Final answer:
The slope of a utility function within an indifference curve illustrates the marginal rate of substitution, reflecting the trade-off a consumer makes between two goods to maintain the same utility level.
Step-by-step explanation:
The slope of a utility function, often found in indifference curves in microeconomics, represents the marginal rate of substitution (MRS). This rate shows the trade-off a consumer is willing to make between two goods while maintaining the same level of utility. In economic terms, the slope is negative because to increase the quantity of one good, the consumer must give up some of the other good. This relationship is visualized as a downward sloping curve from left to right, being steeper on the left and flatter on the right, reflecting the diminishing marginal utility.
At any point along an indifference curve, such as between points A and B on curve Um, the slope shows that if Lilly increases her consumption of books, she must decrease her consumption of doughnuts to maintain the same utility. The magnitude of the slope itself indicates how much of one good is to be given up for an additional unit of the other good. A steep slope indicates a high rate of substitution, while a flatter slope signals a lower rate.