Final answer:
The question pertains to determining the different types of elasticities of demand for a good, the relationship between two goods, and the classification of a good based on how demand changes with income. By analyzing the demand function and using the concepts of income, own-price, and cross-price elasticities, we can find out if goods are substitutes or complements, and if the good is normal, inferior, or a luxury.
Step-by-step explanation:
The student is asking about the elasticities of demand for a product X, given a specific demand function, and the nature of product X relative to income levels and a related product Y. Let's go through the questions one by one:
The income elasticity of demand measures the responsiveness of the quantity demanded to a change in consumer income. It is derived from the demand function and is given by the coefficient of income in the demand equation. The own-price elasticity of demand measures the responsiveness of quantity demanded to a change in the price of the good itself, while the cross-price elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good.
The relationship between goods X and Y can be understood through the cross-price elasticity. If the elasticity is positive, then the two goods are substitutes, meaning that an increase in the price of one leads to an increase in demand for the other. If it's negative, the goods are complements, meaning that an increase in the price of one leads to a decrease in demand for the other.
Good X is deemed a normal good if the income elasticity is positive, which suggests that demand increases as income rises. An inferior good is indicated by a negative income elasticity, where demand decreases as income increases. A luxury good would have a high positive income elasticity, indicating demand increases more than proportionally with income.
To calculate the percentage change in the quantity demanded of good X when factors such as income, price of X, and price of Y change, one would use the pertinent elasticities and the percentage changes in these factors based on the provided function. In this scenario, where income increases by 2%, the price of X increases by 3%, and the price of Y by 0.5%, the combined effect on the quantity demanded of X can be calculated using the respective elasticities derived from the demand function.