The paper is concerned with wheat, however, there are some interesting parallels to dairy. The authors state, "the wheat milling industry is relatively concentrated, while there are a very large number of wheat-producing farms. Consequently, individual farmers have relatively little ability to negotiate effectively.
These factors are reflected in the organization of farmgate grain markets;
generally prices are set by buyers and farmers choose whether or not to accept the take-it-orleave-it offer." Sounds like dairy.
The authors conclude:
"This analysis demonstrates that market power might redistribute the benefits of government intervention. It provides empirical evidence that U.S. wheat millers were able to increase their marketing margins on average by approximately 10 percent when farmers received payments through a marketing loan program. This expected increase in margins was computed controlling for the realizations of a broad set of supply, demand and processor marginal costs shifters in those years. In turn, these findings suggest that millers are extracting a rent from the deficiency payment/marketing loan gain policy. Thus, the analysis suggests that the general assumption that competitive models may be a good approximation for imperfectly competitive agricultural markets does not necessarily hold, particularly if distribution, as well as efficiency, is a concern."
If you substitute milk for wheat and throw in the MILC payment, there should have been no surprise 2009 was Dean Foods most profitable year.