The short run is a period of time in which the output can be increased or decreased by changing only the amount of variable factors such as labour, raw materials, chemicals, etc. In the short run the firm cannot build a new plant or abandon an old one. If the firm wants to increase output in the short run, it can only do so by using more labour and more raw materials. It cannot increase output in the short run by expanding the capacity of its existing plant or building a new plant with larger capacity. Long run, on the other hand, is defined as the period of time in which the quantities of all factors may be varied. All factors being variable in the long run, the fixed and variable factors dichotomy holds good only in the short run. In other words, it is that time-span in which all adjustments and changes are possible to realise.
Short run costs are those costs that can vary with the degree of utilisation of plant and other fixed factors. In other words, these costs relate to the variation in output, given plant capacity. Short run costs are therefore, of two types: fixed costs and variable costs. In the short run, fixed costs remain unchanged while variable costs fluctuate with output. Long run costs in contrast are costs that can vary with the size of the plant and with other facilities normally regarded as fixed in the short run. In fact, in the long run there are no fixed inputs and therefore, no fixed costs, i.e., all costs are variable.
Short Run Average Costs and Output
The cost concept is more frequently used both by businessmen and economists in the form of cost per unit or average cost rather than as totals. We, therefore pass on to the study of short run average cost curves.
Short Run Average Fixed Cost (AFC)
Average fixed cost is the total fixed cost divided by the number of units of output produced. Therefore,
AFC = TFC/Q
where Q represents the number of units of output produced.
Thus, average fixed cost is the fixed cost per unit of output. Since total fixed cost is a constant quantity, average fixed cost will steadily fall as output increases. Therefore, average fixed cost curve slopes downward throughout its length. As output increases, the total fixed cost spreads over more and more units and, therefore, average fixed cost becomes less and less.
Average Variable Cost (AVC)
Average variable cost is the total variable cost divided by the number of units of output produced. Therefore,
AVC = TVC/Q
Thus, average variable cost is the variable cost per unit of output.
We know that the total variable cost (TVC) at any output level consists of payments to the variable factors used to produce that output. Therefore TVC= P1V1 + P2V2 + …. Pn Vn where P is the unit price and V is the amount of the variable input. Average variable cost for a level of output (Q), given P is:
AVC =TVC/Q = PV /Q é= V/Q
The term V is the number of units of input divided by the number of units of output. Since the average product (AP) of an input is the total output divided by the number of units of input (V)
That is, average variable cost is the price of the input multiplied by the reciprocal of the average product of the input. We know that due to first increasing and then decreasing marginal returns to the variable input, average product initially rises, reaches a maximum and then declines. Since average variable cost is 1/AP, the average variable cost normally falls, reaches a minimum and then rises. It first declines and then rises for reasons similar to those operating in case of TVC.
Costs in the Long Run
The long run is a period of time during which the firm can vary all its inputs. None of the factors is fixed and all can be varied to expand output. Long run is a period of time sufficiently long to permit changes in the plant, that is, in capital equipment, machinery, land, etc., in order to expand or contract output. The long run cost of production is the least possible cost of production of producing any given level of output when all inputs are variable including the size of the plant. In the long run there is no fixed factor of production and hence there is no fixed cost.
If Q = f(L, K)
TC = L.PL + K.PK
Given factor prices and a specific production function, one can draw an expansion path which gives the least costs associated with various levels of output which in fact yields the long run total cost schedule/curve. LTC is an increasing function of output. The rates of change in these two variables are not known unless the qualitative relationship is quantified. If one recalls the concept of returns to scale and assumes fixed factor prices, one could see three things:
When returns to scale are increasing, inputs are increasing less than in proportion to increases in output. It follows that total cost also must be increasing less than in proportion to output. This relationship is shown in Figure 7.3(a).
When returns to scale are decreasing, total cost increases at a faster rate than does output. This relationship is shown in Figure 7.3(b).
When returns to scale are constant, total cost and output move in the same direction and same proportion. This is also shown in Figure 7.3(c).
Thus, depending upon the nature of returns to scale, there will be a relationship between LTC and output, given factor prices. It is generally found that most industries and firms reap increasing returns to scale to start with which are followed by constant returns to scale which give place to decreasing returns to scale eventually. In this case, the long run total cost function first would increase at a decreasing rate and then increase at an increasing rate as shown in Figure 7.4. Such a total cost function would be associated with a U-shaped long run average cost function.
From LTC curve we can derive the firm’s long run average cost (LAC) curve. LAC is the long run total cost (LTC) divided by the level of the output (Q). That is,
Similarly, from the LTC curve we can also derive the long run marginal cost (LMC) curve. This measures the change in LTC per unit change in output and is given by the slope of the LTC curve.