Do Subsidized Households Receive Low Quality Utility Services? Electricity Sector Cross-Subsidies in Colombia

Transcription

1 Do Subsidized Households Receive Low Quality Utility Services? Electricity Sector Cross-Subsidies in Colombia Fan Li Preliminary Version Abstract: Created in order to achieve equality in both consumption level and service quality, crosssubsidies are designed to encourage the utility consumption for the poor by charging higher prices to the rich to subsidize lower prices for the poor. In this paper, I develop a utility s profit maximization model incorporating the government transfers used to the subsidies, and then test the model s implications for the service quality. My model predicts that if a utility s deficit associated with crosssubsidies is fully covered by the government transfers, a utility will deliver identical service quality to different consumers; otherwise, a utility will create quality variation. My model also predicts that under a deficit, the production levels vary as the government transfers change. I test the prediction about quality variation using the Colombian electricity sector cross-subsidies as a case study. My ability to precisely identify subsidized consumers from the other consumers allows me to analyze the effects of the unfunded subsidy program on the perceived quality that is received by different consumers. By using an ordered probit model, I find that the utility tends to provide lower quality service to subsidized consumers, while providing higher quality service to surcharged consumers under a deficit; however, this quality variation can be partly mitigated by the government transfers. Keywords: electricity, cross-subsidies, quality, deficit JEL codes: L94, L98, H29, H31 Department of Economics, University of Florida. lifan51@ufl.edu. I am deeply indebted to invaluable guidance and comments from Sanford Berg, Steven Slutsky, Chunrong Ai, Jonathan Hamilton, David Sappington and Sarah Hamersma. I also thank Luis Hernando Gutiérrez and Juan Miguel for providing me with the data. Financial support from Public Utility Research Center is also gratefully acknowledged. All errors are the authors s.

2 1 Introduction Universal service has been an important theme in utilities service worldwide, which implies that not only should the poor be able to afford public utility service, but also service quality delivered to the poor should be equal to that delivered to the rich. The failure of either one will cause inequity. To achieve universal service, implicit subsidies to the poor customers are widely used to reduce the cost of consuming infrastructure services. Those subsidies need to be funded from either government transfer payments or the other utility customers. On one hand, the total value of subsidies presents a significant share of public expenditure, so funding subsidies is challenging in practice. For example, in India, water and sanitation subsidies have been estimated at $941 million per year in the mid- 1990s. On the other hand, when the financial losses associated with subsidizing customers are not fully covered, the utilities may be forced to reduce service expansion, system maintenance, and even utility supply, all of which run counter to the initial objective of subsidy. Accordingly, to guarantee the success of a utility subsidy, it is important to identify sustainable mechanisms for financing subsidies. In this paper, I estimate the negative effect on service quality of the cross-subsidies scheme, which is subject to an undependable funding mechanism. In particular, the Colombian electricity sector is used as an example to address this analysis. Under its cross-subsidies, utilities charge higher prices to one group of consumers to subsidize lower prices for another group. When a utility is not able to reach a balance on its own, the deficits should be covered by national government transfers. Although the Colombian funding mechanism is designed to achieve financial balance by itself, it ends up relying on undeniable fiscal transfers. I first develop a theoretical model of cross-subsidies that allows customers to pay different prices based on their income and allows a utility to vary service quality for different consumers. Here, consumer type is determined by whether a consumer pays a lower price, a standard price or a higher price for utility service. I also incorporate a binding maximum government transfer, which results in 2

3 different scenarios of profit maximum for a utility. Finally, I also allow an identical demand function across consumer types by adjusting utility prices. This is essential to the model, since an identical cost function associated with different quality levels can be derived based on this setting, which is used to compare service quality across consumer types. This analysis is conducted for both a benchmark case, where a utility has no deficit, and a more general case, where a utility has a deficit. In the benchmark case, the model predicts that a utility provides identical service quality across consumer types. However, in the more general case with a deficit, the result is different. The model provides prediction regarding the effects of the deficit on the aggregate production levels for each consumer type, as well as insights into its effects on the service quality across consumer types. First, it predicts that as compared with a high cap, if government sets a low cap for transfers, a utility tends to produce fewer products for subsidized consumers but produce more products for surcharged consumers. Second, it predicts that to limit losses, a utility creates quality variation across consumer types by providing higher quality service to surcharged consumers but providing lower quality service to subsidized consumers. This prediction is consistent regardless the change in the cap of government transfers. Finally, it predicts that government transfers could mitigate this quality variation. The Colombian electricity sector belongs to the general case where the government transfer only partly covers a utility s losses. To test the theoretical model, I evaluate the second and the third implication in my empirical work, although the first one is difficult to test empirically. Most past empirical evaluations of cross-subsidies similar to the Colombian utility sector have addressed the accuracy in terms of targeting the poor and the affordability with subsidy. This led researchers to focus the first consideration of universal service, which is if the subsidies make the poor able to afford public utility service. However, due to the difficulty in identifying consumer type in practice, the second consideration about equal quality service is ignored. This is the first empirical analysis of the service quality effects of unfunded subsidies. By applying the Colombian electricity sector as a case study where consumer type is identified through 3

