Suppose a Technology Is Described by the Production Function

question 16

Essay

Suppose a technology is described by the production function
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 .Derive the first order condition you illustrated in (a) and solve for .
d.For what values of is this first order condition necessary and sufficient for deriving a profit maximizing production plan? Explain.

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Definitions:

Payback Period

The amount of time it takes for an investment to generate cash flows sufficient to recover the initial cost of the investment.

Discount Rate

The interest rate used to discount future cash flows of an investment to present value, reflecting the opportunity cost of capital.

Cost Savings

Reductions in expenditures achieved through methods such as negotiation, effciency improvements, or substitution.

Pretax Return

The profit earned by a business before the deduction of tax expenses.