Final answer:
If the prices of all goods and income increase proportionally, the quantity demanded of good X will remain unchanged, assuming ceteris paribus and that good X is a normal good. Option c is the correct answer.
Step-by-step explanation:
If the prices of all goods increase by the same proportion as income, the quantity demanded of good X will remain unchanged. This economic scenario falls under the concept of ceteris paribus, which means 'all other things being equal.' The question touches on the effects of simultaneous changes in prices and income on the quantity demanded of a good.
When analyzing the effects of price and income changes on demand, economists often use the ceteris paribus assumption to consider one factor at a time. For instance, an increase in price generally leads to a reduction in the quantity a consumer will buy if their income remains unchanged. Conversely, a decrease in income typically means that a consumer can afford to buy less if prices remain unchanged.
However, in the scenario presented in the question, the increase in prices is exactly offset by a proportionate increase in income, leaving the consumer's purchasing power unchanged. As a result, the overall effect on the quantity demanded of good X is neutral, and there is no shift in demand. Therefore, the correct option for this scenario is that the quantity demanded of good X will remain unchanged.
It's worth noting that this answer assumes good X is a normal good and that the proportionate increase in prices and income does not alter consumer preferences or introduce any distortion effects.