Finance:Long-run cost curves

In microeconomic theory, a long-run cost curve is a cost curve (also known as a cost function) that relates costs to quantities of production when long-run decisions and actions can affect costs of production for a firm.

The principal functions (or 'curves') used in microeconomic analysis are:

• long-run total cost (LRTC) the fundamental cost function
• long-run average cost (LRAC), a per-unit normalization of LRTC
• long-run marginal cost (LRMC), the derivative of LRTC with respect to quantity

The idealized "long run" for a firm refers to when no time based restrictions on what inputs (such as the factors of production) a firm can employ in its production technology. For example, in the short run a firm is not able to build an additional factory, but in the long run this restriction no longer applies. Since forecasting introduces more complexity, it is typically assumed that the long run costs are based on the current technology, information, and prices the firm faces currently. The long run cost curve doesn't try to anticipate changes in how the firm, the technology, and the industry will look in the future – it just reflects how costs would be different if there were no constraints on what inputs can be changed in the current period.

An ideal cost curve assumes technical efficiency, since a firm always has an incentive to be as technically efficient as possible. In general, firms have a variety of methods of using various amounts of inputs, and they select the lowest total cost method for any given amount of output (quantity produced). For example, if you wanted to make a few pins, the cheapest way to accomplish this might be by hiring one jack-of-all-trades and buying a scrap of metal and having him work on it in your home. But if you wished to produce thousands of pins, the lowest total cost might be achieved by renting a factory, buying specialized equipment and hiring an assembly line of factory workers to perform specialized actions at each stage of producing the pin. In the short run, you might not have time to rent a factory, or buy specialized tools, or hire factory workers. Then you would be able to achieve short run minimum costs, but you know the long run costs would be much less. The increase in choices available of how to produce in the long run means that long run costs are always equal to or less than the short run costs, ceteris paribus.

The term curves doesn't necessarily mean the cost function has any curvature, however in many economic models it is assumed the cost curves are differentiable so that the LRMC is well defined. Traditionally, cost curves have quantity on the horizontal axis of the graph and cost on the vertical axis.