7.3 Long-run cost estimation
Many of the basic aspects of cost estimation in the long run are similar to those
for the short run, thus the structure of this section is the same as for the previous
one.However, we shall see that there are some different types of constraints and
problems associated with the long run, that different mathematical forms are
Cost estimation 265
often used, and that the implications of empirical studies are of a different
nature.
7.3.1 Types of empirical study
As with short-run studies, empirical studies can be classified into time-series
and cross-section categories. These are now discussed separately, in terms of
the constraints and procedures involved.
a. Time-series studies
In this case it is necessary to use a time period that allows the firm or plant to
experience several changes in capacity; this is because the aim of such a study
is to estimate the effect on costs of these changes in capacity in terms of
economies and diseconomies of scale. We shall see that this creates some
serious problems for this type of study.
b. Cross-section studies
These involve collecting data from firms or plants of different sizes or scales. If
a firm-specific function is desired then this is only possible if the firm has
several plants, each producing the same product, involving the same stage of
the production process and using the same technology, but with the plants
being of different sizes. This constraint may make such a study impracticable,
since it may be that the long-run average cost curve is U-shaped, resulting in
only a certain plant size being efficient. In this situation it would not be
sensible for a firm to operate different plants with different capacities.
However, if a cross-section study is possible, it is generally preferable to a
time-series study, because the problems involved tend to be less serious.
These problems are now examined.
7.3.2 Problems in long-run cost estimation
Since the nature of these problems is different according to whether the study
is time-series or cross-sectional, it is again best to discuss these problems
separately.
a. Time-series studies
The main problem here is that, in order to allow the firm sufficient time to
change its capacity several times, such a long time period is involved that
technology also changes. It then becomes difficult to separate the effects of
increased scale from the effects of improved technology. The problem can
sometimes be overcome by the use of a dummy variable (or more than one
such variable) in the cost function to represent different levels of technology.
Another problem is that the firm may not be operating at maximum efficiency
with each plant size. It is always assumed in drawing the long-run
average cost curve as an envelope to the short-run curves that maximum