# Two views of applied welfare analysis: reply.

I. Introduction

My original article addressed the issue of an inconsistency between the popular Harberger welfare standard and an alternative standard that emphasizes the exhaustion of voluntary exchanges. I illustrated this inconsistency by showing that Harberger-optimal flat rate telephone prices may be unsustainable in a competitive environment.

Without addressing the general point I raised, the preceeding comment by David L. Kaserman, David M. Mandy, and John W. Mayo (KMM) |1~ uses a simple example to show that unsubsidized flat-rate telephone prices may be sustainable against entrants offering measured service. They further assert that a Harberger optimal self-selecting tariff structure will be sustainable against competition, thus resulting in no discrepancy between the Harberger and voluntary exchange maximizing view of economic welfare.

Their first assertion is dependent on the unique model used, and the second is incorrect once heterogeneity within the large customer group is recognized.

II. Firm-Fixed Costs: Plausible or Pathological?

KMM's example illustrating the sustainability of flat-rate pricing depends on the presence of firm-level fixed costs. These are long run costs incurred by a firm even if it has no customers or product. Contrary to their implication that the presence of any "positive firm-level fixed cost" makes Harberger-optimal flat-rate pricing sustainable, their example depends critically on the size of these costs and other special assumptions. Consider the following.

1. In the example used, firm-fixed costs make up 42.9% and 62.5% of total costs for the incumbent and entrant respectively. KMM offer no evidence on the realism of these assumptions. Intuitive empiricism and experience suggests that these percentages are high. In fact, since the presence of large firm-fixed costs imparts strong economies of scale, the co-existence of local telephone providers of widely different size argues against their importance.

2. Instead of having market size and firm-fixed costs fixed at 100 customers and $1000 respectively, let us analyse their model generally for N customers and $Z of firm-fixed costs. Consider their equation (7), which depicts the profits of a maximizing entrant attempting to attract only the incumbent's small customers with a measured service offering. Setting this equation equal to zero, yields

23N/9 - Z/3 = 0. (7|prime~)

Following KMM, let N = 100 and solve for the level of firm-fixed costs that will allow an entrant to just break even. The result is $766.67. Thus, anytime firm-fixed costs fall below $766.67--56.1% and 36.5% of the entrant's and incumbent's total costs respectively--the incumbent's flat-rate price will not be sustainable.

In fact, if the level of firm-fixed costs is below this level, the entrant does not have to serve all of the small subscribers to enter successfully. For example, if firm-fixed costs are as small as 24.2% of his costs--191.67, which does not seem unreasonable, the entrant can break even by serving only one-half (N/3) of the small customers.

3. Further, if we consider the more realistic case where the entrant can pick and choose the size and customer characteristics of the market to enter, he can do so successfully for any level of firm-fixed costs. Using (7|prime~) above, and like KMM let Z = $1000, we find that a market size of 130.4 customers will allow the entrant to enter successfully against the incumbent's flat-rate price.

Again, following KMM, set N = 100 and Z = $1000. If the entrant can find a market where 4/5ths of the 100 customers are small, rather than 2/3rds as KMM assume, he can enter successfully against a flat-rate price.(1)

4. Finally, when one further abstracts from the specific model employed, I believe KMM's point disintegrates entirely. It is not "an empirical question", as they argue.

The relevance of firm-fixed costs for an entrant holds only if entry is de novo. A more realistic case is one where a firm is established elsewhere, with firm-fixed costs either covered there or sunk, and enters new markets as a marginal addition to existing operations. In this case, firm-fixed costs are irrelevant. In terms of (7|prime~) above, if Z = 0 for both entrant and incumbent, flat-rate pricing is unsustainable for any sized market. And if the incumbent has firm-fixed costs covered by his flat-rate price, then the absence of such costs for an entrant makes flat-rate pricing unsustainable a fortiori.

III. The Sustainability of Flat-Rate Pricing

If some pricing structure is not sustainable against competition, then this structure cannot be exhausting voluntary exchanges. Thus, for some Harberger-optimal situation to also exhaust voluntary exchanges, it must be sustainable.

