaction, given their income and the prices of goods and services. This equilibrium point is achieved where the consumer's budget constraint intersects with the highest possible indifference curve. The budget constraint illustrates the various combinations of goods a consumer can afford given their income and the prices of the goods. Indifference curves, on the other hand, depict combinations of goods that yield the same level of satisfaction for the consumer, with higher indifference curves representing higher levels of utility.

Impact of Changes in Income
Increased Income
An increase in income has a significant impact on consumer equilibrium by shifting the budget constraint outward. This outward shift allows consumers to purchase more of both goods, as they have more purchasing power. As a result, the consumer will move to a new equilibrium point on a higher indifference curve, representing higher utility. This signifies that the consumer can now afford to consume a combination of goods that provides greater satisfaction than before the income increase. [1]
Decreased Income
Conversely, a decrease in income shifts the budget constraint inward, effectively reducing the consumer's purchasing power. This inward shift forces consumers to purchase less of both goods. Consequently, the new equilibrium point will be on a lower indifference curve, reflecting lower utility. In a situation of decreased income, consumers are forced to reduce their consumption to accommodate their lower budget constraint, resulting in a lower level of satisfaction. [1]

Impact of Changes in Prices
Price Increase of One Good
A price increase of one good rotates the budget constraint inward, making the good relatively more expensive. This price change affects consumer equilibrium through two channels: the substitution effect and the income effect. The substitution effect encourages consumers to purchase relatively less of the more expensive good and more of the cheaper good. This substitution occurs as consumers seek out alternatives that provide similar levels of satisfaction at a lower cost. The income effect, on the other hand, reduces the consumer's purchasing power, making them feel poorer. This reduction in purchasing power may lead to a further decrease in the consumption of the now more expensive good. [2]
Price Decrease of One Good
A price decrease of one good rotates the budget constraint outward, making the good relatively cheaper. Similar to a price increase, the price decrease impacts consumer equilibrium through both the substitution effect and the income effect. The substitution effect encourages consumers to consume more of the cheaper good and less of the relatively more expensive good. Consumers shift their consumption patterns to take advantage of the lower price and increase their satisfaction. The income effect, in this case, makes the consumer feel wealthier, as their purchasing power has increased. This increase in purchasing power can lead to a further increase in the consumption of the cheaper good. [2]

Conclusion
In conclusion, changes in income and prices have a direct impact on consumer equilibrium by altering the budget constraint and forcing adjustments in consumption patterns to maximize utility under the new constraints. Income changes shift the budget constraint either outward (for increases) or inward (for decreases), leading to a new equilibrium on a higher or lower indifference curve, respectively. Price changes, on the other hand, rotate the budget constraint inward or outward, causing consumers to adjust their consumption patterns through substitution and income effects. These adjustments aim to achieve a new equilibrium that maximizes utility given the altered circumstances. [1,2]

References
[1] Mankiw, N. G. (2021). Principles of macroeconomics. Cengage Learning.
[2] Samuelson, P. A., & Nordhaus, W. D. (2010). Economics. McGraw-Hill Education.