Final answer:
The correct relationship between cross-price elasticity of demand (ηxy) and the types of goods is: positive for substitutes, negative for complements, and zero for independents, corresponding to option a).
Step-by-step explanation:
The relationship between ηxy (cross-price elasticity of demand) and the economic concepts of substitutes, complements, or independents is crucial for understanding consumer behavior. Substitute goods have positive cross-price elasticities of demand; this means that if the price of good B increases, the quantity demanded of good A, which is a substitute, also increases (e.g., coffee and tea). Conversely, complement goods have negative cross-price elasticities of demand; an increase in the price of good B leads to a decrease in the quantity demanded of good A, which is a complement to B (e.g., coffee and sugar). Independent goods would have a cross-price elasticity of demand of zero, as they do not affect each other's consumption. Therefore, the correct relationship is: ηxy is positive for substitutes, negative for complements, and zero for independents, which corresponds to option a).