What kind of person is the Duke in the poem "My Last Duchess"? 

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The entire poem is geared toward a “portrait” of the Duke’s inhumanity and greed.  The casual remark  “I gave commands and all smiles stopped together” is a sinister hint as to his power and malice, and his hypocritical remark about the new candidate’s dowry is a good indication of his greed.  The fact that he treats human beings as owned objects is hidden even in his first remark : “That’s my last duchess painted on the wall.”  This "ownership" attitude is reiterated in the last image in the poem “ Notice Neptune.. which Claus of Innsbruck cast in bronze for me.”  The reader gets the same impression of the Duke as does the ambassador, who undoubtedly takes back a negative report to his employer.  The “kind of person” the Duke displays unconsciously in his exchanges with the ambassador gives a double meaning to the word “last,” since the Duke is very unlikely to ever get a good recommendation and therefore another Duchess.