Final answer:
The statement is true; a doubling of prices or halving of income has the same effect on the consumer's budget constraint, shifting it leftwards, indicating lower utility. Actual changes in consumption depend on individual preferences and the elasticity of demand for different goods.
Step-by-step explanation:
The statement that a doubling of all prices has the same effect on the budget line as reducing income by half is True. In economics, the budget constraint represents the combinations of goods and services a consumer can purchase with a given income. When all prices double, the consumer can only buy half as much of everything, just as they would if their income were halved while prices remained constant. Consequently, both scenarios would shift the budget line to the left in a graphical representation, indicating a lower level of utility because the consumer cannot reach higher indifference curves which represent preferred combinations of goods.
However, how a person alters consumption of goods like books and doughnuts after an income rise depends on their preferences and the relative elasticity of demand for those goods. If the consumer sees both goods as necessities, consumption may increase proportionally. But if one good is a luxury and the other a necessity, the luxury good's consumption might increase more as income increases.
The budget constraint framework is crucial in considering the full effects of changes in income or price, not just for a single product but for a person's entire consumption bundle. It reminds us that changes in either income or prices impact all aspects of consumer choice.