McLelland

THE PROPOSITION:  Accounting information--as the term is commonly used--is not necessarily information at all, it is in general just data. Accounting data becomes information only after it is processed into information for input into a particular decision model.

I will prove the proposition informally through an interesting, special case.  There are a number of different special cases I could have chosen instead, and any one of the cases would show that in general the above proposition is true.  Theoretical purists won't like the unnecessary details in the analysis of the special case, but I want to make the informal proof more accessible to a wider audience.

The decision problem.  A labor union leader in negotiations with a manufacturing services firm must make a decision. Suppose the labor union has been offered a one-year contract for 120,000 labor hours of specific work skills in exchange for compensation equivalent to $40 per labor hour worked. Among other things the labor union leader’s problem is to determine whether the $40 hourly compensation is “fair” to union workers.

The labor union leader’s problem seems simple. She wants to determine whether the $40 per labor hour compensation under the proposed contract is greater than or equal to the (economic) value per labor hour provided to the employer. That is, her problem is to determine whether the offer is at least as good as the likely competitive market value per labor hour:

where the subscript in    is used to denote the employer. At present, her only piece of information is that the average competitive industry output market price for manufacturing services over the next year is $80 per manufacturing labor hour.

Useless competitor accounting data. Unfortunately, the union leader cannot observe market prices for similar labor skills (i.e., the competitive hourly labor wage rate, , for skills required under the proposed contract) unless she can obtain publicly-available financial statements of manufacturing services firms employing union workers with substantially equivalent labor skills. Ideally, she would be able to observe each comparable-skill-set-firm i’s average union labor wage rate per union labor hour  ,

but this kind of data is rarely if ever disclosed in publicly available financial statements since most firms consider this proprietary information about their production processes and methods. So, accounting data normally available from other firms employing union workers does the union leader no good.

Identifying the necessary information. It turns out that the value per labor hour depends on a number of factors including the market price for the specific labor skills required of the union workers, the technology (i.e., production methods) of the firm employing the union workers, and the average effort of the workers. To see this, write the employer’s operating profit function as

where p is the selling price per unit of output, y(x) is units of output as a function of labor hour inputs (x), w_e is the hourly wage rate, and oc represents all other operating costs of the firm which are assumed to be independent of labor hours. Without loss of generality, at least with respect to the proposition at issue, assume the employer’s (decreasing returns-to-scale) production function is

where k_e  is the production elasticity with respect to union labor. So, k_e measures the proportional change in production outputs relative to the proportional change in union labor inputs. Holding all else constant the employer maximizes the profit function shown above by choosing the optimal level of labor input hours, x*.

If the employer sells it services and purchases labor in competitive markets, it can be shown the optimal level of labor hours depends only on its labor productivity represented by the parameter k_e,

I will call the joint assumption that the employer maximizes profits by choosing x* given competitive market prices for labor and production output, The Assumption. Since the firm sells its output and purchases labor in competitive labor markets, the output selling price p and the hourly labor wage rate w (the market price of labor) do not depend on the employer’s actions and, so, do not include subscripts.

If The Assumption is reasonable it can be shown (Trust Me) that

where R represents revenues derived from the labor; i.e., its the aggregate output price of the labor.  The result is interesting: If The Assumption is true, then the employer’s production elasticity with respect to labor is observable through financial analysis. And, by the way, if she combines the production elasticity with respect to labor with the proposed terms of the labor contract, then she can estimate the likely competitive market value per labor hour after rearranging the optimal labor hour input expression above to get

Eureka.  Having done the analysis the labor union leader recognizes she can use the employer’s financial statements to estimate its labor production elasticity. For example, if labor productivity is stable over time (Another Assumption), then she could calculate a simple arithmetic average from quarterly, or perhaps monthly, financial statements available from the employer to estimate the production elasticity:

where t indexes time in terms of historical accounting periods. Then, simply substitute the estimate into the previous expression and evaluate the original decision problem:

Quod Erat Demonstrandum.  So … the example shows one simple, special case where accounting data is not useful at all until it is processed into information relevant to a specific decision model using microeconomic theory and (very simple) econometric methods.  It follows that The Proposition is, in general, true!