What, according to Marx, is the relationship between economic systems and culture? How might this relationship relate to the arts?

For Karl Marx, everything is determined by what he calls the mode of production, or the social relationships by which goods are produced for society.  This mode of thinking is sometimes called economic determinism, seeing the economic sphere--and its corresponding mode of production--as determining everything else in any given social arrangement, from politics to art.  Thus, art, for Marx, is an expression of the material economic relationships out of which it was produced.  In the ...

For Karl Marx, everything is determined by what he calls the mode of production, or the social relationships by which goods are produced for society.  This mode of thinking is sometimes called economic determinism, seeing the economic sphere--and its corresponding mode of production--as determining everything else in any given social arrangement, from politics to art.  Thus, art, for Marx, is an expression of the material economic relationships out of which it was produced.  In the Grundrisse's introduction he asks rhetorically,

is Achilles possible with powder and lead? Or the Iliad with the printing press, not to mention the printing machine? Do not the song and the saga and the muse necessarily come to an end with the printer's bar, hence do not the necessary conditions of epic poetry vanish?

In this brief series of questions, Marx implies that classical Greek epic--here represented by Homer's Iliad--requires a certain mode of production that does not include technologies such as powder, lead, and the printing press.  Thus, all (good) art for Marx requires that the artist express the material conditions of the age in which the artist produces the work.  As he implies, all artworks depend in their form upon certain necessary conditions which are inherently bound up with technological advancements and the mode of production.