In the second part of their paper, KMM argue that a self-selecting, optional, multi-tariff structure that contains both a flat and measured option will yield net social benefits greater than that of either of the two options separately.(2)

However, this situation is stable and sustainable against competition only because KMM assume homogeneity within their large and small customer groups. This assumption allows subsidy-free and sustainable flat and measured tariffs to be tailored for the large and small groups respectively. This situation is like that analysed in the first part of my original paper |2, 342-44~ where all customers were the same. Here there is no cross-subsidy among the large customers that select the flat-rate price because they are all the same.

However, in the real world, there will be a continuum of customer sizes both within and between the large and small groups. Then, any chosen flat-rate price that eliminates the cross subsidy between the large and small groups must over-price the small relative to the large customers within the large customer group. These smaller, large, customers will then not choose the flat-rate price if given an option not to do so. Only if the flat-rate price is tailored to the smallest customer in the large group will that and larger customers choose the flat rate price. But if the flat-rate price is tailored exactly to just the smallest customer, it must underprice service to all larger customers in the large group. This, in turn means that the flat-rate price cannot be recovering the costs for the average large customer, and therefore is not subsidy free. Thus, a flat-rate option will be sustainable, even without competition, only if it is subsidized from somewhere.(3)

In short, looking at just the large customer group, the analysis reduces exactly to the situation of heterogeneous subscribers analysed in my original paper. Further, the situation analysed by KMM in the first part of their comment, and discussed above, is similarly relevant to the sustainability of flat-rate pricing for the large customer group.

Looked at another way, if the incumbent is able to arbitrarily divide customers into small and large groups, and not allow them to self-select, it will be possible for the incumbent to structure his flat and measured offerings so there is no subsidy between the small and large groups. However, in this case it will be impossible to eliminate the cross-subsidies inherent in a flat-rate price uniformly applied to all large, but heterogeneous, customers, thus opening the door to competition for these smaller, large customers.

Thus, with a continuum of customer sizes, it will either be impossible to design a stable, subsidy-free, self-selecting optional multi-tariff structure that contains a flat-rate price, or it will be impossible to design one that is sustainable against competition, even if it is Harberger optimal.

IV. Concluding Comment

We should not forget the general observation of my paper |2, 340-41, 347-48~. Harberger benefit/cost relationships are derived by aggregating benefits and costs across individuals. No matter how this relationship comes out, it is highly unlikely that benefits less costs will have the same sign for all individuals. Those whose benefit/cost relationship is the opposite of the aggregate result will be vulnerable to alternative, competitive provision if the Harberger-optimal alternative is implemented. That is, the Harberger-optimal outcome may not be sustainable to competition.

John T. Wenders University of Idaho Moscow, Idaho

1. Solving the KMM's equation |7~ for the entrant's break even point yields (N/2)|n.sup.2~ + ((19N/2) - Z)n - 10N = 0, where N is the size of the market, Z is firm-fixed costs, and 1/n is the fraction of N customers that are large. For N = 100 and Z = 1000, this equation becomes |n.sup.2~ - n - 20 = 0, for which the only positive solution is n = 5.

2. If this situation were stable and sustainable, it would further confirm my point that flat rate pricing for all customers is not sustainable.

3. Recall, following my original paper |2, fn 7~, that the analysis abstracts from the possibility that calls made under flat-rate service may be valued higher than those under measured service. If customers value flat-rate service higher due to the insurance against unexpected bills, or if they value measured calls lower because they perceive a "meter running", then this conclusion may not hold.

References

1. Mayo, John W., David L. Kaserman, and David M. Mandy, "Two Views of Applied Welfare Analysis: The Case of Local Telephone Service Pricing: Comment." Southern Economic Journal, April 1993.

2. Wenders, John T. "Two Views of Applied Welfare Analysis: The Case of Local Telephone Service Pricing." Southern Economic Journal, October 1990, 340-48.

