We use a New Empirical Industrial Organisation (NEIO) approach to estimate industry marketing margins for several Australian dairy products. Our model allows for differences in input- and outputmarket conjectural elasticities under the assumption of a fixed proportions production technology. Other assumptions on the production technology include the use of a single agricultural input to produce multiple outputs, and substitutability between agricultural and non-agricultural inputs. Two alternative methods are used to decompose the price of manufacturing milk into the prices of components used to produce different manufacturing milk products. We estimate margins equations for carton milk, wholemilk powder (WMP), butter, cheese and skim-milk powder (SMP) using state-level data. Nonlinear least squares is used to impose a number of inequality constraints implied by economic theory. The results suggest that, in price-deregulated markets, only three market intermediaries possess market power: carton milk retailers possess market power in output markets; carton milk processors possess market power in both input and output markets; and butter processors possess market power in input markets.