Final answer:
The question covers the concept of indifference curves and finding the utility-maximizing choices for consumers given their budget constraints in Economics. Lilly's optimal choice lies where her budget line is tangent to the highest indifference curve, and when Manuel and Natasha experience an income increase, their choices shift based on their preferences and the nature of the goods (normal or inferior).
Step-by-step explanation:
The question relates to the concept of indifference curves and utility maximization in the context of consumer choice, which is a fundamental topic in Economics. Indifference curves represent different combinations of goods that provide the consumer with the same level of satisfaction or utility. Lilly's utility-maximizing choice will be the point where her budget constraint, which is dictated by the amount she can spend on goods, is tangent to the highest indifference curve accessible to her.
As Lilly has $60 to spend, with books costing $6 and doughnuts costing 50 cents each, her budget line reflects all possible combinations of books and doughnuts she can afford. The utility-maximizing choice would typically be at the point where an indifference curve is tangent to the budget line, indicating the highest level of utility she can achieve given her budget.
When Manuel and Natasha's incomes increase to $60, their budget constraints shift to the right, showing they can now afford more goods. Manuel's and Natasha's utility-maximizing choices are identified at points X and Z respectively. The new choices reflect their personal preferences, with Manuel spending more on movies and Natasha spending more on yogurts. If both movies and yogurts are normal goods, typically they would buy more of both as their incomes rise. If one of the goods is an inferior good, the quantity purchased might decrease with the increase in income, depending on individual preferences.