The purpose of this paper is to show that the assumption of linear homogeneity of the neoclassical production function only leads to concavity at the two ends of the production contract curve. The other part of the curve may be either convex or concave to the diagonal, depending on the changes in the elasticities of substitution of factors of production. However, in the special case when the production functions are of the constant elasticity of substitution type, the contract curve will then be strictly concave. We also show that the concavity of the production possibility curve does not depend on that of the contract curve. Consider a simple closed model in which two commodities Y1 and Y2 are produced separately by two production sectors using labor (N) and capital (K): Y, = F(N1, K1), Y2 = G(N2, K2), where F and G are production functions with constant returns to scale, positive marginal productivities (Fi > 0, Gi > 0), and diminishing returns (Fjj < 0, Gjj < 0). If the factors are fully employed (N1 + N2 = N, K1 + K2 = K), the contract curve in the Edgeworth box diagram is given by