Cost and Supply Curves

Abstract

In microeconomic theory we usually suppose that an individual firm has a production technology which can be characterized by a production function $\phi :{\mathrm{\Re}}_{+}^n\to {\mathrm{\Re}}_{+};$ where the quantity ϕ : (υ), for $\in {\mathrm{\Re}}_{+}^n,$ is interpreted as the maximum quantity of output which can be produced, given the vector of quantities of inputs, υ. Using the generic notation ‘x’ to denote the quantity of output, we also suppose that the firm’s revenue and cost are described by functions $R:{\mathrm{\Re}}_{+}\times P\to {\mathrm{\Re}}_{+}$ and $K:{\mathrm{\Re}}_{+}^n\times \Omega \to {\mathrm{\Re}}_{+},$ where: