Final answer:
True, if both a consumer's income and all prices triple simultaneously, the consumer's optimum will not change because the purchasing power and the budget constraint remain constant. The proportional increase in income and prices means that the consumer can still afford the same combinations of goods, maintaining the same level of utility.
Step-by-step explanation:
It's based on the economic principle that if both income and prices increase proportionally, the consumer's purchasing power remains the same. To understand, we can consider a concept in economics known as 'ceteris paribus', which means 'all other things being equal'. Typically, an increase in the price leads to a decrease in the quantity consumers will buy, assuming income and other factors affecting demand remain unchanged. Conversely, a decrease in income results in consumers being able to afford less, assuming prices are unchanged. However, in the scenario where both the consumer's income and prices triple, these effects offset each other. The consumer would be able to purchase the same quantity of goods because their real income—their purchasing power—has not changed. This is a foundational concept in consumer theory, which assumes that consumers will make choices to maximize their utility or satisfaction, given their budget constraints. When income and prices scale up equally, the budget line's slope remains the same, indicating that the rate at which consumers can substitute one good for another has not altered, allowing them to reach the same level of utility.