Final answer:
The statement that the slope of the budget line represents the trade-off rate between two goods is true. It is a core concept in economics that helps in analyzing consumer choices and behavior based on changes in income and relative prices of goods.
Step-by-step explanation:
The statement "The slope of the budget line represents the rate of change of the quantity of one good in relation to the other" is True. The slope of the budget constraint in an economic context is determined by the relative price of two goods. It represents how much of one good a consumer must give up to obtain one more unit of another good, which is essentially the rate of trade-off between two goods in a budget constraint scenario. In economics, when we analyze a consumer's choice between two goods, a budget line graphically represents the combination of goods a consumer can purchase given his income and the prices of goods.
Changes in income can shift the budget line. A rise in income shifts the budget constraint to the right and the consumer can reach a higher indifference curve, indicating a higher utility level. Conversely, a decline in income shifts the budget line to the left and the consumer moves to a lower indifference curve, indicating lower utility. The slope of the budget line changes with relative prices and is critical in analyzing consumer behavior, including the substitution and income effects, when prices or income levels change.