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The labor demand curve of a purely competitive seller:

What exactly is your question?

Is it something like: what is the slope (elasticity) of the demand for labor labor faced by a producer who sells in a perfectly competitive market?

I would argue that selling in a perfect competitive market has nothing do do with the shape of the demand for labor. If the firm hires a significant portion of the local labors, or if the type of labor hired has special skills, the demand curve for labor will be relatively inelastic. If the firm is a small employer hiring common laborers, the curve will be flat (elastic).

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