Final answer:
The statement is false as a good that is demanded in the same amount regardless of income changes has a zero income elasticity, not a positive one.
Step-by-step explanation:
The statement that if a consumer demands the same (positive) amount of a good no matter what their income, then the income elasticity is also positive, is false. The quantity of a good that is demanded in response to changes in consumers' income is measured by the income elasticity of demand. For most products, the income elasticity of demand is indeed positive, meaning as income rises, so does the quantity demanded. These goods are referred to as normal goods. However, there are goods known as inferior goods where an increase in income actually leads to a decrease in the quantity demanded, hence a negative income elasticity. If a consumer's demand remains unchanged regardless of changes in income, the good would exhibit zero income elasticity since the consumer's income level does not influence the quantity demanded of that good.