certain goods are demanded even when price is zero does it mean those goods are not scarce

Scarcity implies that resources are limited in relation to the human wants. It can be said that it is because of scarcity that goods command a price. However, zero price for a commodity should not always be taken as a situation of no scarcity. For instance, consider the free distribution of medicines by the government. In this case, zero price for the medicines does not imply that it is not scarce, it just that the government distributes free medicines for social welfare motive. 

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No, medicines distributed in govt hospitals free of cost are surely scarce and are demanded

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