Cobb-Douglas Productivity Functions Have the Form $p ( x , y ) = k x ^ { a } y ^ { 1 - a }$

question 58

Short Answer

Cobb-Douglas productivity functions have the form
$p ( x , y ) = k x ^ { a } y ^ { 1 - a }$
where P stands for the number of items produced per year, x is the number of employees, and y is the annual operating budget. The numbers k and a are constants that depend on the situation we are looking at, with $0 \leq a \leq 1$ .

How many items will be produced per year by a company that has 250 employees and an annual operating budget of $100,000 if $k = 1,000$ and $a = 0.5$ (Round your answer to one significant digit.)

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Definitions:

Raw Materials

These are the basic, unprocessed inputs used in manufacturing to produce finished goods.

Selling and Administrative Expense Budget

A detailed plan that estimates the expenses related to selling products and managing the business.

Fixed Costs

Costs that remain constant regardless of the amount of output or sales.

Variable Costs

Costs that change in proportion to the level of production or sales activity.