Here’s a classic, super-simple paper. I think I can give you the idea in two paragraphs. I know price and quantity sold for some good. I know supply and demand must equate. I use whatever method I like to deal with simultaneity of the supply and demand functions (say, a cost shifter approach). How can I identify whether the industry is acting as if it had market power? That is, how can I separate collusive behavior from competitive behavior?
A numerical example will help. Let marginal costs and demand be linear. Let demand be P=11-Q. Shift demand and supply (meaning shift the intercept) however you like. The price-quantity bundle you see under monopoly with MC constant and equal to 1 will be identical to the price-quantity bundle you see under perfect competition with MC increasing and equal to 1+Q. For instance, price=6 and quantity=5 is found by letting P=MC for MC=1+Q or by letting MR=MC for MR=11-2Q. And demand shifters don’t help us! If demand shifts to P=R-Q, where R is any y-intercept, then under perfect competition with MC=1+Q, we have equilibrium price such that 1+Q=R-Q, or Q=(R-1)/2, and equilibrium price under monopoly with MC=1 such that MC=MR, or R-2Q=1, or Q=(R-1)/2. Supply shifters are equally unhelpful: for inverse demand P=11-Q, shifting the y-intercept for the cost curve of both the hypothetical monopolist and the hypothetical perfectly competitive market changes equilibrium quantity by exactly the same amount. So what to do? The simplest method is to assume, a priori, something about the nature of marginal costs in the industry; if they are constant, the the price patterns we saw in the numerical example can only be explained by monopoly/collusive behavior. But Bresnahan points out that we don’t even need to make this assumption. Just note that a rotation of the demand curve through some equilibrium point affects those with market power and those without differently. Since rotating the demand curve retains the P=MC equilibrium condition under perfect competition, such a rotation only affects equilibrium price and quantity if competition is not perfect. If I have, say, demand-side instruments, one of which only affects the y-intercept and one of which affects the slope (and perhaps also the intercept), then not only can I identify whether perfect competition exists, but I can even identify the degree to which behavior is monopolistic. Useful.
A Fine Theorem 