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

question 27

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.

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Definitions:

ADP

Adenosine diphosphate, a molecule involved in ATP synthesis, it releases energy when it is converted to ATP in cellular respiration.

Muscle Contraction

The tightening of muscle fibers initiated by electrical impulses, leading to shortening of the muscle and movement or force generation.

Sarcoplasmic Reticulum

Smooth endoplasmic reticulum of skeletal muscle cells; surrounds the myofibrils and stores calcium ions.

Calcium Ions

Electrically charged calcium atoms (Ca2+) that play a crucial role in various physiological processes, including muscle contraction, neurotransmitter release, and bone formation.