Final answer:
A parallel shift in the budget line is caused by a change in income, not the relative prices of goods, making the initial statement false. When income rises, the budget line shifts right; when it falls, it shifts left, affecting utility levels and consumption based on personal preferences.
Step-by-step explanation:
The statement that a parallel shift in the budget line is caused by changes in the relative prices of the two goods is false. In fact, a parallel shift in the budget line represents a change in income, not a change in relative prices. When income changes, the entire budget constraint shifts parallel to the original because the consumer can now afford more or less of both goods, while the relative prices of the goods remain the same.
If there is a rise in income, the budget constraint will shift to the right, and the new budget line will be tangent to a higher indifference curve, signalling an increased level of utility. Conversely, a reduction in income will cause the budget line to shift to the left, tangent to a lower indifference curve, indicating a reduced level of utility. The extent to which consumption of goods will change depends on personal preferences, and it's possible that consumption of one good increases significantly, while the other increases slightly or even decreases.