Since cost curves and supply curves derive from pro duction functions, it seems apparent that producer's surplus is to be traced by operating on the isoquant, or production indifference map. The K and L axes of the isoquant in Figure I measure respectively real units of capital and labor. If we relate this isoquant to the firm, its long-period cost curve (with unchanged factor prices) can be derived from the output path along OR which, for homogeneous production functions, is a ray through the origin. In order for the familiar U-shaped envelope curve to be generated it is necessary that along OR we first pass through an area of increasing returns to scale until we reach the isoproduct curve x0 after which we pass through an area of decreasing returns to scale. Once a plant size, say K0, is chosen by the firm, its short-period average inclusive cost, with minimum point at R0, can be derived from the output path K0K'0• The actual short-period expansion path, with labor the
To conclude, the area above the supply curve referred to as 'producer's surplus' may be used along with con sumer's surplus only for a particular type of supply used in partial equilibrium analysis; namely, that con structed for a period during which the output of the good in question can be increased only by adding to fixed-factors amounts of other factors that are imperfect substitutes for it but are perfectly elastic in supply with respect to their money prices. In such cases the rent of the fixed factor is exactly equal to the area above the supply curve under the conditions mentioned - zero . welfare effect and complete indifference to nonpecuniary advantages. The further we move from these conditions, especially the latter condition, the greater the divergence between the true rent (either compensating or equivalent variation) and the area in question. Provided price everywhere else is equal to social marginal cost the familiar qualitative tax-subsidy propositions, based on the geometry of consumer's and 'producer's surplus' , hold true even though the areas involved are generally only an approximation to the combined losses or gains.