Traditional Theory of Costs: Long Run

Long-Run Costs of Production

In the long run, all factors of production are variable. All costs are variable costs. The firm can alter the size and scale of the plant to meet the changed market conditions. Therefore, there is LAC curve and LMC curve. Long-run costs are known as PLANNING COSTS, as the firm has to plan its future expansion of output. The long-run cost curves are subject to the law of returns to scale as the scale of production may undergo change.

1. Derivation of Long Run Cost Curve

The Long-run Average cost curve or the LAC curve is the locus of points denoting the least cost of producing different levels of output in the long run. It shows the minimum average costs of producing the corresponding output in the long-run.

The LAC curve is thus a planning curve that guides the firm in deciding on the most optimal size of the plant for producing a given level of output. An optimal-sized plant is one which enables the production of the output at the minimum costs per unit of output.

Given the technology, the firm is free to choose the plant size which entails the least cost. For example, if the firm decides to produce OQ1 level of output, then it will choose the plant size SAC2 and not SAC1.

If the demand for the firm’s output increases to OQ3, then the average costs start increasing along the plant SAC2, and the firm decides to set up a larger plant size SAC3, to minimize its average costs of production in the long-run.

The long-run average curve does not touch the short-run average cost curves on their minimum points. Graphically it can touch the minimum points of SACs only under constant returns to scale. In the phase of increasing returns to scale and decreasing cost, the LAC curve touches the SAC curves to the left of the minimum points of the SAC curves, and in the phase of diminishing returns, it touches the SAC curves to the right of their lowest point.

The LAC is, therefore, not the locus of the lowest points of SAC curves. The downward-sloping portion of LAC comprises of only increasing returns and diminishing cost portions of SAC curves.

The LAC curve is also known as the ‘Envelope curve’ as it envelops the short-run cost curves.

2. Long Run Marginal Cost Curve (LRMC)

It is the additional cost of producing an additional unit of output in the long-run. Both short-run MC curve and long-run MC curve refer to the change in total cost due to a unit change in output. The key difference is that LRMC is not attributable to just one or two variables/factors but to all inputs/factors.

In the short run, the firm maximizes its profit by equating short-run MR= MC. And in the long run, the firm maximizes profit by equating long-run MR=MC.

Long-run marginal cost shows the change in total cost consequent upon a small change in total output when the firm has adequate time to achieve the output changes by making the appropriate changes in the inputs/factors.

The only difference between SMC and LRMC is that while in the short run, the existing plant size is continued but in the long run, the plant itself is changed due change in output.

Since there is no fixed factor in the long-run, the law of diminishing marginal returns is irrelevant to the LRMC. In the long-run, marginal cost is affected by returns to scale- economies and diseconomies of scale.

3. Derivation of Long Run Marginal Cost Curve

Given the SAC and SMC curves and the LAC curves, we can derive the LRMC curve with the following steps:

1. By drawing perpendiculars from the tangency points A, B and C, which intersects the SMC curves at M1, M2 and M3.
2. Join the points M1, M2, M3, to obtain the LRMC curve.

Relationship Between Long Run Average Cost Curve (LAC) and Long Run Marginal Cost Curve (LRMC)

The relationship between LAC and LRMC is the same as it exists between the short-run average cost SAC and the SMC. LRMC lies below the LAC when LAC is falling and above it when LAC is rising. Thus LAC and LRMC intersect when LAC is the minimum.

Why is the Long Run Average Cost Curve (LAC) ‘U’ Shaped?

In the short run, the shape of the average cost curves essentially reflects the returns to a variable factor as determined by the law of variable proportions.

According to this law, as increasing amounts of the variable factor are added to the fixed factor, then in the initial stages of production, they yield increasing returns, but eventually, they yield diminishing returns.

This explains why per unit costs of production tend to fall initially and ultimately rise up when diminishing returns to the variable factor sets in. Thus, the shape of the SRAC curve is ‘U’ shaped.

The shape of the LAC is, however, explained by the ‘returns to scale’. Returns to scale refer to the change in “optimum cost of production” when the scale of the plant is changed and comprises of-

1. Constant returns to scale – when the successive plants have the same optimum cost
2. Diminishing returns to scale – when the optimum cost increases with an increase in scale
3. Increasing returns to scale – when the optimum cost decreases with an increase in scale

The term ‘returns to scale’ signifies two things-

• It reflects the technical relationship between inputs and output.
• It shows the changes in the cost of production due to non-technical reasons also.

These two traits manifest themselves in the form of economies & diseconomies of scale. The ‘U’ shape of the LAC curve is explained by the economies and diseconomies of scale. Economies mean lower per unit cost as output increases, and diseconomies are higher per unit cost as output increases.

Economies can be internal and external. Internal economies arise on account of the expansion of the firm itself. Internal economies arise due to specialization, choice of more suitable inputs, choice of technology, benefits of large-scale production, managerial and supervisory economies and so on. Internal diseconomies arise from exhaustion, difficulties in management, lack of accountability and work culture and so on.

External economies arise from external factors, and the firm has no role in it. External economies arise due to the expansion of technical knowledge, growth of ancillary industry, development of transport facilities, and availability of banking systems and so on. External diseconomies arise due to rises in wages, rise in input prices, pollution and so on.

In case of constant returns to scale, the LAC curve is parallel to the X- axis. The LAC curve is upward-sloping in case of diminishing returns to scale and downward-sloping in case of increasing returns to scale.

Thus, the LAC curve is initially downward sloping, parallel to the X-axis up to a point and then upward sloping. The returns to scale determine the shape of the LAC, given the external economies.

Limitations of Traditional Theory of Costs

The traditional theory of costs assumes that each plant is designed to produce optimally a single level of output. Additional production will come at increasing costs. Further, according to the traditional theory, the firm can switch over to a larger plant size only in the long-run and meet the demand at lower costs.

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