4 his/her home address, I can divide consumers into the subsidized group, the standard group and the surcharged group, and then test if subsidized consumers receive lower quality service. I use demographic characteristics, consumer income and municipal infrastructure services to control for additional determinants of quality evaluation. Although my analysis is limited to the Colombian electricity sector, the Colombian leadership in utility subsidy reform efforts makes it an excellent setting for my study. I examine the effects of unfunded subsidies on service quality in two specific ways. First, I compare the perceived electricity quality across consumer types by estimating the effect of consume type on perceived quality. Second, I take into account the heterogeneous effects of government transfer on service quality and apply a similar comparison. I estimate these effects using an ordered probit model that allows me account for the discrete nature of quality evaluations. Finally, since my empirical results are subject to using subjective evaluations of electricity service quality as dependent variable, I apply a falsification test where I use perceived quality of garbage removal as dependent variable and repeat an identical estimation. By comparing results between them, I could control for additional determinants of quality variation, and reach a relatively objective conclusion given the lack of standard technical measurement of electricity quality. My empirical results highly support the theoretical prediction about service quality: under a deficit, the subsidized consumers receive lower quality services than the others. My estimates indicate 2.54 percentage point increase in the probability of receiving bad service quality for the consumers who receive the largest subsidy, as compared to the standard consumers. This effect is striking, since about 12.51% of such consumers report that they receive bad quality electricity as compared to 1.94% of standard consumers (the difference is 10.57%). This result suggests that a utility tends to create quality variation across consumer types, which causes the inequity of service quality even though the poor may afford public utility. In other words, suffering from an undependable funding mechanism, cross-subsidies end up with the poor paying a lower price for lower quality service, which is against the motivation of the subsidy programs. My estimates also suggest that with increase 4

5 in government transfers, perceived quality is improved for subsidized consumers but reduced for surcharged consumers. Accordingly, under a deficit, government transfers could mitigate the quality variation that is created by a utility. Therefore, to implement cross-subsidies, it is crucial to address the funding of subsidies. The remainder of the paper is organized as follows. Section 2 notes some key elements of the Colombia cross-subsidies and discusses the related studies. Section 3 describes a profit maximization model under cross-subsidies. After presenting the implication of the theoretical model, Section 4 describes the data I use to test them. Section 5 presents empirical methodology and results. Section 6 concludes with policy implications of these results and suggestions for future research. 2 The Colombian Utility Cross-subsidies System The goal of the Colombian cross-subsidy system is to provide affordable utility service to poor segments of society, and thus, facilitate the achievement of universal service. The Public Residential Services Law 142 and 143 of 1994 explicitly laid out the national cross-subsidy system and its geographic targeting scheme (Gόmez-Lobo and Contreras 2003, Medina et al. 2007). The scheme is applied in electricity, natural gas, telephone and water services. Unlike the other countries who evaluate the eligibility of subsidy recipients based on current socioeconomic circumstance of households, the Colombian system employs the residential dwelling as the only factor to tag the poor: a geographic targeting scheme. All residential dwellings in the country are divided into six strata from poor to rich, based on physical quality and surroundings of the dwellings, following the methodology provide by the National Planning Department. Households are eligible for subsidies of up to 50% of the average service cost if they live in dwellings classified as strata 1, up to 40% if they live in dwellings classified as strata 2, and up to 15% if they live in dwellings classified as strata 3. Households in strata 4 pay the cost recovery price. In principle, the system is designed to internally fund subsidies through surcharges. Households in strata 5 and 6 pay 5

6 surcharges that are no more than 20% of the cost recovery price. Industrial customers also pay a maximum of 20% of the cost recovery price. Under this geographic targeting system, utilities only need consumers home addresses to identify the subsidy recipients. Moreover, the dwellings of the identical strata are spatially connected and located in the same geographic areas. For example, two neighbors are usually identified as the identical strata. This makes utilities able to provide different service quality to dwellings across the strata depending on the network design and associated local maintenance outlays. Unlike the geographic targeting system, it is unreasonable for utilities to create quality variation across the strata under the targeting system that tags subsidized households based on their current socioeconomic circumstance. First, utilities may not be able to identify the subsidy recipients. Second, if one dwelling is identified as high strata while a close dwelling is identified as low strata, quality variation between these two dwellings is costly and technically difficult. Therefore, it is the unique geographic targeting system that creates the possibility for the quality variation across the strata, and also makes the Colombian case an excellent setting for my empirical study. Colombia applies decentralized administration in utility service. Municipal governments are required to create a balance account called Solidarity Fund in which the value of subsidies granted and the amount of surcharges are both registered. If utilities fail to balance subsidies through surcharges on their own customers, the difference can be financed by the transfers from public funds. From the Decentralisation Law No. 715 (2001), the regular earmarked transfers from the nation to districts are the most important source of public funds: providing 86% of district funds. In addition to finance the deficits between subsidies and surcharges, municipal governments are allowed to use the earmarked transfers to invest in utility assets. 1 In practice, most utilities fail to break even on revenues from system sales alone and highly depend on the transfers from public funds. However, it is also difficult for the national government to 1 Departamenta Nacional de Planeaciόn (2004) provides a description of the transfer from national to municipal governments. 6

