The case of price differentiation over seasons

In order to simplify the exposition, we confine the analysis in this section to the case of differentiation in the prices of electricity and heat over seasons only. The year is divided into three periods: winter, spring/autumn and summer. The exact duration of these periods is defined by the high-voltage tariff (see Table 6.1 and Figure 6.1).

6.3.2.1 Prices and quantities.

Given the data assumptions presented above, we can determine the optimal prices of heat and electricity locally consumed by applying conditions (6.1) and (6.2).

Table 6.3. Prices, quantities and welfare gains when high-voltage electricity prices are differentiated over seasons.

Winter

* Locally consumed. f Purchase price

Prices, quantities and welfare gains for the three seasons are presented in Table 6.3. The initial prices refer to the actual prices for heat and electricity, where the price for heat is expressed in electricity terms.

Electricity prices are given for both the local and the national markets.

The total price refers to the joint products and is given by the sum of the prices for heat and electricity on the grid. Thus, for the winter season, SEK 340 + 171 = SEK 511.

The initial quantities are also listed. The quantities for heat are ex-pressed in electricity terms. As we assume that there will always be an equilibrium between production (supply) and consumption (demand) of heat, there is no reason to distinguish between these concepts. With regard to electricity, the locally demanded quantity is specified in the table. The difference between the initial quantity for heat and for local consumption of electricity is electricity sold to or bought from the grid.

For example, during the winter season, 154 - 83 = 71 MWh are sold each hour.

The optimal prices for the joint products are determined by the marginal cost or a higher value that gives an equilibrium at the existing capacity

limit. These prices have to be distributed between the two goods in order to obtain the optimal price for heat and the optimal price for electricity consumed locally. This kind of distribution must be carried out separate-ly for each season. As the price of electricity on the grid is exogenousseparate-ly given, the price for heat can be determined residually.

The optimal price of the joint products during the winter season is SEK 201, as the consumption level must be restricted to the existing produc-tion capacity of 250 MWh each hour. Thus, in this case there will be a scarcity rent of SEK 201 -164 = SEK 37 for this capacity. As the price of electricity sold on the grid is SEK 171, part of this scarcity rent is attributable to electricity (SEK 171 -164 = SEK 7). The remaining part of the scarcity rent for capacity determines the optimal price of heat, i.e., SEK 37 - 7 = SEK 30.

In the new equilibrium obtained after the optimal prices have been introduced, the amount of electricity sold to the grid has increased by 96 MWh each hour. This increase is equal to the increase in heat produc-tion/consumption; see Figure 6.2.

During spring/autumn, the optimal price of the joint product will be SEK 164, i.e., equal to the marginal cost. Since the price of electricity sold on the grid is SEK 129, the price of heat will be SEK 35. The corresponding optimal production quantity is 154 MWh each hour, which falls short of the existing capacity. The increase in the electricity sold to the grid is 56 MWh each hour; see Figure 6.3.

The difference between the spring/autumn and summer seasons is that in the former, electricity production exceeds local consumption, but in the latter, the reverse occurs. The balance is sold to the grid in spring/autumn while it is bought from the grid in summer. This explains why, in our example, the electricity price in summer is determined by the selling price on the grid and not by the purchase price as in spring/autumn and winter.

The optimal price structure over the seasons is specified in Table 6.3.

The optimal price for local electricity is highest in the winter (peak) season and lowest in the summer (extreme off-peak) season. However, the optimal price structure for heat reveals a reverse pattern, in spite of the similarity in load conditions. It is worthwhile observing that the prices for heat differ between spring/autumn and summer, although the capacity limit is not binding in any of these periods.

The net welfare gains per hour of switchingfrom the initial to the optimal prices are presented in Table 6.3 and illustrated in Figures 6.2,6.3 and

Price SEK/MWh A

201 164171

D

77//Y//////////////////,

96

Capacity limit

E30 7^

37

154 250 MWh Figure 6.2. Welfare gains during the winter season (20 weeks).

6.4. The welfare gains during the winter season consist of three parts.

In Figure 6.2, the first part, which is the consumers' surplus arising from reduction of heat net of the revenue decrease for the producer, cor-responds to the area ABC. The second part is the total scarcity value of the increase in heat production, which is given by the area BCDE. The third part, given by the area DEFG, is the total scarcity value of the increase in the quantity of electricity sold to the grid. These three parts combined can also be regarded as the total net willingness to pay for increased production of the joint products.

The welfare gains during spring/autumn and summer are illustrated in Figures 6.3 and 6.4. The decrease in the prices of heat and local electricity gives rise to two net consumers' surpluses in each season, one for heat and one for electricity. The area HIJ in Figure 6.3 is the surplus on the heat market in spring/autumn, whereas the area KLM is the surplus on the local electricity market. The corresponding surpluses during the summer are given by the areas NOP and QRS.

Given the duration of the various seasons, the annual net welfare gains can be calculated. These gains are presented in Table 6.4.

Price SEK/MWh 340

129

164121 129

K

Capacity limit

60 63.5 98 154 250 MWh Figure 6.3.Welfare gains during spring/autumn (14 weeks).

Table 6.4 Total annual net welfare gains (SEK million) Winter

Spring/autumn Summer

Total

42.1 11.1 5.4 58.6

Thus, substantial net welfare gains for our local community can be obtained by switching from the existing price structure to the optimal one. If this gain is related to the number of subscribers, it corresponds to around SBK1500 (approximately £150) per household connected to the district-heating network.

The changes in energy prices also give rise to a considerable transfer from the producer to the consumers amounting to SEK 270.2 million/year.

Such a revenue fall can cause a deficit problem. But an analysis of this effect is outside the scope of this chapter.