Question

i) What is fully distributed cost pricing? Derive fully distributed cost prices algebraically in linear market demand and costs system?

ii) Is there any better pricing scheme than fully distributed cost pricing? Explain.

Answer 1

i) Fully distributed costs are that costs which make every service pay for part of the historic cost. It is also known as fully allocated cost. As the name suggests, cost is completely allocated to every factor to which have service provided. This involves common cost - that is, these costs cannot be specifically attributed to one service or customer class but rather apply to all.

To figure it out algebraically, let us assume an market of 2 product natural monopolist of electricity to two class of customer - 1) residential users(X) and 2) industrial users(Y). The product varies as high voltage is supplied to industrial users.

Linear market demand are as follows : PX = 100 - X and PY = 60 - 0.5Y

Cost functions are given by : CX = 700 + 20X and CY = 600 + 20Y . Moreover, to produce both CXY = 1050 + 20X + 20Y

Note that joint fixed costs are 1050 as compare to individual ones(600+700 = 1300). The allocation of 1050 cost is allocative to both X and Y as this cannot be explicitly attributed to either X or Y. Suppose we distribute 3/4 of common costs to X and 1/4 to Y. Hence FDC average costs would be given by:

ACx = 787.5/X + 20 and ACY = 262.5/Y + 20

FDC prices are obtained by setting demand functions equal to average cost. That is, let
PX = ACX and PY = ACY. The results are as follows:

              X = 68.5; PX = AC X = $31.50 and    Y = 72.8; PY = ACY = $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. We know that the efficient pricing is those which entail smallest Dead weight loss(DWL).

ii) Ramsey pricing scheme is better formula to have efficient pricing. It's basic idea is to set prices on various service provided by the regulated firm such as to maximise social welfare subject to profit constraint. TR - TC = M , Total revenue - total cost = producer surplus, we need to maximise total surplus(consumer surplus + producer surplus) with subject to TR - TC = M .

By using lagrangian method, we can derive pricing of service as Pa - MCa/ Pa = /a where Pa = Price of service a ; MCa = Marginal cost of service a ; = constant ; a = elasticity of demand for service a.

For our example  PX - MCX/PX = /X , note elasticity of Y is greater than elasticity of X.

For PX = 30, X = 70 and for PY = 25, Y = 70.

Now service X contributes 700 to common costs and rest 350 will be paid by service Y, makes a total of 1050.