What can we say if we want to read Browning's "My Last Duchess" via a Marxist perspective?

Marxism is both a political philosophy and a type of sociology. In thinking about "My Last Duchess" from a Marxist perspective, it makes sense to consider Marxist sociology. A key question of Marxist sociology is how economic factors influence social inequalities. In Browning's dramatic monologue, Duke Ferrara is at the highest level of the socioeconomic hierarchy compared to anyone else in the poem. As such, he controls the capital of his estate and therefore controls the labor. Thus, he hired Fra Pandolf, the painter who painted the portrait of his last Duchess. He seems derisive of the techniques he supposes the painter used to "call that spot of joy into the Duchess' cheek." Yet the fact that he routinely shows the painting to visitors, prompting them to ask about it, shows that he appreciates the workmanship even as he maintains complete control over the product of the painter's labor: "none puts by the curtain I have drawn for you but I." He is similarly proud of having commissioned the bronze statue of Neptune from Claus of Innsbruck.

Ferrara is clearly rankled by the actions of a hired gardener who dared to overstep his bounds by complimenting the Duchess with a "bough of cherries," calling the man "some officious fool." Because he controls the capital, Ferrara evidently feels he should be able to control the workers' every action, making sure they do not arouse pleasure in his Duchess, who is in a different class than they are.

The Duchess herself felt the inequality caused by wealth. Since she married into the Duke's household, she brought no wealth of her own except what her father would have paid as dowry to purchase the match with the Duke. All ownership of the estate, however, was Ferrara's, not hers; she was powerless to the point of succumbing to the Duke's ultimate command, the one that made "all smiles [stop] together." 

The person to whom Ferrara speaks in the poem is a representative of a Count who is there to negotiate the dowry for the next Duchess. Again, Ferrara wields all the power in the conversation, being the person of higher social rank not only to the representative, but also to the representative's employer, since a Duke ranks higher than a Count. Ferrara takes control over the agent's movements, saying, "Nay, we'll go together down, sir." 

From a Marxist perspective, the poem shows that the economic power wielded by the Duke allows him to employ artists but control the products of their labor; to control and take advantage of lower-ranking nobles; and to control, oppress, and even murder his wife, who is, interestingly, probably the least empowered person mentioned in the poem. The poem reveals the inequalities that result from having economic power in the hands of a single man.