7 deliver such a large amount of reimbursement to utilities as promised. Thus, the utilities suffer losses associated with subsidizing the poor. For example, the electricity sectors suffer structural losses which equal about 12 percent of turnover. The problem may be due to the socioeconomic composition of the customer base. In particular, the percentage of dwellings classified in the lower strata has increased significantly during in the last decade. Table 1 shows that from 1993 to 2003, the percentage of household eligible for the subsidy increased from 75% to 90.5%. Table 1 Percentage of Dwellings Classified as Strata 1, 2 and 3 Strata 1 Strata 2 Strata 3 Strata Source: World Bank 2004a; Gómez-Lobo and Contreras 2003 Many researchers have examined the Colombian utility cross subsidy scheme in terms of the first consideration of universal service (that is if the poor can afford public utility). For example, Gόmez- Lobo and Contreras (2003) compare the water subsidy policies between Chilean and Colombian schemes using relative concentration curves and show that Colombia geographical target scheme is less able to identify poor people than the means-tested scheme applied by Chile. Melendez (2004) and Fernandez (2004) assess the accuracy in targeting the poor of stratification and estimate that 51% of consumers that receive a tariff subsidy have an income that lies above the national poverty line but only 0.7% of the connected people with an income below the poverty line do not receive a tariff subsidy. Their findings suggest that in Colombia, most of the poor do receive subsidies and can afford the public utilities, which achieves the partly goal of universal service in terms of affordability. However, too many rich people also receive subsidies by taking advantage of this geographic target system, which explores the possible reason why there is a huge deficit in the subsidy account. Medina et al. (2007) find that most of subsidies end up being incorporated into the price of dwellings (that generates the subsidies) rather than going into the pockets of poor people. Their research indicates that the Colombian system fails even in terms of affordability, because despite electricity subsidies, households have to pay more for their dwellings. 7

8 Despite this research activity on affordability, there are few studies on whether the recipients of subsidized utility services receive low-quality service. INECON (2006) finds significant cash-flow deficiencies caused by the current cross-subsidy policy. The study concludes that it is mostly due to the socioeconomic composition of the customer base in Colombia. Although showing the existence of imbalance, this line of research does not focus on the effect of the deficit on utility service quality or network expansion. My research is similar to that of Ángel Gómez and Aguilera (2002) s study of drinking water sector in that the imbalance of subsidies system causes many service providers to show a low service quality with respect to continuity, pressure and flavor in drinking water sector. Focusing on the electricity sector, this paper examines the effect of deficit on perceived quality across the strata, which is related to the second consideration of universal service, equality of service quality between the rich and the poor. Intuitively, given the utility prices across the strata are regulated, to lower their losses by providing service to low-strata dwellings, utilities have an incentive to reduce the quality of electricity that offers to low-strata dwellings for two reasons. First, lowering quality can reduce the service cost. Second, poor-quality public utility can cause the customers to decrease their consumption amount, which results in the decline in a utility s losses. 3 Theoretical Model 3.1 Setup To simply the problem, I consider a model where a utility provides electricity service to three different types of consumers: subsidized consumers (type 1), standard consumers (type 2) and surcharged consumers (type 3). Consumer type is determined by whether the consumer receives a subsidy, pays a standard price or pays a surcharge for utility service. Under the cross-subsidies, governments set the standard price, the subsidy per consumption unit and the surcharge per unit, where, and are exogenous. Accordingly, the price charged by a utility to type consumers is, or respectively, where denotes consumer type. Besides paying different prices, consumers of different type differ in their incomes and the service quality that they receive. 8

