Maximum Variable Proportions for Inputs X and Y

The rational limits of substitution between Y and X occur where the isoquant slopes become positive.

additional units of X results in production of successively lower output quantities. For example, if the firm combines Y1 and X4, output is equal to Qj units. By reducing usage of X from X4 to X3, output can be increased from Qa to Q2. Only for input combinations lying between the ridge lines will both inputs have positive marginal products. It is here and along the negatively sloped portion of the isoquant that optimal input combinations are found.

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