Profit maximizing cost allocation for firms using cost-based pricing

This work develops a profit maximizing cost allocation scheme for firms that allocate all costs to their various outputs and then use these costs to set prices, a process known as fully-distributed cost-based pricing. If the costs incurred by the firm are not easily traced to a particular output (for example, the electric bill for a shared manufacturing plant), the costs must be allocated. The demand for a given output is assumed to be a function of the price. Hence, the cost allocation scheme that is selected will affect both the price and the demand for the output. The allocation of common costs that maximizes the firm’s overall profit under these conditions is identified. Frequently, the profit maximizing allocation allocates none of the untraceable common costs to one or more of the outputs. This allocation scheme stands in contrast to common practices of sharing costs equally or proportionally across outputs. Examples explore the implications of such a profit maximizing cost allocation on prices and demand in four scenarios: (i) no constraints, (ii) constraints on maximum allowable prices, (iii) a change in market size, and (iv) cost containment incentives.