<p>The marginal profit you calculate is correct.</p>

<p>We can rearrange the solution of the problem you are given. This is equivalent to</p>

<p>$$ \frac{dP}{dq} = 192 -176q + 48q^2 -4q^3$$</p>

<p>This derivative has as <em>primitive function</em> the following profit function:</p>

<p>$$P(q) = c + 192q -88q^2 + 16q^3 - q^4$$</p>

<p>where $c$ is a constant (e.g. $c=0$).</p>

<p>This is clearly different from the original profit function in your problem. In consequence, <strong>either the profit function or the solution is wrong.</strong></p>

CC BY-SA 3.0
2017-02-07T14:03:24.900Z
2017-02-07T14:42:14.767Z
2017-02-07T14:42:14.767Z
luchonacho
<p>Find the marginal profit of a firm with a profit function:</p>

<p>$$P(q) = -192q + 88q^2 - 16q^3$$</p>

<p>I got</p>

<p>$$\frac{dP}{dq} = -192 + 176q - 48q^2$$</p>

<p>However, the solution reads </p>

<p>$$ \frac{dP}{dq}= -4(q-2)(q-4)(q-6)$$</p>

<p>Is this a typo, or am I missing something?</p>

<microeconomics><marginal>
Marginal Profit Derivation
Laura K
# Marginal Profit Derivation

(Asked by: username_0 on 2017-02-07)

Find the marginal profit of a firm with a profit function:

$$P(q) = -192q + 88q^2 - 16q^3$$

I got

$$\frac{dP}{dq} = -192 + 176q - 48q^2$$

However, the solution reads

$$ \frac{dP}{dq}= -4(q-2)(q-4)(q-6)$$

Is this a typo, or am I missing something?

**Tags:** microeconomics, marginal


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## 1 answers

### Answer by username_1 on 2017-02-07. Score: 3 | Accepted answer

The marginal profit you calculate is correct.

We can rearrange the solution of the problem you are given. This is equivalent to

$$ \frac{dP}{dq} = 192 -176q + 48q^2 -4q^3$$

This derivative has as *primitive function* the following profit function:

$$P(q) = c + 192q -88q^2 + 16q^3 - q^4$$

where $c$ is a constant (e.g. $c=0$).

This is clearly different from the original profit function in your problem. In consequence, **either the profit function or the solution is wrong.**


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