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This paper expands on the application of non‐linear programming to cover the equilibrium of a firm operating according to Islamic laws (Sharia). Islamic teachings impose certain constraints that have serious economic applications. Kuhn‐Tucker conditions reveal that the equilibrium of an Islamic firm is quite different from that of a traditional (non‐Islamic) firm. In particular, optimality of an Islamic firm will result in greater output and higher prices relative to those of its non‐Islamic counterpart.