Distributing Overhead Costs: Implications for Rate Structures

Where the cost function for delivering a group of services is subadditive there will be substantial overhead costs that must be distributed among the various services provided. These overhead costs (such as costs for power plants, transmission lines, switching centers, pipelines) are also common costs--that is, these costs cannot be specifically attributed to one service or customer class but rather apply to all.

The distribution of common costs to various customer classes or services is a major determinant of rate levels. For example, the allocation of a disproportionate share of common costs to residential electric customers will, ceteris paribus, raise residential rates relative to commercial/industrial rates.

Fully Distributed Cost (FDC) Pricing

Consider a two-product natural monopolist that sells electricity to two classes of customers: (1) residential users; and (2) industrial users [Note that higher voltage electricity is sold to industrial users. Thus, we have distinct products as well as customer classes].

Electricity sold to residential users is denoted by X; electricity sold to industrial users is denoted by Y.

The cost functions are given by:

For X alone: C_X = 700 + 20X

For Y alone: C_Y = 600 + 20Y

To produce both: C_XY = 1050 + 20X + 20Y

Note that joint production of X and Y is subadditive. Joint fixed (or overhead costs) are equal to $1,050 whereas overhead costs associated with producing X and Y separately are $1,300.

The allocation of $1,050 in common costs to X and Y is necessarily arbitrary since these costs, by definition, cannot be explicitly attributed to the provision of either X or Y.

Example: Suppose we distribute 3/4 of common costs to X and 1/4 to Y. Hence FDC average costs would be given by:

AC_x = 787.5/X + 20

AC_Y= 262.5/Y + 20

At this point we need to specify demand functions for X and Y:

P_x = 100 - X

P_Y = 60 - 0.5Y

FDC prices are obtained by setting demand functions equal to average cost. That is, let

P_X = AC_Xand P_Y = AC_Y. The results are as follows:

X = 68.5; P_X= AC _X = $31.50

Y = 72.8; P_Y = AC_Y = $23.60

Notice that the prices of X and Y exceed marginal cost; therefore, these are inefficient prices in the sense of producing dead weight losses.

It turns out that the most efficient prices (that is, those which entail the smallest deadweight loss) can be found by using the Ramsey Pricing formula. For service X, for example:

P_X- MC_X/P_X= l /h _X

Note that h _Y> h_c

	Click here to view the graph
	P_X= $30; X = 70
	P_Y = $25; Y = 70
	Note that service X contributes $700 to common costs and service Y contributes $350, for a total of $1,050

Back to Lesson 12

ECON 4333 Links

ECON 4333 Page