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

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Part $1$

A$.$

A linear cost function is a cost function$$ where, within the relevant$$ range, the graph of total costs 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$$ range, the graph of total costs versus the level of a single activity related to that cost is not a straight line. Examples include a cost function for use of a telephone line where the terms are a fixed charge of$$ $$10,000$ per year plus a$$ $$0\mathrm{.}20$ per minute charge for phone use.

B$.$

A linear cost function is a cost function$$ where, within the relevant$$ range, the graph of total costs 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 videoconferencing line where the terms are a fixed charge of$$ $$10,000$ per year plus a$$ $$0\mathrm{.}20$ per minute charge for line use. A nonlinear cost function is a cost function$$ where, within the relevant$$ range, the graph of total costs 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.

C$.$

A linear cost function is a cost function$$ where, within the relevant$$ range, the graph of total costs 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 a$$ $$0\mathrm{.}01$ per page charge for each copy. A nonlinear cost function is a cost function$$ where, within the relevant$$ range, the graph of total costs versus the level of a 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$1,000$ unites purchased at a time.

D$.$

A linear cost function is a cost function$$ where, within the relevant$$ range, the graph of total costs 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$$ learning$-$curve$-$based costs. A nonlinear cost function is a cost function$$ where, within the relevant$$ range, the graph of total costs versus the level of a single activity related to that cost is a straight line. An example of a linear cost function is a cost function for use of a videoconferencing line where the terms are a fixed charge of$$ $$10,000$ per year plus a$$ $$0\mathrm{.}20$ per minute charge for line use.