Duality with sector-specific externalities under social constant returns

We develop dual approaches to quantity and price relationships of production in a general multisectoral model with sector-specific externalities. The production of each good exhibits socially constant returns to scale but privately decreasing returns. We find that the Stolper-Samuelson theorem holds for factor intensity ranking from the social perspective and that the Rybczynski theorem holds for factor intensity ranking from the private perspective. The price-output dual fails to hold in general. Moreover, we re-establish the Heckscher-Ohlin theorem in the two-sector case, as well as the factor endowment-factor price and price-output comparative statics in the high-dimension case under proper conditions.