Question

What is the difference between a linear and a nonlinear cost function? Give an example of each type of cost function.

1) A linear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is not a straight line. An example of a linear cost function is a cost function for use of a copier where the terms are a fixed lease payment of $1,000 per month plus $0.01 per page charge for each copy. A nonlinear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of single activity related to that cost is a straight line. Examples include quantity discounts for material purchases for each 1,000 units of material purchased. The cost per unit of material will fall for each 1,000 units purchased at a time.
2) A linear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is a straight line. An example of a linear cost function is a cost function for use of a telephone line where the terms are a fixed charge of $10,000 per year plus $2 per minute charge for phone use. A nonlinear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is not a straight line. Examples include economies of scale in advertising where an agency can double the number of advertisements for less than twice the costs, step-cost functions, and learning-curve based costs.
3) A linear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is a straight line. Examples include economies of scale in advertising where an agency can double the number of advertisements for less than twice the costs, step-cost functions, and learning-curve based costs. A nonlinear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is not a straight line. Examples include a cost function for use of a telephone line where the terms are a fixed charge of $10,000 per year plus $2 per minute charge for phone use.
4) None of the above are correct.

Answer 1

A linear cost function is a straight line, while a nonlinear cost function is not. Examples include a telephone line cost function and economies of scale in advertising.

Step-by-step explanation:

A linear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is a straight line. An example of a linear cost function is a cost function for use of a telephone line where the terms are a fixed charge of $10,000 per year plus $2 per minute charge for phone use.

A nonlinear cost function is a cost function where, within the relevant range, the graph of total cost versus the level of a single activity related to that cost is not a straight line. Examples include economies of scale in advertising where an agency can double the number of advertisements for less than twice the costs, step-cost functions, and learning-curve based costs.

Therefore, the difference between a linear and a nonlinear cost function lies in the shape of the graph of total cost versus the level of activity.