<p>You're probably confusing two things: the objective function <span class="math-container">$pf(x) - wx$</span> being used in profit maximization problem: <span class="math-container">$\max pf(x) - wx$</span>, the objective function is concave in <span class="math-container">$x$</span> and thus, you can solve the maximization problem. However, a profit function <span class="math-container">$\pi(p,w)$</span> being a result of maximization problem identifies the maximum profit given level of prices and wages <span class="math-container">$\pi^*(p,w)$</span> (and it's convex in <span class="math-container">$p$</span> and <span class="math-container">$w$</span> as you said).</p>

CC BY-SA 4.0
2019-11-10T17:42:53.803Z
2019-11-10T17:42:53.803Z
bajun65537
<p>I know that a profit function is defined by <span class="math-container">$\pi(p;w)=\max_{x\in\mathbb{R}}pf(x)-w\cdot x$</span> and <span class="math-container">$\pi$</span> is a convex function (i.e. <span class="math-container">$\pi$</span> is convex in <span class="math-container">$(p, w)$</span>. My concern is how we can find the max value of the profit function when the profit function itself is convex. </p>

<p>From my previous knowledge on convex function, I also know that a convex function has a global minimum on its domain (correct me if I was wrong), but how can we find the maximum?</p>

<p>Can anyone please explain this for me? I am so confused. Thanks in advanced!</p>

<profit-maximization>
Questions about profit function
Christopher Hernandez
# Questions about profit function

(Asked by: username_0 on 2019-11-10)

I know that a profit function is defined by $\pi(p;w)=\max\_{x\in\mathbb{R}}pf(x)-w\cdot x$ and $\pi$ is a convex function (i.e. $\pi$ is convex in $(p, w)$. My concern is how we can find the max value of the profit function when the profit function itself is convex.

From my previous knowledge on convex function, I also know that a convex function has a global minimum on its domain (correct me if I was wrong), but how can we find the maximum?

Can anyone please explain this for me? I am so confused. Thanks in advanced!

**Tags:** profit-maximization


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## 1 answers

### Answer by username_1 on 2019-11-10. Score: 1

You're probably confusing two things: the objective function $pf(x) - wx$ being used in profit maximization problem: $\max pf(x) - wx$, the objective function is concave in $x$ and thus, you can solve the maximization problem. However, a profit function $\pi(p,w)$ being a result of maximization problem identifies the maximum profit given level of prices and wages $\pi^\*(p,w)$ (and it's convex in $p$ and $w$ as you said).


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