M.J. Kaiser r Energy Economics 22 2000 463]495 469
To understand the extent of the hardship and to provide a first-order analysis of this problem, a model which incorporates revenue and equity factors is developed.
The main task of this paper is to design an ‘optimal’ tariff that maximizes the revenue generation of the government while simultaneously maximizing the ‘equity’
of the designed tariff. This will lead us to precisely define the notion of an equity measure.
2. Survey methodology
A survey covering 250 households from Yerevan, Armenia, was obtained in personal interviews during July 1997 and provides the database for this study. One
major difficulty facing research on expenditure patterns is the availability of reliable data. The personal interviews were conducted by students, and although
time-consuming, provided for a small but accurate data set. Since the students tended to interview friends, relatives, and neighbors, however, the sampling can not
Ž be considered ‘random.’ The trade-off between collecting accurate data from a
. Ž
. biased sample set or deleting inaccurate data from unwilling participants is
believed to be evenly balanced in this study. The collected data included:
v
household income, size, and education;
v
type of energy carriers used by the household; and
v
consumption patterns of energy carriers. There are essentially two seasons in Armenia, summer and winter, and although
monthly data collected over an extended duration, aggregated, and averaged would provide an ideal statistical sample, for the purpose of this study data for 2 months
Ž .
was considered sufficient. Data for the months of July summer and January Ž
. winter were collected. For a complete analysis of the data, including Engel curve
computations and energy carrier patterns, the reader is referred to Kaiser. In the present work, only the data necessary to develop the tariff model is discussed.
2.1. Percentage of household income spent on electricity Histograms that represent the percentage of household income spent on electric-
ity is depicted for the summer and winter season in Figs. 1 and 2. The distributions Ž
. Ž
. are Lognormally distributed with parameters 8.8, 6.7 and 10, 7.3 , respectively,
i.e. an average of 8.8 and 10 of income is spent on electricity consumption. The discrepancy between these values and the estimated ‘average’ described in Section
1.2 can be attributed to a general decrease in electricity consumption, under-re- ported income, or more likely, a combination of these factors. Note that other
Ž .
energy sources are available to the consumer Table 3 , and in Armenia, the cross-price elasticity of substitute fuels play a significant role in the mix of fuel
types used by the population. The variability of the data is relatively high, and the Ž
absolute values of usage may seem quite comparable to Western standards as
M.J. Kaiser
r Energy
Economics 22
2000 463
] 495
470
Fig. 1. Histogram representing the percentage of household income spent on electricity during the summer season.
M.J. Kaiser
r Energy
Economics 22
2000 463
] 495
471
Fig. 2. Histogram representing the percentage of household income spent on electricity during the winter season.
M.J. Kaiser
r Energy
Economics 22
2000 463
] 495
472
Fig. 3. Histogram representing the average consumption pattern of electricity.
M.J. Kaiser r Energy Economics 22 2000 463]495 473
. discussed earlier, where expenditures typically range from 3 to 7 total income ,
but the situation is really of a completely different nature due to the wide disparity in average incomes, the distribution type and large standard deviation. Since the
distributions are Lognormally distributed with a large standard deviation, the area to the right of the average of these curves represent households who use a large
percentage of their income on electricity use.
2.2. Electricity consumption histogram Ž
The electricity consumption histogram describes the quantity of electricity in .
4
kWh consumed and serves as an estimate for the population density function. Survey data describes the amount of money spent on electricity consumption
Ž .
under the two-tier tariff rate in effect during data collection , and thus the data is Ž
processed in a reverse manner using the economic data coupled with the tariff .
structure to determine the quantity consumption pattern as shown in Fig. 3. The average amount of energy consumed during the summer and winter season is 246
kWh with a standard deviation of 200 kWh.
3. The design of optimal tariff rates
