# Cost Curve & Relationship between LMC & SMC

Contents in the Article

Cost Curve: Nature, Relationship between LMC & SMC

1. ##### Total Cost-

Total cost, that is, the total amount that it costs the firm to produce increases in output is shown in Fig. It is clear from, the figure that (a) there is some positive fixed cost at zero level of output. So the total cost curve has a positive origin on the vertical axis and begins from point A. (b) It is also clear from the graph that total cost curve slopes continually upward to the right with increase in output. (c) The third property of short-run total cost curve is that it increases at varying rates in response to increase in output. It first increases at a decreasing rate and then begins to increase at an increasing rate as output goes on increasing. This corresponds to the behaviour of the law of proportions.

2. ##### Total Fixed Cost-

In the short period the firm does not have time to vary the quantities of fixed resources used, total fixed cost will therefore remain at a constant level regardless of the output produced, as given in Fig. The total fixed cost curve is parallel to the quantity axis A and lies above it by the amount of total fixed costs.

3. ##### Total Variable Cost-

Total variable cost stands at a different footing. It rises as the firm’s out-put increases. It is so because larger output needs larger capital and investment.

### Nature of Cost Curve in the Long Period

The long period is defined as a period of time which is sufficient to bring about proper changes in the scale of output through an adjustment of the quantity of the various factors employed. The quantity of all the factors can be increased or decreased according to the requirements of production. Thus, in the long-run all factors are variable. There is nothing like the fixed cost of production. In fact the long-run is “a series of alternative short-run situations into any one of which can move. The long- run may be compared with the action sequence of motion picture. If we stop the firm and look at a single picture we have a short-run concept”.

Since in the long-run, there would be no distinction between fixed and variable costs, we shall be interested only in long-run average cost curve (LAC) and long-run marginal cost curve (LMC).

#### Long-run Average Cost Curve or Envelope Curve

Long-run average cost refers to minimum possible per unit cost of producing different quantities of output in the long period.

Definition: In the words of Mansfield, “The long-run average cost curve is that curve which shows the minimum cost per unit of producing each output level. Corresponding to different scales of productivity.” It is determined by dividing long-run total cost by the quantity of output produced. It is the lowest average cost attainable when all inputs are variable; that is when any plant size can be constructed.

Let us elaborate this point with a simple example suppose there are three different plants available and for the sake of simplicity we name them as SACX, SACy and SACz. To produce say 1000 units of the commodity, average or per unit cost on SACx is say Rs. 200 while SACy it is Rs. 250 and on SACz is Rs. 320. But, to produce say 2000 units, average cost on plant SACY is Rs. 180 while it is Rs. 280 on SACz but Rs. 300 on SACx. Similarly, to produce say 3000 units, average cost is lowest on plant size SACy.

If the firm decides to produce 1000 units only. It is profitable to choose plant SACx where AC is lowest. However if decides later to produce 2000 units, it has the option to produce 2000 units on plant SACx or alternatively to choose plant SACy, where AC is Rs. 180.

Thus, each ‘Scale’ of operation indicated by this specific plant is represented by a separate average cost curve. Since this curve represents a single plant, it is a short run average cost curve. Thus, in our example there are three ‘scale’ of operation represented by three plants SACx, SACy and SACz. Hence there will be three short run average cost curve. Their positions and different cost of different output levels are shown in Fig.

In Figure 1,

1. If the firm wants to produce Q₁ level of output, it can produce average cost by choosing plant SACX.
2. Similarly, if the firm wants to produce a higher level output at Q2, he can choose plant SACy where AC is at C₂Q2. But it chooses to produce Q1 output on the earlier plant SACx, then AC will be higher at TQ₂.

It is clear that the firm will use plant SACx if the level of output is Q₁. However if it is Q₂ the firm will prefer to shift to a new plant SACy where per unit cost is lower.

