Suppose a Technology Is Described by the Production Function $f ( \ell )$

question 16

Essay

Suppose a technology is described by the production function $f ( \ell )$
a.For a price taking producer who faces output price p and wage w,derive the first order condition and interpret it.
b.Without knowing more about the function f,is the condition you derived in (a)either necessary or sufficient for deriving the profit maximizing production plan? Explain.
c.Suppose
$f ( \ell ) = \ell ^ { \alpha }$ .Derive the first order condition you illustrated in (a)and solve for
$\ell$ .
d.For what values of
$\alpha$ is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain.

---

Definitions:

Battery

A criminal offense involving the unlawful physical acting upon a threat, notably harming another person.

Negligence

A failure to behave with the level of care that someone of ordinary prudence would have exercised under the same circumstances, often leading to harm or damage.

Standard Of Care

The level of care and attention expected of a person or organization in carrying out activities, especially to avoid harm to others.

Tort Action

A lawsuit or legal action based on civil wrongs not arising from contracts, which can lead to a remedy in the form of damages or other relief.