# Revenues and cost functions

Let's assume that there is a firm that produces a single good, $$q=f(x)$$, where $$x$$ is a single input. The firm can sell it on the market at a price $$p$$. It's production cost is given by a cost function $$c(x)$$.

In the most microeconomics textbooks the profit maximization problem is expressed as

$$maxΠ=max\{pq-c(x)\}$$, where $$q$$ is assumed to be linear function of $$x$$.

I am wondering if there is a textbook (or a resource in general) in which profit function is expressed as

$$Π=pf(x)-c(x)$$, where $$f$$ is concave in $$x$$ and $$c$$ is convex in $$x$$.

• This is almost always the case with $c(x)=w'x$ – Bertrand May 26 '20 at 11:33
• what do you mean by $w'$? – Yorgos May 26 '20 at 19:08
• $w$ denotes the vector of input prices – Bertrand May 26 '20 at 22:15