Whereas polynomial functions tend to be the favoured form for short-run cost
functions, it has been seen in the previous chapter that, in the long run, power
functions are the favoured form. These can be expressed as follows (assuming a
single product firm):
C ¼ aQ b (7:14)
In this case we are using the symbol C for total costs, since in the long run there
is no distinction between total costs and variable costs; all costs are variable.
Alternatively, the cost function can be written in log-linear form:
ln C ¼ a0 þ b ln Q (7:15)
If a dummy variable is required to indicate a different level of technology this
equation can be expanded to:
ln C ¼ a0 þ b ln Q þ c T (7:16)
where T¼0 for the base technology and T¼1 for a newer technology.
Obviously additional dummy variables are necessary if there are more than
two different levels of technology.
The advantage of this power form, as we have again seen in the previous
chapter, is that it allows us to estimate cost elasticities, which in turn are an
indicator of the existence of economies or diseconomies of scale. The solved
problem SP7.2 involves this type of analysis, including the problem of allowing
for different technologies.