The characterisation of the competitive equilibrium set as a smooth manifold using a differentiable approach is a major contribution in economic theory. While there is a detailed characterisation of the equilibrium manifold using differentiable topology and geometry, there are no worked example to illustrate the various properties that have been derived. This paper presents several examples, one with a globally unique equilibrium, and three where there can be multiplicity of equilibria. The algorithm to compute the equilibrium is given and can be used for other economies of interest
