On the relationship between historic cost, forward-looking cost and long run marginal cost

This paper considers a simple model where a firm must make sunk investments in long-lived assets in order to produce output, there are constant returns to scale within each period, and the replacement cost of assets is weakly falling over time. It is shown that, so long as demand is weakly increasing over time, a simple formula can be used to calculate the long run marginal cost of production each period and that the firm breaks even if prices are set equal to long run marginal cost. Furthermore, the formula for calculating long run marginal cost can be interpreted as either a formula for calculating forward looking cost (where the current cost of using assets is based on the current replacement cost of assets) or as a formula for calculating historic cost (where the current cost of using assets is based on the actual historic purchase cost of assets.) In particular, then, the paper identifies a set of circumstances in which traditional accounting rules that allocate the cost of purchasing assets across all periods that the assets will be used can be used to calculate the true long run marginal cost of production. The result has applications both to the theory of calculating efficient prices under cost-based regulation and to the theory of how for-profit firms use accounting data to organize and guide their decision-making.