The production process involves the interaction of inputs, or factors of production, to produce output. The inputs are categorized as either fixed or variable, depending upon whether or not their input can be varied in the short run. By convention, and for graphical simplicity, we call all the variable inputs “labor” and all the fixed inputs “capital.” In a particular short-run period, with capital fixed at a given level, output can be varied by varying the input of labor. Output is positively related to input of the variable factors, except at high ratios of the variable inputs to the fixed inputs, when overcrowding of the workplace may cause total product to actually decrease. The total product curve, in its most general form, reflects output as a cubic function of the variable inputs, with marginal product rising at first and then falling. The law of diminishing returns in production, or more generally, the law of variable proportions, is evidenced by the behavior of the marginal product of the variable inputs.
The total variable cost (TVC) curve is derived from the total product (TP) curve by multiplying the variable inputs by their price per unit. Thus the shape of the TVC curve reflects the shape of the TP curve and the underlying increasing, constant, or diminishing returns to the variable factors. If the TP curve is a straight line, or a quadratic function, for example, then so too is the TVC curve. From the TVC curve we can derive the average variable cost (AVC) curve and the marginal cost (MC) curve. Adding total fixed cost (TFC) to TVC we find total cost (TC), from which we derive the short-run average cost (SAC). If production is a cubic function of the variable inputs,
the SAC, AVC, and MC curves will be U-shaped, and the MC curve will pass through the minimum point on both the SAC and the AVC curves.
The AVC and MC curves may be horizontal if there are constant returns to the variable inputs or if the fixed inputs are divisible such that the ratio of variable to fixed inputs can be held at the optimal ratio (where AVC is minimized). Other ways to avoid fluctuations in the value of AVC and MC include keeping the output rate constant and using inventories to accommodate fluctuations in demand, contracting out for production, and having customers wait when demand is unexpectedly or abnormally high.
The long-run average cost (LAC) curve is the envelope curve of all the short-run AC curves. Larger plant sizes are reflected by SAC curves lying further to the right. The LAC curve is the locus of minimum average cost of production when the firm is free to choose any size of plant. If plant size is continually adjustable, the LAC curve will be a smooth line, and the long-run marginal cost (LMC) curve will lie below LAC when it slopes downward to the right (economies of plant size) and lie above it when LAC slopes upward to the right (diseconomies of plant size). If there are several discretely different plant sizes, the LAC curve will comprise elongated sections (rather than simply points) from each of the underlying SAC curves, and it will exhibit kinks where costs would be reduced by changing to a new plant size.
The firm’s choice of plant size depends on its desired level of output. If demand is predictable with certainty, the plant size chosen is the one that allows the production of the quantity demanded at minimum average cost. If demand is uncertain, the plant size chosen is the one that minimizes the expected value of average cost, given the probability distribution formed by the meshing of the demand probabilities and the known cost values at each output level. Choosing plant size on this basis typically means that the firm builds in some excess capacity, which benefits the firm in case of market growth or successful competitive strategies that lead to sales gains at the expense of rivals.
The short-run cost curves of a particular plant, and thus the long-run cost curve as well, will shift downward if the firm benefits from reduced input prices, if it can spread some of its fixed costs over more than one plant through multiplant operation, or if the productivity of its inputs improves because of the learning effect.