Fixed Input
A fixed input is an input whose quantity cannot be varied in the short run. Fixed inputs are distinguished from variable inputs, whose quantity can be adjusted. The distinction is central to the analysis of short-run production and of cost.
Definition
The fixed input is an input that is held constant in the short run. Capital, in the form of plant and equipment, is the classic example: a firm cannot easily change the size of its factory in response to a change in demand, so the factory is a fixed input in the short run.
The distinction between fixed and variable inputs depends on the time horizon. In the long run, all inputs are variable, since the firm can adjust all of them. The short run is defined as the period in which at least one input is fixed.
Short-Run Production
The presence of a fixed input gives rise to the law of diminishing returns. As more of the variable input is applied to the fixed input, the additional output eventually declines, because the fixed input becomes a constraint on production.
The law of diminishing returns is reflected in the shape of the short-run production function, which rises at a decreasing rate and eventually declines. It is also reflected in the shape of the short-run cost curves, which rise as output increases.
Short-Run Costs
The fixed input gives rise to fixed costs, which do not vary with output. The variable inputs give rise to variable costs, which do. The sum of the two is total cost.
The presence of fixed costs affects the relationship between average cost and marginal cost. Average fixed cost declines as output rises, since the same fixed cost is spread over more units. Average total cost therefore declines at first, as average fixed cost falls, and then rises, as diminishing returns raise average variable cost.
The minimum of the average total cost curve is the point at which the firm is producing at the lowest average cost, given the fixed input. The firm will produce at this point only if the price equals the minimum average cost, which is the condition for zero profit in the long run.
Implications for Firm Behaviour
The distinction between fixed and variable inputs has implications for the behaviour of the firm. In the short run, the firm will continue to produce as long as the price covers average variable cost, even if it does not cover average total cost, because the fixed cost must be paid regardless.
The firm will shut down in the short run if the price falls below average variable cost, since continuing to produce would add to its losses. In the long run, the firm will exit if the price falls below average total cost, since it can avoid the fixed cost by exiting.
The Short Run and the Long Run
The distinction between fixed and variable inputs defines the short run and the long run. The short run is the period in which at least one input is fixed, and the long run is the period in which all inputs are variable. The length of the period depends on the industry and on the input in question.
The distinction is analytical rather than chronological. A firm may be able to adjust some inputs quickly and others slowly. The short run for one input may be different from the short run for another.
The distinction matters for the analysis of the firm's response to changes in demand and in prices. In the short run, the firm can adjust only the variable inputs, so that its response is constrained. In the long run, it can adjust all inputs, so that its response is more complete.
Economies of Scale and the Long Run
In the long run, the firm can choose the scale of all its inputs, and the long-run average cost curve reflects the economies and diseconomies of scale. Over the range where the curve slopes down, the firm has economies of scale; over the range where it slopes up, it has diseconomies.
The shape of the long-run average cost curve determines the efficient scale of the firm and the structure of the industry. Where the curve is relatively flat over a wide range, many firms can operate efficiently, and competition can be sustained. Where it slopes down over a wide range, the industry tends towards concentration.
The long-run curve is the envelope of the short-run curves, each of which corresponds to a different level of the fixed input. The envelope is flatter than the individual curves, since the firm can choose the scale that minimises cost for each level of output.
Sunk Costs
Fixed inputs are often associated with sunk costs, which are costs that cannot be recovered if the firm exits. The distinction between fixed and sunk costs is important for the analysis of entry and exit.
A cost may be fixed in the short run, in the sense that it does not vary with output, without being sunk. For example, a payment for equipment that can be resold is fixed but not sunk. A cost is sunk if it cannot be recovered, for example expenditure on advertising or on research that has no resale value.
The presence of sunk costs affects the behaviour of firms. A firm with sunk costs will continue to operate as long as it covers its variable costs, even if it does not cover its total costs, since the sunk costs must be paid regardless. Sunk costs also deter entry, since a potential entrant must bear the cost without the assurance of recovering it.
Summary
The concept of a fixed input is central to the analysis of short-run production and cost, and it defines the distinction between the short run and the long run. Its implications for firm behaviour, for industry structure, and for the analysis of sunk costs inform the understanding of production.