Solution:

Short Run Cost Function:

• The short-run refers to that period within which a firm can vary its output by varying only the amount of variable factors, factors such as labor and raw material.

• In the short run period, the firm cannot alter the fixed factors such as capital equipment management personnel, the factory buildings, etc.

• Suppose a firm wants to increase production in the short run it can do so only by hiring more workers or buying and using more raw materials. In the short run, a firm cannot enlarge the size of the existing plant or build a new plant of a bigger capacity.

• Thus in the short run only variable factors can be varied while the fixed factors remain the same.

Short-run Fixed and Variable Costs:

• During the period, the prime costs relating to labor and raw material can be varied whereas the fixed costs remain the same.

• On the other hand, in the long period, even the fixed costs relating to plant and machinery, staff salaries, etc, can be varied. That is, in the long run, all costs are variable and no costs are fixed.

Short-run Cost Curve:

• Generally, in the short run, a firm will adjust output to demand by varying the variable factors. When the factors of production can be used in varying proportions, it means that the scale of operations of the firm can be changed.

• Each time the scale of operations is changed, a new short-run the curve will have to be drawn for the firm such as SAC‘ SAC and SAC in the next.

  

• Suppose, a firm has the short-run cost curve SAV''. In this case, the optimum will be OM''.

• When it wants to increase the output to OM in the short-run it can be obtained at the average cost M''L'' along with the short-run cost curve Sac: because in the short-run the scale of operation is fixed.

• On the other hand, in the long run, a new and bigger plant can be built on which OM'' is the optimum output.

• That is, the firm has now a short-run average cost curve SAC'', and by increasing the scale of its operations, the firm can produce the OM'' output at a cost of M''L'' instead of M''L''.

• It is evident from the above figure that at any scale of operations in the short-run, a firm will have regions of rising and falling costs.

• On the other hand, in the long run, the firm can produce on a completely short-run cost curve, and there will be an output where the average cost is minimum. This is the optimum output.

Long-Run Average Cost Curve:

• In the following diagram SAC‘, SAC'' and SAC''‘ refer to the short run cost curve corresponding to the different scales of operations.

• In the following situations the firm will be producing the desired output at the lowest cost.

• For example. OM output is produced at PM in the scale of operations represented by the curve SAC. OM will be produced on SAC, and so on.

  

• However, it is imperative that only in the long run the scale of operations can be altered; in the short run, it will be fixed and the average cost of output above or below the optimum level will necessarily rise along the short-run cost curve in question whether it will be SAC1, SAC2 and SAC3.

• A long-run average cost will show what is the long-run cost of producing each output. The short-run average cost curve SAC2 has a lower minimum point than either the curves SAC1, SAC2, and SAC3.

• The maximum output of the firm is obtained at OM. The long-run average cost curve LAC is a tangent to all the short-run cost curves. SAC1, SAC2, and SAC3. The LAC curve will, therefore, be U-shaped like the short-run cost curve. It will be flatter.

• That is why the long-run cost curve is called an Envelope because it envelops all the short-run cost curves.

• According to Dewitt and Varma, the cost curve, whether short-run or long-run is U-shaped because the cost of production first starts falling as output is increased owing to the various economies of scale.

• But after touching the lowest point at the optimum output level, it starts rising and goes on rising if production is continued beyond the optimum level. This makes a U-shape. The U-shape of the long-run cost curves is less pronounced.

• In other words, the long-run average costs are then the short-run curves. The longer the period to which the curve relates the less pronounced will be the U-shape of the curve.

• Over a long period, the size and organization of the firm can be altered to meet the changed conditions.