The speaker in this one seems, well, refined. Part of what gives us this refined sense of the speaker is diction, the words she uses. Words like "loveliness," "splendid," "wonder," and "ecstasy" feel like the words of an educated, genteel speaker. And notice: we referred to the speaker as she.
Feels right doesn't it ? And it isn't just because Teasdale is a woman (remember, it's almost always best to separate the poet from the poem). The gaze (what the speaker notices) as well as the language feels, for the most part, more feminine than masculine. For example, the speaker notices "children's faces," "eyes that love," and "arms that hold." These feel more like the observances of an early-twentieth-century woman than a man of the same period.
The speaker also feels just a tad desperate. This comes out in the repetition of "life has loveliness to sell" as the first line of two of the poem's three stanzas. It feels like she's not just telling us about it. She's reminding, or perhaps, trying to convince herself, that what she is saying is true. This feeling becomes even stronger in the poem's last stanza, when the speaker turns on the hard sell, telling us to "Spend all you have for loveliness/Buy it and never count the cost" (13-14). This does not seem like rational, well-considered financial advice, does it?
Choosing a slightly desperate, refined, educated speaker helps Teasdale support her ideas about loveliness/happiness. The fact that this speaker still struggles with the pursuit of happiness reinforces the idea that money can't buy the kind of peace she's talking about. If it could, this speaker would know, since it sounds like she might have a few bucks—and some smarts to boot.