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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.

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.

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.

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,

LAC= LTC/Q

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.