Suppose You Solve the Profit Maximization Problem for a Single-Input,price-Taking $f ( \ell )$

Essay

Suppose you solve the profit maximization problem for a single-input,price-taking producer whose technology is given by $f ( \ell )$ The labor demand function is $\ell ( w , p )$
a.Suppose
$\frac { d \ell ( w , p ) } { d w } < 0$ Might
$\ell ( w , p )$ in fact be the correct labor demand function? Explain.
b.Suppose
$\frac { d \ell ( w , p ) } { d w } > 0$ Might
$\ell ( w , p )$ in fact be the correct labor demand function? Explain.
c.Intuitively explain how (b)might arise from the profit maximization problem.