Friday, March 09, 2007

Sraffian Prices As Accounting Prices

I want to consider an issue raised by Andrew Kliman in chapter 6 of his new book. As part of his argument for the Temporal Single System Interpretation (TSSI) of Marx, Kliman considers a production period embedded in a discrete time sequence in which prices are changing over the sequence. He considers three cost concepts:
  • Historical cost: The sum of the costs over time of the capital goods used in production discounted to the start of the production period.
  • (Pre-production) reproduction cost: The cost, at the start of the production period, of producing the capital goods used as input into production.
  • (Post-production) replacement cost: The cost, at the end of the production period, of producing the capital goods needed to continue production in the next period.
If profits were evaluated at the end of the production period by comparing output prices to replacement costs, inputs and outputs would be evaluated at the same set of prices. On the other hand, if profits are evaluated at the end of the production period by comparing output prices to reproduction costs, the price of an output can differ from the input cost of that good. Kliman argues Sraffians (and others) argue that replacement costs, not historical costs, are the relevant costs for calculating profits. He argues that Sraffians are correct to argue that historical costs are irrelevant, and that Marx agreed. Kliman, however, thinks that Marx (correctly) calculates prices of production with reproduction costs, thereby allowing inputs and outputs to differ in price.

I don't want to argue here about how to read Marx. Rather, I want to offer an alternative interpretation of the single (simultaneous) set of prices characterized by Sraffa's price system - that of accounting prices at the start of the production period for a stock equilibrium (as opposed to a flow equilibrium).

As an example, consider, at the start of the production period, a fictional vertically-integrated firm that produces a net output of corn. The managers of the firm know various processes for producing corn from inputs of labor, iron, and corn. They also know various processes for producing iron from inputs of labor, iron, and corn. The firm is supposed to start the production period with a stock of iron and corn, in appropriate proportions to continue production. The firm is assumed to have already sold its net output of corn (to consumers?) produced in the last production period. How much should the managers of the firm, at the start of the production period, say their stock of iron and corn is worth?

Although I don't present the results in this way, one can read my 2005 paper as stepping through the mechanics of answering this question. Managers are assumed to know, at the start of the production period, the current market price of corn and the wage. My paper formulates a Linear Program in which firms maximize how much the value of the firm is incremented over the production period. This formulation requires a known price for iron, which I am asserting here can be a book price. The wage and price of corn pin down accounting prices such that managers will be willing to continue production of both corn and iron, thereby allowing the firm to continue in existence into the future. The decision variable in the dual Linear Program is the rate of profits which minimizes the value of the initial stock of inputs. Adopting a convention of using a single set of prices for inputs and outputs prohibits the accountants from using one method to manipulate that measure of profitability. Have I not now presented Sraffa’s prices as a method of deriving Kliman’s pre-production reproduction cost, the cost measure that he says Marx uses?

Depicting Sraffa prices as a stock equilbrium is not original with me. Keiran Sharpe (1999) says the same, albeit he starts with time indices and different prices for inputs and outputs. Sharpe sets his discussion in an evolutionary context, with the rate of profits as a measure of fitness. Sharpe, after having dropped the time indices, is still explicit that Sraffa is not assuming "constancy of prices over time".

I forget where I read this - probably in a paper by Kurz and Salvadori, but an early twentieth century Italian accounting manual was apparently one work Sraffa used as a mathematical aid when developing his system. This may be one reason why some who worry about computability and economics might find something worthwhile in Sraffa.


1 comment:

blackstone said...

Damn, i gotta pay to read this paper!? I want my hands on it.