In standard microeconomic theory, short-run and long-run marginal costs are equal for production equipment with adjusted capacity. When the production of joint products from interdependent equipment is modeled with a linear program, this equality is no longer verified. The short-run marginal...

Linear programming is widely used by multiproduct oil-refining firms which minimize a refinery’s variable cost under a set of constraints. In addition to operating costs, this variable cost can include the cost associated with the refinery’s CO2 emissions. We suggest a quite general approach...