Question

In a purely communist society, the means of production are owned by

the government
the market
the prices
the supply

Answer 1

The government.
In a communist society the government own practically everything with the means of production being one of them

Answer 2

The communists governments would say that in their countries, the means of production were in the hands of "the people" but in reality they were controlled by the government.

(the other options are abstract nouns and can't own anything...)