Suppose the consumer's income elasticity for good $x$ is -0.10 when monthly income is $1,000, and the consumer's income elasticity for good $x$ is 0.10 when monthly income is $2,000. From this information we can infer that good $x$ is a Giffen good.

Question

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The income elasticity of -0.10 when monthly income is $1,000 indicates that good $x$ is an inferior good, meaning that as the consumer's income increases, the demand for good $x$ decreases. The income elasticity of 0.10 when monthly income is $2,000 indicates that good $x$ is a normal good, meaning that as the consumer's income increases, the demand for good $x$ increases. A Giffen good is a special type of inferior good that violates the law of demand, meaning that as the price of the good increases, the quantity demanded also increases. There is no information in the question to suggest that good $x$ is a Giffen good. The income elasticity of demand for a Giffen good is positive, not negative. When the income of the consumer increases, the quantity demanded of a Giffen good also increases. The information given in the question shows that the income elasticity for good x is positive when income changes from $1,000 to $2,000, which contradicts the assumption that it is a Giffen good.

Suppose the Consumer's Income Elasticity for Good xxx Is -010 When Monthly Income Is $1,000, and the Consumer's Income

Suppose the Consumer's Income Elasticity for Good $x$ Is -010 When Monthly Income Is $1,000, and the Consumer's Income