9 Let denote the income of type consumers. It is reasonable to assume that. Armed with the ability to offer multiple levels of service quality and to identify consumer type, a utility could deliver different service quality across consumer types. Let denote the service quality that type consumers receive. The overall demand of each consumer type for electricity service will be denoted. Assume that the same type consumers have the identical individual demand, so, where denotes the number of type consumers. Assume that individual s demand is a linear function of quality, price and income, so for type consumers, individual s demand functions are given by, where,, are positive constants. Since and are exogenous and different across consumer types, consumers of different types have different demand functions. That is, given identical, varies across consumer types. In the model, and are not determined by utility firms. These three price instruments are chosen by government to either balance government s account associated with cross-subsidies or to ensure equality in terms of consumption level. For the first purpose, government can choose and such that. As a result, the government budget of cross-subsidies can be balanced as well as the utility firms subsidy account, so government does not need to reimburse utility firms. For the second purpose, the government could set and so that the positive income effect on demand is countervailed by the negative price effect on demand. Accordingly, consumers of different type have the identical demand for the same quality level. It is apparent that the value of the price instruments varies for these two purposes generally, so government cannot achieve both of them by choosing and. However, to achieve universal service, I assume that government will choose and to ensure equality of demand between the rich and the poor (the second purpose). Therefore, each individual s demand function can be written as given that is exogenous to the utility firms. Assume and, where the subscripts 9

10 denote partial derivatives. The inverse demand function is ) with, and. Hence, denote service quality for type consumers ( ). Since government does not choose and to balance its budget, a utility will incur losses associated with cross-subsidies,. To reimburse utilities, the earmarked government transfers from public funds are applied. The model will analyze a utility s rational behavior when a utility depends on the government transfers to balance its losses. As a benchmark, the case where transfers are just equal to a utility s losses will be studied at first. In this case, with transfers, a utility does not incur deficits. The paper then will discuss the more general case where the deficits still exist given insufficient transfers from government. Intuitively, on one hand, this can be due to a small cap on transfers. On the other hand, even if government sets a very high upper bound for transfers, a utility still has deficits if government only partial funds its losses. Formally, let the government transfers be, where multiplier. This implies that there are two limits for : and. To obtain the most government transfers, one of the limits has to be binding at least. Note that transfer payments are not determined by the productions that offer type 2 consumers, since they pay a standard price. However, transfer payments are related to the productions that provide to type 1 and type 3 consumers, because these productions affect the deficits. Assume constant variable returns to scale for the cost function. Let the aggregate cost for serving Type consumers be, where and. Using the inverse demand function, a utility s total cost of producing and of product is ( ). 3.2 Benchmark Case: A Utility Has No Deficit With Government Transfers To maximize profits, a utility could adjust production costs and consumer demands by providing multiple levels of service quality across consumer types. A utility s profit function is maximized with respect to the overall production level for each type consumers. Once the demand is determined, the corresponding quality level can be determined from the inverse demand function. 10

11 First, I discuss the benchmark case where a utility s losses,, are fully covered by government transfers, so. Formally, a utility s profit maximization problem is: ( ), where, and ( ), (1) for which the first order conditions are:, (2), (3). (4) By setting marginal cost equal to marginal revenue for serving each type consumers, the optimal demands can be solved. Specifically, the marginal cost of producing an additional unit of the product for type consumers is, where is determined by the demand function. This implies that for identical service quality, the marginal cost is identical across consumer types, so consumers of different types have the same marginal cost function. By applying this setup, the comparison of quality offered to different type consumers can be derived as follows. Substitute and ( ) into (2)-(4) yields. Since, the comparison among, and is shown in Proposition 1. 2 Proposition 1 If the government transfers fully cover a utility s deficits associated with crosssubsidies, a utility will deliver identical quality service to different type consumers. Proposition 1 show that equality in terms of service quality can be achieved if a utility s subsidy account is fully balanced by the government transfers. Intuitively, by offering service to subsidized 2 The proof of is in appendix. 11

12 consumers, a utility charges a low price, but the losses associated with this price discount can be countervailed by the same amount of reimburse per consumption unit from government. Analogously, by offering service to surcharged consumers, a utility charges a high price, but the additional marginal revenue is countervailed by the same amount of reduction in government transfers. As a result, the price distortion is completely mitigated by government transfers, so the marginal revenue is identical for providing service to different type consumers. By using the same structure cost function, a utility will offer identical quality service across consumer types. 3.3 General Case: A Utility Has A Deficit With Government Transfers Compared with the benchmark case, the more general case is that the government transfers only partly finance a utility s losses. Here, transfer payment is subject two limits: and. Formally, a utility s profit maximization problem is: ( ), where, and ( ). (5) It is clear that the profit function ( ) varies as the cap on the government transfers changes. Intuitively, if government sets a very low upper bound for transfers, then by producing more products for type 1 consumers, a utility incurs big losses since a small cap can just cover a very limited part of deficits. However, a very high upper bound of transfers will allow government to cover more deficits, so a utility is more flexible in determining the production levels. Thus, the problem will be solved for different ranges of. However, the ranges of relies on and, the unknown variables that need to be solved in the problem. To solve this circular problem, I first assume just one limit of transfer payment is binding. In particular, the binding limit and unbinding limit imply that, while the binding limit and unbinding limit imply that. I then define corresponding optimal aggregate productions respectively (Definition 1 and Definition 2) 12