Thus in the long run a producer or a firm has a choice in the selection and use of plant where it will select that where per unit cost is minimum at a given level of output.

Now suppose instead of just three plant sizes, there were many plants available, each capable for producing a different level of output. In such a case we shall be able to obtain the points of intersection of consecutive plants and obtain the LAC.

In Fig. the LAC is the locus of points representing the least unit cost of producing different outputs. The AC curve can, therefore, be defined as the lowest possible average cost of producing any output when the management has adequate time to make the desirable changes and adjustments. The LAC curve is sometimes called the ‘normal cost’ curve or the ‘planning’ curve of a firm. It is called the planning curve causes it enables a firm to plan its size.

Long-run average cost curve also defined as an ‘envelope’ curve, since it envelops all the short-run average cost curves. However, opinions differ as to this nomenclature of LAC-curves, Stonier and Hague observe: “In a sense the term ‘envelope’ is misleading. An envelope is physically distinct from the letter which it contains. But every point of an ‘envelope’ long-run cost curve is also a point on one of the short-run cost curves which it envelops”. The main features of the LAC curve may be observed as under:

1. By joining the loci of various plant curves relating to different operational short-run phases, the LAC curve is drawn as tangent curve.
2. The LAC is tangent to the whole set of SAC curves relevant for different plant sizes.
3. It touches the minimum of the SAC curves only in the special case of constant returns.
4. The LAC can never cut a SAC curve (though they are tangential to each other). This implies that for any given output, average cost cannot be higher in the long-run in the short-run.
5. LAC curve will touch the ‘optimum scale’ curve at the latter’s least-cost point.
6. LAC curve will touch SAC curves lying to the left of the optimum scale curve at the left of their least-cost points.
7. LAC curve will touch SAC curves lying at the right of the optimum scale curve at the right of their least-cost points.
8. LAC curve will also tend to be U-shaped just as the short-run average cost curve. But it will be less pronounced in U-shape and will be more flatter than short-run ones. This is because in the long run, such economies are possible as cannot be had in the short-run. Likewise, some of the diseconomies, which are faced in the short-run, may not be faced in the long-run.

#### Long Run Marginal Cost

Change in the total cost, in the long-run due to production of one more or one less unit of commodity is called long-run marginal cost.

Definition: In the words of Ferguson, “Long-run marginal cost is the addition to total cost attribute to an additional unit of output when all inputs are optionally adjusted.”

Long-run Marginal Cost (LMC) = Change in Long-run Total cost (∆LTC) / Change in output (∆Q)

### Relation between LMC and SMC

SMC refers to the effect on total cost due to the production of one more unit of output on account of change in variable factors. LMC refers to change in total cost due to production of one more or less unit of output due to change in all factors. We have already noted that in the long period all factors are variable. The long run marginal cost is derived from short run marginal costs, but does not envelope them. The long run marginal cost (LMC) must be equal to SMC for the output at which the corresponding SAC is tangent to the LAC.

Relation between LMC and LAC is also explained with the help of fig.

The behaviour of the LMC curve is shown in Fig. The LAC and LMC curves will behave in the same way as the SAC and SMC curves, i.e.,

1. So long as the LAC curve is falling the LMC curve will lie below the LAC curve.
2. So long as the LAC curve is rising, the LMC curve will be rising and will lie above it.
3. The LMC curve will intersect the LAC from below and at its minimum point. This property follows (i) and (ii) above.

#### Usefulness of LAC curves

The usefulness of LAC curve lies in its ability to assist the firm in the determination of the best size of the plant to be adopted for producing the given output. For outputs less than the low- cost combination at the optimum scale, that is, when the firm is operating subject to increasing returns to scale it is more economical to underuse a slightly larger plant operating at less than its minimum cost output than to overuse a smaller plant. Conversely, at outputs beyond the optimum level, that is, when the firm experiences decreasing returns to scale, it is more economical to overuse a slightly smaller plant than to underuse a slightly larger one.