Consider the following two policies:

(1) per unit subsidy for each unit of good X consumed

(2) per unit subsidy for each unit of good X in excess of standard (unsubsidized level of consumption)

Is it true that consumer with fixed money income M will never reduce his consumption of good X when the second policy is introduced but might reduce his consumption of good X under the first policy (in comparison with the initial unsubsidized level)? Explain carefully (You should refer to some theoretical results that explain the result)