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No,two goods cannot be inferior at the same time.We know that the demand for the inferior goods decreases with increase in income.

suppose the income increases, to compensate this increase and to satisfy the new budget line and with the assumption that the consumer is rational,the amount of any one of the good must increase so as to leave the consumer with a bundle on his new budget line .If both the goods are inferior then the amount demanded of both these goods would decrease thus violating the axiom of revealed preferences.

even if they are one of the good would be relatively more inferior to the other.

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