Economic Effects of Subsidization

How would you explain how a subsidy leads to net economic losses for consumers as a whole? I seem to get that it would arbitrarily direct resources to to economically arbitrary things at the expense of things actually desired by consumers, but is that the only way of looking at it because this never works on leftists. Suppose a leftist claimed that since health care service x currently cost $100, he wanted to means test people to qualify for a $50 subsidy toward the service. What would happen/how is the net economic loss best described? Channel your inner Bastiat.

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