Long Run Costs and Cost curves

Long Run refers to the time frame over which all production process inputs can be changed (no inputs are fixed). There are neither fixed expenses nor fixed components in the long run. The costs and variables should all be flexible. The company can keep altering the size of the plant to find the best one that produces a certain unit of production for the least amount of money. The costs that are incurred over a long enough time horizon to allow for changes in all production factors are known as long-run costs.

TC = f ( Q, T, Pf ) where, TC = Total cost, Q = output, T = technology, Pf = Prices of factors. Long-term, a business can alter all of its inputs and the entire production scale.

Derivation of Long-Run Average Cost Curve (LAC)

When all elements are changeable, the long-term average cost is the cost per unit. The cost of manufacturing variables per unit over the long term makes up the long run average cost. It is the result of dividing the total quantity produced by the long-term total cost. It is the total of the producer's variable costs incurred while making the good. When all inputs have been changed, it shows the lowest cost of manufacturing at each level of output. When the company can switch from one plant to another, it is calculated by connecting all the pertinent points on the short run average cost curves. The lowest (unit) cost at which a corporation can achieve a specific amount of production is indicated by the LAC curve. By choosing a modest scale of the plant that minimizes its costs, a company tries to increase long-term profitability.

Assume there are three distinct facilities, each with a different output capacity, in a specific technological condition at a specific period. As follows:

• Small Plant (SAC1)
• Medium Plant (SAC2)
• Large Plant (SAC3)

Why is LAC U – shaped?

The function of long-term production is connected to LAC. Due to the action of the rules of returns to scale, LAC has a U-shaped slope. The average product rises while the average cost falls when growing returns to scale are in operation. When declining returns to scale apply, similarly. The average cost rises while the average product size shrinks. However, when economies of scale take hold, the average product stabilizes and the average cost declines. Due to the application of the rules of returns to scale, the LAC is U-shaped since the connection between the average product and the average cost is inverse.

Features of LAC

• Because of the rules of returns to scale, the LAC has a flatter U-shaped curve.
• Because it encompasses all of the short run cost curves, it is also known as the envelope curve.
• Tangent to the downwardly sloping segment of SAC is a section of LAC that slopes downward.
• When LAC is at its lowest point, SAC's lowest point is tangent to it.
• Tangent to the upwardly sloping segment of SAC is an upwardly sloping section of LAC.

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan