# Has anybody seen anything this expression before?

Suppose that $$z(\cdot)$$ is the demand function of an individual (consumer/investor) and $$p$$ is the price of the commodity/asset demanded. Does anybody know what is the intuition behind the following expression? \begin{align}pz^{'}(p)+z(p)\end{align}

It seems to me like the derivative of $$(pz(p))^{'}$$ with respect to $$p$$. What is the intuition behind this? Has anybody seen anything this expression before?

• Marginal revenue – Herr K. Aug 25 at 16:49
• Thank you @Herr K. My mind has stuck! You are absolutely right! – Hunger Learn Aug 25 at 16:57

$$p\cdot z(p)$$ is total revenue (price times quantity), and so its derivative $$\frac{\mathrm d}{\mathrm dp}pz(p)=pz'(p)+z(p)$$ is marginal revenue.

You're correct. Many useful things can be shown by taking this derivative.

Perhaps you were confused because you are used to solving for quantity rather than price - in which case you are more likely to take the derivative of R = z * p(z) with respect to z which gives you p(z) + z * dp(z)/dz