you increase the quantity of the input while holding all other inputs constant, the marginal product is never negative in the empirically observed range since a rational firm would never increase an input to decrease output. Shapes of an Isoquant If the two inputs are perfect substitutes, the resulting isoquant map generated is represented in fig. A; with a given level of production Q3, input X can be replaced by input Y at an unchanging rate. The perfect substitute inputs do not experience decreasing marginal rates of return when they are substituted for each other in the production function. If the two inputs are perfect complements, the isoquant map takes the form of fig. B; with a level of production Q3, input X and input Y can only be combined efficiently in the certain ratio occurring at the kink in the isoquant. The firm will combine the two inputs in the required ratio to maximize profit. Isoquants are typically combined with isocost lines in order to solve a cost-minimization problem for given level of output. In the typical case shown in the top figure, with smoothly curved isoquants, a firm with fixed unit costs of the inputs will have isocost curves that are linear and downward sloped; any point of tangency between an isoquant and an isocost curve represents the cost-minimizing input combination for producing the output level associated with that isoquant. A line joining tangency points of isoquants and isocosts (with input prices held constant) is called the expansion path. Non convexity Under the assumption of declining marginal rate of technical substitution, and hence a positive and finite elasticity of substitution, the isoquant is convex to the origin. A locally nonconvex isoquant can occur if there are sufficiently strong returns to scale in one of the inputs. In this case, there is a negative elasticity of substitution - as the ratio of input A to input B increases, the marginal product of A relative to B increases rather than decreases. A nonconvex isoquant is prone to produce large and discontinuous changes in the price minimizing input mix in response to price changes. Consider for example the case where the isoquant is globally nonconvex, and the isocost curve is linear. In this case the minimum cost mix of inputs will be a corner solution, and include only one input (for example either input A or input B). The choice of