My original article addressed the issue of an inconsistency between the popular Harberger welfare standard and an alternative standard that emphasizes the exhaustion of voluntary exchanges. I illustrated this inconsistency by showing that Harberger-optimal flat rate telephone prices may be unsustainable in a competitive environment.

Without addressing the general point I raised, the preceeding comment by David L. Kaserman, David M. Mandy, and John W. Mayo (KMM) |1~ uses a simple example to show that unsubsidized flat-rate telephone prices may be sustainable against entrants offering measured service. They further assert that a Harberger optimal self-selecting tariff structure will be sustainable against competition, thus resulting in no discrepancy between the Harberger and voluntary exchange maximizing view of economic welfare.

Their first assertion is dependent on the unique model used, and the second is incorrect once heterogeneity within the large customer group is recognized.

II. Firm-Fixed Costs: Plausible or Pathological?

KMM's example illustrating the sustainability of flat-rate pricing depends on the presence of firm-level fixed costs. These are long run costs incurred by a firm even if it has no customers or product. Contrary to their implication that the presence of any "positive firm-level fixed cost" makes Harberger-optimal flat-rate pricing sustainable, their example depends critically on the size of these costs and other special assumptions. Consider the following.

1. In the example used, firm-fixed costs make up 42.9% and 62.5% of total costs for the incumbent and entrant respectively. KMM offer no evidence on the realism of these assumptions. Intuitive empiricism and experience suggests that these percentages are high. In fact, since the presence of large firm-fixed costs imparts strong economies of scale, the co-existence of local telephone providers of widely different size argues against their importance.

2. Instead of having market size and firm-fixed costs fixed at 100 customers and $1000 respectively, let us analyse their model generally for N customers and $Z of firm-fixed costs. Consider their equation (7), which depicts the profits of a maximizing entrant attempting to attract only the incumbent's small customers with a measured service offering. Setting this equation equal to zero, yields

23N/9 - Z/3 = 0. (7|prime~)

Following KMM, let N = 100 and solve for the level of firm-fixed costs that will allow an entrant to just break even. The result is $766.67. Thus, anytime firm-fixed costs fall below $766.67--56.1% and 36.5% of the entrant's and incumbent's total costs respectively--the incumbent's flat-rate price will not be sustainable.

In fact, if the level of firm-fixed costs is below this level, the entrant does not have to serve all of the small subscribers to enter successfully. For example, if firm-fixed costs are as small as 24.2% of his costs--191.67, which does not seem unreasonable, the entrant can break even by serving only one-half (N/3) of the small customers.

3. Further, if we consider the more realistic case where the entrant can pick and choose the size and customer characteristics of the market to enter, he can do so successfully for any level of firm-fixed costs. Using (7|prime~) above, and like KMM let Z = $1000, we find that a market size of 130.4 customers will allow the entrant to enter successfully against the incumbent's flat-rate price.

Again, following KMM, set N = 100 and Z = $1000. If the entrant can find a market where 4/5ths of the 100 customers are small, rather than 2/3rds as KMM assume, he can enter successfully against a flat-rate price.(1)

4. Finally, when one further abstracts from the specific model employed, I believe KMM's point disintegrates entirely. It is not "an empirical question", as they argue.

The relevance of firm-fixed costs for an entrant holds only if entry is de novo. A more realistic case is one where a firm is established elsewhere, with firm-fixed costs either covered there or sunk, and enters new markets as a marginal addition to existing operations. In this case, firm-fixed costs are irrelevant. In terms of (7|prime~) above, if Z = 0 for both entrant and incumbent, flat-rate pricing is unsustainable for any sized market. And if the incumbent has firm-fixed costs covered by his flat-rate price, then the absence of such costs for an entrant makes flat-rate pricing unsustainable a fortiori.

III. The Sustainability of Flat-Rate Pricing

If some pricing structure is not sustainable against competition, then this structure cannot be exhausting voluntary exchanges. Thus, for some Harberger-optimal situation to also exhaust voluntary exchanges, it must be sustainable.

