Empirical Evidences on the Shape of Cost Curves

The importance of cost of production in determining the production decisions of producers points to the existence of so many empirical studies to prove the shape of cost curves. The whole theory of costs is based on the basic and fundamental concept of cost functions. The cost functions are derived from the technological relationships implied by the production function.

In fact, the theory of costs is a restatement of the theory of production in monetary terms. The shape of cost curves depends upon the time period, the type of industry, the economies and diseconomies of scale and so on. The shape of the long-run cost curves has been different under traditional cost theory and modern theory.

Since the process of production involves planning and constant vigilance, the producer aims at efficiency and maximizing gains. The Modern theory takes cognizance of ‘managerial and technological economies’ to explain constant returns to scale and, thus, the ‘L-Shaped long-run average cost curves.

Empirical Evidences

1. Statistical Cost Studies

Statistical cost studies are based on regression analysis to time-series and cross-section data. The procedure used in statistical cost studies begins once the data are collected by the researcher.

A linear function is fitted between cost-output observations.

C = b1X1 + u

Where,

C = total variable cost,

X = output

u = a random variable that absorbs all influences on costs by explicit factors that do not appear in the cost function.

This function implies that the AVC and the MC are constant at all levels of output (refers to the flat –stretch from e1 to e2 in fig-1 below, as propounded by the modern theory of costs)

MC = ∂C/∂X = b1

AVC = C/X = b1

With a higher output, C = b1 X + b2 X² + u, implying increasing AVC and MC at all levels of output

MC = ∂C/∂X = b1 + 2b2 X

AVC = C/X = b1 + b2 X

The empirical evidence from most statistical studies is that in the short-run, the AVC is constant over a considerable range of output, and in the long run, the AC is generally L-shaped.

The MC curve intersects the SAVC curve at its minimum point. Since the SAVC curve reaches its minimum point not at a single point but over the whole flat stretch e1e2, therefore the short-run marginal cost curve (SMC) coincides with the SAVC over the entire range of output corresponding to the flat stretch of the SAVC Curve.

For any output less than OX1, the SMC curve will lie below the Saucer-shaped SAVC curve, and for any output higher than OX2, the SMC curve will be above the SAVC curve. Thus, over the flat stretch pertaining to the Reserve Capacity, the short-run marginal cost curve coincides with the SAVC Curve.

The falling portions of the SAVC Curve show the reduction in costs due to better utilization of the fixed factors and the consequent rise in productivity of the variable factors. The rising portion of the SAVC Curve depicts the rise in costs on account of diminishing returns from the variable factor and also overutilization of the fixed factors. The SAVC Curve has a flat stretch over a range of output wherein the SAVC is equal to the short-run marginal cost, both being constant per unit of output.

The short-run Average cost curve continues to fall even over the range of output X1 and X2, corresponding to the flat stretch of the SAVC Curve where in SAVC is assumed to be constant. As Average cost consists of Average fixed cost and Average variable cost, and Average fixed cost continues to fall as the level of output increases.

Even after the Planned Reserve capacity is exhausted, the Short-run Average cost curve continues to decline despite the rise in SAVC because AFC continues to fall throughout. Eventually, the rise in short-run Average cost becomes greater than the fall in Average fixed cost, and the short-run Average cost starts to rise.

The SAC Curve is intersected at its lowest point by the short-run marginal cost curve as in the case of the traditional theory of costs. Beyond OX3 level of output, the SAVC Curve asymptotically approaches the short-run Average cost SAC since the gap between the two curves gradually diminishes on account of falling AFC but the two can never coincide because AFC cannot be zero.

2. Engineering Cost Studies

This method is based on the technical relationship between inputs and outputs. The cost function includes the cost of the optimal method of producing various levels of output. The L. Cookenboo’s study of the costs of operation of crude oil trunk lines employs the engineering method.

The first stage involves the estimation of the production function, where output is measured as barrels of crude oil per day, and the main inputs in a pipeline system are a pipe-diameter, horse-power of pumps, and a number of pumping stations. The second stage in the engineering method is the estimation of the cost curves from the production function.

Out of the various combinations of inputs to produce a given level of output, the least expensive combinations are chosen. The long-run cost curve is formed by the least-cost combinations of inputs for the production of each level of output.

The Cookenboo study concluded that the long-run costs fall continuously over the range of output covered by his study. However, it should be noted that engineering cost studies are mainly concerned with production costs and pay less attention to other costs.

3. Questionnaires Based Studies

A Questionnaire consists of a set of well-formulated questions to probe and obtain responses from respondents. Studies based on questionnaires where most of the firms reported that their costs would not increase in the long –run and also would remain constant over some period of time.

4. Statistical Studies of Production Function

According to the modern approach to the theory of costs, the long-run average costs essentially consist of production and managerial costs, and the average production costs continue to fall even at considerably large scales. The managerial costs per unit of output may rise only gradually, and that too at very large scales of output.

Further, a modern theory of costs proponents points out that such managerial diseconomies can be controlled by using improved knowledge of management sciences. Also, the technical and production economies of large-sized plants make the managerial diseconomies seem insignificant. Production costs tend to fall continuously with increases in output in the long run.

These costs fall steeply in the beginning and then gradually as the scale of production expands. This behaviour of the production costs is explained by the ‘Technical Economies’ of large-scale production. Most statistical studies of a production function, such as Cobb-Douglas production function and CES (Constant Elasticity of Substitution), reveal constant returns to scale when costs are constant over a certain range of output.

5. Survivor Technique

George Stigler developed this technique based on Charles Darwin’ Survival of the fittest doctrine. Stigler‘s study of the economics of scale of the steel industry of the USA concluded that small and large firms have high costs and are thus inefficient, but medium-sized firms constitute the optimum firms.

The basic idea of this technique is that competition between different sizes of firms will lead to the survival of the more efficient ones. There are certain assumptions on which the validity of the theory would depend-

1. The firms have the same objectives.
2. Firms operate in similar circumstances.
3. Prices of factors and the state of technology are constant.
4. The firms are operating in a competitive market structure.

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