Slope of Indifference Curve and Budget Line at Equilibrium

At equilibrium, the consumer is satisfied with the combination of goods and services that he or she can purchase with their income. At this point, the consumer has found the optimal combination of goods and services that maximize their utility given their budget constraint.

The slope of the indifference curve represents the rate at which the consumer is willing to trade one good for another while keeping their satisfaction level constant. The slope of the budget line represents the rate at which the consumer can trade one good for another given their budget constraint.

At equilibrium, the slope of the indifference curve is equal to the slope of the budget line. This is because at this point, the consumer has found the combination of goods and services that maximizes their satisfaction while staying within their budget constraint.

If the slope of the indifference curve was greater than the slope of the budget line, then the consumer could increase their satisfaction level by purchasing more of one good and less of another, which would violate their budget constraint. Similarly, if the slope of the indifference curve was smaller than the slope of the budget line, then the consumer could increase their satisfaction level by purchasing more of one good and less of another, but they would not be fully utilizing their budget constraint.

Therefore, at equilibrium, the slope of the indifference curve is equal to the slope of the budget line. This represents the optimal combination of goods and services that maximizes the consumer's satisfaction while staying within their budget constraint.