Electricity Trading in a Successive Oligopoly Market: A Social Welfare Comparison between the Generation and Retail Sectors’ Liberalization

This study models the electricity industry as a successive Cournot oligopoly market to compare the market performance between the generation and retail sectors’ liberalization. We show that, assuming identical fixed costs on free entry into both generation and retail sectors, liberalization of the retail sector can dominate that of the generation sector with regard to social welfare.


Figure 1. The Vertical Structure in the Electricity Market
This study undertakes an equilibrium analysis in the electricity market as a successive oligopoly and compares the market performance between the generation sector's liberalization and the retail sector's liberalization, which is a new field of research in the related literature. (Note 3) This study boldly regards liberalization as free entry to obtain simple and clear results.
The rest of this paper is organized as follows. In section 2, we introduce the models of the two types of liberalization for the generation sector and the retail sector. In section 3, we discuss the results. The last section concludes.

Liberalization of the Generation Sector
An important property of electricity-supplying structures is that the network sector, (Note 4) which lies between the generation and the retail sectors, usually receives the access price (Note 5) from the retail firms. Based on this principle, we construct the multiple-stage game as follows. In the first stage, the network sector determines the access price. In the second stage, (potential) generation firms observe know the access price and determine whether to enter the upstream market. In the third stage, the generation firm entrants compete in quantity. In the last stage, the retail firms, whose number is given, compete in quantity. Consumers buy the good distributed. (Note 6) The basic model is as follows. The reverse demand is given by where Q is total demand, and A is assumed to be sufficiently large. As for the generation firms, (Note 7) we assume that (i) the number is 1  m , which is determined endogenously through free entry, (ii) the marginal costs, which are identical among all the firms, are constant 0  c , and (iii) potential entrants bear the fixed costs of 0  G k . As for the network sector, its cost function is given by costs. As for retail firms, we assume that (i) n firms exist and (ii) each of them receives retail price p from consumers and pays access price a , and wholesale price w to the network sector.
Furthermore, we assume that retail firms bear no fixed costs.
Note that w is determined such that total quantity of generation equals total quantity of retail supply.
In other words, in equilibrium, w satisfies where i x and j q indicate the quantity of electricity generated by firm i and the quantity sold by retail firm j , respectively. Now, we solve the game by backward induction. In the retail firms' competition stage, firm j 's profit function is denoted as From the First-Order Conditions (FOCs) and the symmetry, we obtain the equilibrium quantity in this stage as follows: from the symmetry and substituting (3) into the right-hand side of it, we obtain the equilibrium wholesale price in this stage: Next, we consider the third stage. Substituting (4) into the generation firm i 's profit function, , and using the FOCs and the symmetry, we obtain Using (5), we obtain the equilibrium wholesale price and production as follows: We turn to the second stage. Substituting (5) and (6) into the profit function of a potential entrant to the generation sector,  Thus, the wholesale price and total demand under the endogenous number, using (8), are described as respectively.
Lastly, we turn to the first stage. As we assume that the network sector is a public firm rather than a private firm, we define its profit function as follows: (Note 10) Here, we obtain the following result.
). Otherwise, the network sector earns no profits.
Proof. First, from (11) and (13), the equilibrium profit of the network sector, * N  , is described as a function of  : This concave function can be positive when the first condition holds. Next, denoting 1  and 2  as As an extreme example that applies to Proposition 1, 0  F satisfies both conditions.

Liberalization of the Retail Sector
This subsection constructs the multiple-stage game as follows. In the first stage, the network sector determines the access price. In the second stage, the generation firm entrants, whose number is given, compete in quantity. In the third stage, the potential retail firms determine whether to enter the market; if they enter, each bears fixed costs R k . In the last stage, the retail firm entrants compete in quantity.
Consumers buy the electricity distributed. We solve this game by backward induction.
The basic assumption is the same as presented in the previous subsection. The solution in the last stage is the same as (3). Here, note that holds because we assume inner solutions. Next, we consider the free entry in the third stage.
Substituting (3) into the potential retail entrant's profit function, solving the free-entry condition, as the endogenous number of retail firms. Now, since the wholesale price is expressed as (4), substituting (16) into (4) yields From the condition of (15), we obtain as the equilibrium wholesale price in this stage.
We turn to the second stage. Substituting (17) Substituting this equation into (17), we obtain the equilibrium wholesale price in this stage as follows: Lastly, we turn to the first stage. Following the same procedure as in the previous subsection, we obtain the main values in equilibrium in this game: www.scholink.org/ojs/index.php/rem Research in Economics and Management Vol. 3, No. 4, 2018 T m m

Welfare Comparison
Our main interest is which of the retail or generation sector's liberalization yields higher welfare. Since this model holds four kinds of variables, the analysis is not easy. However, in reality, liberalization and technical revolution in generating and retailing will surely create sufficiently low entry costs, and hence, enough large entrants. In other words, as a strong but not impractical assumption, Since all the valuables are non-negative, the term S T  determines the sign. Here, imposing the other condition, The logic behind this result is simple. Under the dual conditions for the sunk costs and the number of players, both consumer surplus and producer surplus in retail firms' free entry exceed those in generation firms' free entry, so that social welfare under the former free entry dominates the latter free entry. This result implies that liberalization in the downstream sector, which is close to consumers, improves consumer welfare more strongly than the liberalization in the upstream sector does, which is disrupted by the bottleneck sector.

Conclusion
Three directions should refine future study. First, we should generalize the model. For instance, we should review the validity of the assumption behind the second proposition. Second, although we have simply compared the two types of successive oligopoly game, the model structures are different between the two. We must review the methodology for comparing and evaluating dual liberalization.