13 for these two cases. After solving for, and, I compare the optimal productions between these two simple cases for each consumer type (Lemma1). Secondly, I consider the more complicated case, where both limits are binding,. Without solving it directly, I derive the general profit function as the range of changes. By comparing the optimum where one limit is binding with the potential optimum where both limits are binding, finally I could solve the maximum generally and find the bounds for. I summarize the solutions for different ranges of to the profit maximization problem with deficits (5) in Proposition Derive Optimal Production Levels First, I assume a small upper bound for the government transfers and solve for, and. Formally, if, rewrite the maximization problem: ( ) ( ), (6) for which the first order conditions are:, (7), (8), (9) where the marginal cost of producing an additional unit of the product for type consumers is. If, rewrite the maximization problem: ( ) (10) for which the first order condition are:, (11), (12). (13) 13

14 By setting marginal cost equal to marginal revenue of offering service to each type consumers, the optimal demands can be defined respectively in the following. Definition 1 Let,, be the unique optimum for (6) such that [ ( )],, and [ ( )], where. Definition 2 Let,, be the unique optimum for (10) such that [ ( )],, and [ ( )], where. According to Definition 1 and 2, the optimal solutions,,,, and can be solved independently of each other. Different from the benchmark case, the marginal revenue of offering service to different type consumers are different under both cases. Before comparing the corresponding quality level across consumer type, I will use these two definitions to solve the maximum generally. Lemma1 compares the optimal demand between these two cases for each consumer type respectively. Lemma 1, and. Lemma 1 shows that compared with, a utility tends to produce more products for type 1 consumers but produce less products for type 3 consumers where. It is clear that the transfer payment is different for these two cases. Specifically, if, while if. Related with transfer payments, the marginal revenue of offering service to type 1 consumers is higher where providing one more unit of such service, a utility is able to obtain its losses. Accordingly, a utility will produce more where, since by transfer payments to compensate. At the same time, the marginal revenue of offering service to type 3 consumers is less where, since by providing one more unit of such service, a utility loses transfer payments. As a result, a utility will produce less where. Moreover, the change in transfer payments does not affect 14

15 the marginal revue of offering service to type 2 consumers, so the optimum for should be the same for those two cases. Now I am ready to solve the more complicated case where, where both limits of the government transfers are binding. Without solving it directly, I derive a general profit function as changes. By doing this, I not only solve for, and generally, but also find the real bounds for. For any and satisfying, the profits function varies with even a small change in and. In particular, a small decrease in will cause a utility s profit function to become just like where, while a small increase in will cause a utility s profit function to become just like where. Therefore, to derive the general profit function, it is essential to compare the optimum for those three cases. I first define and for the third case and then solve for each of them respectively. Definition 3 Let satisfy the condition for a given. Let satisfy the condition for a given. Definition 3 specifies the production levels when both limits of the government transfers are binding. To solve the maximum generally, I will first solve for, and then solve for latter. Suppose and, by Definition 3,, so the critical value for can be solved to be. To simply notation, let and, which implies that profits depend only on given and. Using the critical values for, rewrite a utility s profits function generally with respect to : {. (14) To maximize this general profit function, it is straightforward to find the maximum from Definition 1 and Definition 2. However, those optimum may not satisfy the corresponding constraint in the profit function. For example, the maximum for is at. To make the optimum 15

16 for the profit function (14), must be hold, which may not be true. Therefore, to find the general optimum subject to the constraint associated with, I first compare and in Lemma 2, and then based on this I illustrate the general profit function (14) as the comparison among, and changes. Finally, I find the maximum generally. Lemma 2 if ; if ; and if. Proof. See Appendix 1. Lemma 2 compares profits with under three different regions of associated with. Following Lemma 2, the general optimum for is solved for three different relative values of compared with and. Note that the comparison between and in Lemma 1 simplifies the cases I need to discuss here. Case 1:, so. To satisfy Lemma 2, Figure 1 illustrates, and under Case 1. To maximize profits, a utility will set for any given value of and.the optimum is just the optimal solution for. Figure1. 16

17 Case 2:, so. To satisfying Lemma 2, Figure 2 illustrates, and under Case 2. To maximize profits, a utility will set for any given value of and. The optimum is just the optimal solution for. Figure 2. Case 3:, so. To satisfy Lemma 2, Figure 3 illustrates, and under Case 3. To maximize profits, a utility will set for any given value of and.the optimum may not be either the optimal solution for or the optimal solution for. Figure 3. 17

