Marginal cost The total weekly cost (in dollars) incurred by...

Marginal cost The total weekly cost (in dollars) incurred by Lincoln Records in pressing $x$ compact discs is $$ \begin{array}{ll} C(x)=2000+2 x-0.0001 x^{2} & (0 \leq x \leq 6000) \\ \end{array} $$ a. What is the actual cost incurred in producing the 1001 st disc and the 2001 st disc? b. What is the marginal cost when $x=1000$ and $2000 ?$

Marginal cost The total weekly cost (in dollars) incurred by Lincoln Records in pressing $x$ compact discs is
$$
\begin{array}{ll}
C(x)=2000+2 x-0.0001 x^{2} & (0 \leq x \leq 6000) \\
\end{array}
$$
a. What is the actual cost incurred in producing the 1001 st disc and the 2001 st disc?
b. What is the marginal cost when $x=1000$ and $2000 ?$

Key Concepts

Cost Function

A cost function represents the total expense incurred by a firm in producing a given quantity of output. It typically includes both fixed costs, which do not change with production volume, and variable costs, which vary with the level of output. The cost function provides a foundational tool for analyzing production efficiency and cost behavior in economic decision-making.

Marginal Cost

Marginal cost is the additional expense incurred when producing one more unit of a good or service. It is a crucial concept in economics and production management, often calculated as the derivative of the cost function. This measure helps firms decide the level of production that minimizes costs while maximizing profits.

Discrete Cost Difference

The discrete cost difference refers to the actual change in total cost when production increases by a specific number of units. This approach involves computing the difference between the total cost at two production levels, offering a precise measure of the cost impact for a given increment in production.

Derivative as an Approximation

Using the derivative of a cost function to approximate marginal cost is a method grounded in calculus. The derivative provides the instantaneous rate of change of the cost with respect to production, serving as a continuous approximation that is particularly useful when evaluating small changes in output.

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