For q units of a product, a manufacturer's cost is C(q)...

For $q$ units of a product, a manufacturer's cost is $C(q)$ dollars and revenue is $R(q)$ dollars, with $C(500)=$ $7200, \quad R(500)=9400, \quad M C(500) \quad=\quad 15, \quad$ and $M R(500)=20$ (a) What is the profit or loss at $q=500 ?$ (b) If production is increased from 500 to 501 units, by approximately how much does profit change?

For $q$ units of a product, a manufacturer's cost is $C(q)$ dollars and revenue is $R(q)$ dollars, with $C(500)=$ $7200, \quad R(500)=9400, \quad M C(500) \quad=\quad 15, \quad$ and
$M R(500)=20$
(a) What is the profit or loss at $q=500 ?$
(b) If production is increased from 500 to 501 units, by approximately how much does profit change?

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Key Concepts

Marginal Analysis

Marginal analysis involves evaluating the incremental change in cost or revenue that results from producing one additional unit of a product. Marginal cost (MC) and marginal revenue (MR) are determined by taking the derivative of the cost and revenue functions, respectively, and are crucial for decision-making regarding production levels.

Differentiation as an Approximation Tool

Differentiation is used in economics to approximate small changes in functions. When the quantity changes slightly, the change in cost, revenue, or profit can be estimated using the derivatives of these functions. For instance, the change in profit due to a one-unit increase in production can be approximated by the difference between marginal revenue and marginal cost.

Profit Function

The profit function is defined as the difference between the revenue function and the cost function, typically represented as P(q) = R(q) - C(q). This function helps in determining the profitability of producing a certain quantity of a product by indicating whether revenue exceeds cost or vice versa.

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