18 Lemma 3 To maximize profits, for any given, a utility will set if ; set if ; set if. Lemma 3 specifies the global optimum for given for three different regions of. The result is consistent with Lemma 1 such that the optimum is for a small, while the optimal is for a big. It is interesting to find out that when is over the moderate range, the optimal is (see Case 3), which is not either or. Under this case, and so and. This implies that either or may not be in the corresponding required region of to maximize the profits, for example, to maximize by setting, must satisfy. Figure 3 illustrates that increases at when and decreases at when, so maximize if. Next solve the optimum for generally. Suppose and, by Definition 3,, so the critical value for can be solved to be. To simply notation, let and. Using the critical values for, a utility s profits function with respect to is rewritten: { (15) Lemma 4 if ; if ; if. Proof. See Appendix 1. Lemma 4 compares profits with for three different regions of associated with. Following Lemma 4, the general optimum for is solved for three different relative values of Case 1:, so. To satisfy Lemma 4, Figure 4 illustrates, and under Case 1. To maximize profits, a utility will set for any given value of and. The optimum is just the optimal solution for. 18

19 Figure 4. Case 2:, so. To satisfy Lemma 4, Figure 5 illustrates, and under Case 2. To maximize profits, a utility will set for any given value of and. The optimum is just the optimal solution for. Figure 5. Case 3:, so. To satisfy Lemma 4, Figure 6 illustrates, and under Case 3. To maximize profits, a utility will set for any given value of and.the optimum may be not either the optimal solution for or the optimal solution for. 19

20 Figure 6. Lemma 5 To maximize profits, for any given, a utility will set if ; set if ; set if. Lemma 5 specifies the global optimum for under three difference regions of. It is consistent with Lemma 1 such that the optimum is for a big, while the optimum is for a small. It is also interesting to find out that when is over the moderate range, the optimum is (see Case 6), which is not either or. As Figure 2 illustrates, increases at when and decreases at when, so would maximize if. Now I have solved the optimum for and independently of each other for different regions of. Clearly, the optimal solution for such that is identical regardless the change in the regions of, but the optimal solutions for and are different across the regions. Next I will solve the optimal combination for (,, ) to maximize a utility s profits. Note that in the optimal combination, must be, so I only need to solve for and. After solving the optimal combination generally, I could find the bounds for. The general solution is that a utility will set, and if ; set, and if ; set, and if, where and. Proposition 2 To maximize profits, for a small upper bound of transfers, a utility will set a small and a big ; for a moderate upper bound of transfers, a utility will set a moderate and a 20

21 moderate for a large upper bound of transfers, a utility will set a big and a small. At the same time, is fixed regardless the change in the upper bound of transfers. Proof. See Appendix 1. Proposition 2 shows that the aggregate production levels that offer each consumer type vary as the region of changes. A utility tends to produce fewer products for type 1 consumers but produce more products for type 3 consumers under than under. It is clear that the transfer payment is different under these two cases. Intuitively, if government sets a very small upper bound for transfer payments, then a utility obtains transfer payment and has deficit. Accordingly, a utility may incur heavier deficit with a big and a small. However, if government sets a very large upper bound for transfer payments, then a utility obtains transfer payment and has deficit. Although the deficit may become heavier as increases and reduces too, but it is less than the former case. As a result, a utility could secure more profits by increasing and decreasing where, so and. Moreover, since the aggregate demand for type 2 consumer does not affect the transfer payments, the optimum for should remain the same as transfer payments change. The interesting case is where is in the moderate range (i.e.,. Under this case, a utility gets transfer payments, but the optimal production levels are not either of the above two case. To find the optimum for and if, a utility s profit maximization problem is: [ ( )] ( ) ( ) (16) (17) (18). (19) Solving this maximization problem provides Proposition 3. 21

22 Proposition 3 The unique optimal solution for and the unique optimal solution for satisfy [ ( )] [ ( )] and. Proof. See Appendix 1. Proposition 2 shows that there is a unique interior optimal solution for and if is in the moderate range (i.e.,. Such an optimum satisfies the conditions that the weighted marginal cost of serving type 1 consumers and serving type 3 consumers equals to the standard price. Besides this condition, the optimum is subject to the condition. That implies, if a utility produces one more unit product for either type 1 consumers or type 3 consumers, a utility s production for the other type consumers must increase too. As a result, the additional cost of producing one more unit product for either type 1 consumers or type 3 consumers is determined by the marginal cost of both of them. Accordingly, the optimum is solved by setting the weighted marginal cost between them equal to marginal revenue. This is different from the previous cases where the optimum is solved independently of each other Compare Quality That Received By Different Type Consumers After I solve the optimal production level for each type consumers, to compare with the benchmark case, it is interesting to check whether the service quality varies across consumer types. Although the optimal production levels vary as the region of changes, Proposition 4 shows that the comparisons of service quality are similar. Proposition 4 To maximize profits, if the transfer payment only partly covers the imbalance, then as compared to the standard consumers, a utility tends to deliver better quality service to the surcharged consumer but deliver lower quality service to subsidized consumers; if the transfer payment could fully cover the imbalance but is subject to the upper bound, then a utility has the same behavior as under. Proof. See Appendix 1. 22

