Economic Analysis of Production Price Indexes.

• Author: Primont, Daniel
• Position: Review

By Franklin M. Fisher and Karl Shell.

Cambridge, UK: Cambridge University Press, 1998. Pp. xiii, 226. $59.95.

This is a sequel to Essay II in Fisher and Shell (1972). In the earlier work, the authors set out to find a measure of an output deflator that is grounded in the economic theory of production. All of the results in that essay pertained to the closed economy case, that is, the case in which the economy's production possibility frontier is specified for a given vector of inputs. This is an appropriate model for a national economy that is closed to trade for which the economy's input supply curves are vertical.

The purpose of this new volume is the extension to more general types of market structure. In the first two chapters, the authors provide a very nice overview of the subject. They begin with an extensive discussion of the definition of a production theoretic input price index and a production theoretic input quantity index. They adopt the view that once the input price index has been defined in a suitable way, the input quantity index should be defined implicitly by the property that the product of the relative price index and the relative quantity index should equal the relative expenditure index. This is often called the product test. Later, they adopt the same position with regard to the output price index and the output quantity index.

It should be pointed out that not every economist agrees with this point of view. The output price index used here is homogeneous of degree one in prices while the output quantity index is not necessarily. An alternative approach is to define the price and quantity indexes separately so that they are both homogeneous of degree one in the relevant variables. In general, however, the product test would not be satisfied. Thus, the construction of price and quantity indexes will always involve trade-offs between different desirable properties of the indexes. Fisher and Shell do make a good case for their approach. However, they only present results for the output and the input price index. They leave the properties of the implicitly defined quantity indexes for the reader to infer. Thus, even if one disagrees with their choice of the quantity index, this book stands on its own as a study of output and input price indexes.

One important extension in the current book is to the case of a fully open economy. The economy is fully open if all of the inputs are variable and can be purchased by the...