Final answer:
Without specific details regarding Tom's utility function or the nature of good X (whether it is a normal or inferior good), it is not possible to accurately determine the demand function for good X. The concept of an inferior good and how price changes impact consumer choices has been explained to provide a theoretical foundation.
Step-by-step explanation:
To determine Tom's demand function for good X, we need to understand his preferences and how these translate to his choices between different goods given the constraints of his budget and prices.
When preferences are mentioned without specifics, typically a utility function is given or the types of goods are defined (e.g., normal or inferior goods). Without this specificity, we cannot provide an exact demand function for good X.
Inferior goods are those for which demand decreases as income rises because consumers can now afford more expensive alternatives they prefer.
An example of this would be if Tom considers good X an inferior good, he would buy less of it as his income goes up. Conversely, if good X is a normal good, Tom's demand for it would generally increase with his income.
Regarding price changes and consumer choices, if the price of good X increases, assuming it is not a Giffen good, the demand for it would generally decrease because it would consume a larger portion of Tom's budget.
To complete the demand function, details about Tom's income, the prices of goods, and how he perceives the satisfaction from consuming different quantities of good X are necessary.
Without such information, we can only discuss demand in theoretical terms.