23 Proposition 4 shows that suffering from deficits, a utility will create quality variation to maximize profits. Intuitively, if the transfer payment could only partly covers the imbalance, a utility incurs losses by providing electricity to subsidized consumers. Accordingly, a utility would reduce the service quality to those consumers for two reasons. First, a utility can lower production cost by reducing the service quality. Second, the demand of subsidized consumers would decrease as quality reduces, so a utility could reduce its deficits. At the same time, a utility has incentive to improve the quality to the subsidized consumers. By doing that, the demand of such consumers would increase, so a utility could obtain more surcharges to cover its deficits. If the transfer payment could fully cover the imbalance but it is subject to, a utility tends to create quality variation just like the case of deficits. From Proposition 3, the optimal solution and for is correlated with each other, since. This correlation causes that the optimum cannot be easily solved by setting the marginal revenue equal to the marginal cost for each type consumers. Comparison between Proposition 4 with Proposition 1 shows that to implement cross-subsidies, it is crucial for governments to address funding subsidies; otherwise, the policy will be unsuccessful in terms of inequality of the service quality. Now, it is interesting to look at how change in the transfer payments affects the quality variation under a deficit. Proposition 5 Under a deficit, if remains in the region (0,, then a small change in the transfer payments does not affect the quality variation; otherwise, an increase in the transfer payments could partly mitigate the quality variation across consumer types. Proof. See Appendix 1. Proposition 5 shows the heterogeneous effects of transfer payments on service quality across consumer types under a deficit. When the upper bound of the transfer payments is small, the optimal production levels do not depend on the transfer payments from Definition 1, so does the service quality that offers to each type consumers. Thus, a small change in the transfer payment does not 23

24 affect the quality variation if the change of transfer payment keeps the upper bound in the region. However, when the upper bound of the transfer payment is large such that, the optimal production levels rely on the transfer payments from Definition 2 and Proposition 3. Intuitively, as the transfer payment increases, a utility incurs fewer deficits. As a result, on one hand, a utility has a less incentive to reduce quality to the subsidized consumers to save its cost. On the other hand, a utility tends to use transfer payments to finance subsidies instead of using surcharges collected from type 3 consumers, so it has a less incentive to attract more consumption through improving service quality to those consumers. According to these two opposite effects, an increase in the transfer payments could partly mitigate the quality variation across consumer types. Moreover, if a big improvement in the transfer payments could move up the region of from, the quality variation across consumer types could be also mitigated. As mentioned earlier, to ensure equity in terms of consumption level, governments or regulators will set,, where and are positive constants. This implies, as type 1 consumers income increases, they receive fewer subsidies, while as type 3 consumers income increases, they pay more surcharges. Previous analysis showed that a utility tends to create quality variation across consumer types under a deficit. Two important factors that related to the deficit are subsidy per unit and surcharge per unit, which is determined by consumers income. Proposition 6 will show how the change in income affects service quality that consumers receive. Proposition 6 Under a deficit, service quality level for subsidized consumers is reduced as their income decreases. Proof. See Appendix 1. For subsidized consumer, the effect of their income on service quality that they receive is shown in Proposition 6. Intuitively, as subsidized consumer become poorer, they can receive more subsidies. As a result, by providing service to them, a utility incurs more losses under a deficit. Thus, a utility has incentive to reduce service quality to them as their income decreases. 24

25 For surcharged consumer, I also consider how change in income affects service quality they receive. Under or, service quality level is improved as their income increases. However, under, the optimal quality that offers to each type consumers dependents on the other type, which causes the ambiguity of the result. In the model, I assume that there is only one subtype of subsidized consumers and also only one subtype of surcharged consumers. To be consistent with my empirical work, it is interesting to check whether a utility will reduce quality by the same amount to each of them if there are multiple subtypes of subsidized consumers and each subtype differs in the subsidy per unit. It is also interesting to look at if a utility will improve quality by the same amount to each of them if there are multiple subtypes of surcharged consumers and each subtype differs in the surcharged per unit. Now assume that there are subtypes of subsidized consumers and each subtype receives the subsidy per unit, where denotes the subtype of subsidized consumers. Also assume that there are subtypes of subsidized consumers and each subtype pays surcharge per unit, where denotes the subtype of surcharged consumers. The maximization problem here can be solved analogously as before. Let denote and the optimums under ( ) and denote and the optimums under ( ). Proposition 6 shows the quality comparison among the subsidized consumers and among the surcharged consumers in these two cases respectively. Proposition 7 Under a deficit, if ( ) or ( ), service quality level for the subsidized consumers is reduced as subsidy per unit increases, while service quality level for the surcharged consumers is increased as surcharge per unit increases. 3 Proof. See Appendix 1. 3 Proposition 6 is derived based on the liner individual demand function that I assume at the beginning. If the individual demand function changes, the result in Proposition 5 may be changed. 25