In the second part of their paper, KMM argue that a self-selecting, optional, multi-tariff structure that contains both a flat and measured option will yield net social benefits greater than that of either of the two options separately.(2)

However, this situation is stable and sustainable against competition only because KMM assume homogeneity within their large and small customer groups. This assumption allows subsidy-free and sustainable flat and measured tariffs to be tailored for the large and small groups respectively. This situation is like that analysed in the first part of my original paper |2, 342-44~ where all customers were the same. Here there is no cross-subsidy among the large customers that select the flat-rate price because they are all the same.

However, in the real world, there will be a continuum of customer sizes both within and between the large and small groups. Then, any chosen flat-rate price that eliminates the cross subsidy between the large and small groups must over-price the small relative to the large customers within the large customer group. These smaller, large, customers will then not choose the flat-rate price if given an option not to do so. Only if the flat-rate price is tailored to the smallest customer in the large group will that and larger customers choose the flat rate price. But if the flat-rate price is tailored exactly to just the smallest customer, it must underprice service to all larger customers in the large group. This, in turn means that the flat-rate price cannot be recovering the costs for the average large customer, and therefore is not subsidy free. Thus, a flat-rate option will be sustainable, even without competition, only if it is subsidized from somewhere.(3)

In short, looking at just the large customer group, the analysis reduces exactly to the situation of heterogeneous subscribers analysed in my original paper. Further, the situation analysed by KMM in the first part of their comment, and discussed above, is similarly relevant to the sustainability of flat-rate pricing for the large customer group.

Looked at another way, if the incumbent is able to arbitrarily divide customers into small and large groups, and not allow them to self-select, it will be possible for the incumbent to structure his flat and measured offerings so there is no subsidy between the small and large groups. However, in this case it will be impossible to eliminate the cross-subsidies inherent in a flat-rate price uniformly applied to all large, but heterogeneous, customers, thus opening the door to competition for these smaller, large customers.

Thus, with a continuum of customer sizes, it will either be impossible to design a stable, subsidy-free, self-selecting optional multi-tariff structure that contains a flat-rate price, or it will be impossible to design one that is sustainable against competition, even if it is Harberger optimal.

IV. Concluding Comment

We should not forget the general observation of my paper |2, 340-41, 347-48~. Harberger benefit/cost relationships are derived by aggregating benefits and costs across individuals. No matter how this relationship comes out, it is highly unlikely that benefits less costs will have the same sign for all individuals. Those whose benefit/cost relationship is the opposite of the aggregate result will be vulnerable to alternative, competitive provision if the Harberger-optimal alternative is implemented. That is, the Harberger-optimal outcome may not be sustainable to competition.

John T. Wenders University of Idaho Moscow, Idaho

1. Solving the KMM's equation |7~ for the entrant's break even point yields (N/2)|n.sup.2~ + ((19N/2) - Z)n - 10N = 0, where N is the size of the market, Z is firm-fixed costs, and 1/n is the fraction of N customers that are large. For N = 100 and Z = 1000, this equation becomes |n.sup.2~ - n - 20 = 0, for which the only positive solution is n = 5.

2. If this situation were stable and sustainable, it would further confirm my point that flat rate pricing for all customers is not sustainable.

3. Recall, following my original paper |2, fn 7~, that the analysis abstracts from the possibility that calls made under flat-rate service may be valued higher than those under measured service. If customers value flat-rate service higher due to the insurance against unexpected bills, or if they value measured calls lower because they perceive a "meter running", then this conclusion may not hold.

References

1. Mayo, John W., David L. Kaserman, and David M. Mandy, "Two Views of Applied Welfare Analysis: The Case of Local Telephone Service Pricing: Comment." Southern Economic Journal, April 1993.

2. Wenders, John T. "Two Views of Applied Welfare Analysis: The Case of Local Telephone Service Pricing." Southern Economic Journal, October 1990, 340-48.

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Title Annotation: | Communications; response to article by John W. Mayo, David L. Kaserman and David M. Mandy in this issue, p. 822 |
---|---|

Author: | Wenders, John T. |

Publication: | Southern Economic Journal |

Date: | Apr 1, 1993 |

Words: | 1527 |

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