Marginal Revenue Interpretation of Auctions
This analogy is due to Bulow and Roberts.

Think of a diagram from Econ 101 with price on the vertical axis and quantity on the horizontal axis and consider a monopolist with constant marginal cost of zero. Given a demand curve, you can draw the marginal revenue and find the monopoly quantity where this function intersects the axis.

Now take that same diagram and interpret "quantity" as "probability that a buyer accepts price $p$", i.e., $q = 1- F(p)$. Now, maximize revenue $pq=q F^{-1}(1-q)$ wrt $q$ to reach some form of the well known marginal revenue = marginal cost. The derivative of the revenue above is
$$\frac{\partial pq}{\partial q} = F^{-1}(1-q) - \frac{q}{f(F^{-1}(1-q)} = v - \frac{1-F(v)}{f(v)}, $$
where I replaced $q=1- F(p)$ and set $p=v$. This is Myerson's virtual value. The expected revenue of an optimal auction is the expectation of the highest virtual value. The part $\frac{1-F(v)}{f(v)}$ is the information rent, which takes care of the fact that you don't bid your true value in a first-price auction.