26 Proposition 7 shows that under a deficit, a utility reduces service quality to each subtype of subsidized consumers by different amount, and also improves quality to each subtype of surcharged consumers by different amount. Intuitively, for the subsidized consumers who receive the largest subsidy, a utility will incur the most losses by providing them service under a deficit. Accordingly, a utility has incentive to reduce service quality to them by the largest amount. Analogously, for the surcharged consumers who pay the highest surcharge, a utility can collect the most funding by offering them service. As a result, a utility has incentive to improve service quality to them by the largest amount to attract consumption. This result is derived under ( ) or ( ), where the optimal productions for each type consumers can be solved independently of the other type. However, under ( ) ( ), the optimal production level for each type consumer dependents on the other type, which causes the ambiguity of the result. 3.4 Model Summary This profit maximization model incorporates the government transfers that used to finance a utility s deficit associated with cross-subsidies. A subsidy can benefit the poor by providing them price discount for utility consumption, which facilitates the achievement of universal service in terms of affordability. However, this positive effect will be countervailed by reduced service quality if a utility s deficit is only partly financed by government transfers. The model suggests that to limit losses of subsidizing the poor, a utility creates quality variation across consumer types by providing higher quality service to surcharged consumers but providing lower quality service to subsidized consumers. In this sense, the unfunded subsidy causes inequality of service quality, which is against the objective of universal service. The model provides two possible factors causing insufficient government transfers: the limited cap on the transfers and the limited quota. The changes in the nature of government transfers will affect the optimal production levels across consumer types, but under a 26

27 deficit, a utility will create quality variation regardless theses changes. Finally, the model highlights another factors that affects service quality, including consumers income, subsidy per unit and surcharge per unit. 4. Data I obtained data on perceived quality of electricity service from the Living Standard Measurement Survey (ECV: Encuesta de Calidad de Vida) in This survey also provides data about dwelling stratification, household demography characteristics and general living conditions. I combine this household-level data with three municipal-level datasets: the fiscal performance index in 2003, from which I obtained the overall government transfers from the nation to each municipality; the development index in 2003, which measures municipal socioeconomic condition and public facilities; and the 1993 population census, which is used to calculate the population density for each municipality. There can be multiple families living in one residential dwelling unit, so one dwelling has at least one family. The ECV survey asks demographic questions to each person living in the dwelling, including sex, age, education, income. In addition it asks questions about dwelling strata, housing conditions, and living satisfaction, answered by family heads. The observations are at the family level rather than at dwelling level, because each family in the same dwelling unit varies in terms of demographic factors and family characteristics, which may affect the family head s evaluation of electricity quality Dependent Variable: Perceived Electricity Quality The dependent variable, perceived electricity quality, is constructed based on the answers to the ECV survey question How was the quality of electricity service last month? The answers to this question captures the family head s evaluation of electricity quality, ranging from very bad, bad, regular, good, very good in the survey. These rankings are coded as 1=very bad, 2=bad, 4 When the models are re-estimated using dwelling-level observations, similar results are obtained. 27

28 3=regular, 4=good and 5=very good. To utilize perceived electricity quality reported by family head as the dependent variable, the observation is at family level rather than at household level. Overall, 1.5% of the family heads in the sample report that they receive very bad quality of electricity service, 4.8% of the family heads report bad quality of electricity service, 13.5% of family heads perceive regular quality of service, 77.5% of the family heads evaluate the service as good quality, and the rest of family heads report that they receive very good quality of electricity service. 4.2 Explanatory Variables The main explanatory variables are the following: dwelling stratification from Strata 1 to Strata 6 based on the geographical classification method of cross-subsidies; and government overall transfer payments from nation to each municipality. The expected signs for these factors are discussed as following Dwelling Stratification The ECV survey provides the data about dwelling characteristics from Strata 1to Strata 6, which is reported by family heads only. I drop 1172 observations from samples whose family heads either report the strata beyond the stratification possible range or do not report the strata. The stratification for each family living in the same dwellings should be identical, so I drop 2 dwellings from the sample because the family heads report different strata for the same dwellings. By offering utility service to the dwellings located in Strata 1, 2 and 3, the utility firms incur deficits because the prices they charge consumers are below the cost recovery price. The greater the discount provided to those dwellings, the more the utility lose. By offering utility service to dwellings located in Strata 5 and 6, the utility firms can collect surcharges because the prices exceed the average cost. When the system cannot achieve financial balance on its own, in principle, government transfer payments are supposed to reimburse the difference. However, in practice, the government does not fully reimburse utilities or delay their monetary transfers. To lower their deficit associated with crosssubsidies, utilities have incentives to reduce service quality to the dwellings in low strata. Moreover, 28