Cost Curves In The Long-Run: LRAC and LRMC

Since, in the long run, all factors are variable; therefore there is only variable cost. In the long run, to increase the level of production, all factors have to be increased, and this results in the expansion of scale.

The relationship between Total, Average and marginal cost concepts is the same. In the long run, the relationship between LRMC and LRAC is the same as it exists in the short run. The derivation of TC, ATC and MC can be explained in the same manner as in the short run.

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 industrial 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 their right.

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.

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

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

Relationship Between LAC and LRMC

The relationship between LAC and LRMC is the same as it exists between the short-run average cost of 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.

In the long run, the plant size can be changed, while in the short run, the existing plant will continue to be used for producing larger output. Since, in the long run, all factors are variable, therefore, all costs of production are variable. There is no need to distinguish between fixed and variable costs.

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