In this section, we characterize electricity trading after the completion of the electricity system reform. The post-reform retail market will be perfectly liberalized, and retailers will be able to price freely based on retail electricity load. Following Joskow and Tirole (
2006), we characterize the problem of a retailer assuming perfect competition as profit maximization under the restriction of consumer reservation utility:
$$\begin{aligned} \max _{\{p^{r}_{t}\forall t\;\mathrm{and}\; e\}}\sum _{i}\sum _{t}\left( p^{r}_{t}-p^{w}_{t}\right) q_{it}-C(Q,e)-F(e) \end{aligned}$$
(12)
s.t.
$$\begin{aligned} U_{}(q_{it})-p^{r}_{t}q_{it}\ge \bar{U}_{}\quad \forall t, \end{aligned}$$
(13)
where
\(\bar{U}_{}\) is the reservation utility level. The retailer can freely determine
\(p^{r}_{t}\) and
e provided the consumer’s utility does not become less than
\(\bar{U}_{}\). If this constraint is violated, the consumer will buy their electricity from other retailers who offer electricity with a more attractive tariff. Because Eq. (
13) is satisfied by equality at the optimum, the problem can be rearranged as
$$\begin{aligned} \max _{\{p^{r}_{t}\forall t\;\mathrm{and}\; e\}}\sum _{i}\sum _{t}\left( U_{}(q_{it})-\bar{U}_{}-p^{w}_{t}q_{it}\right) -C(Q,e)-F(e). \end{aligned}$$
(14)
The FOCs of this problem are
$$\begin{aligned} U'=p^{w}_{t}+C_{Q}\quad \forall t, \end{aligned}$$
(15)
$$\begin{aligned} -C_{e}=F_{e}. \end{aligned}$$
(16)
Consumers determine the electricity load so as to satisfy the condition that the marginal utility equals the electricity price, that is,
\(U'_{}=p^{r}_{t}\). Then, the equilibrium price and corresponding electricity load are
$$\begin{aligned} p^{r}_{t}=p^{w}_{t}+C_{Q},\quad q^{}_{it} =\theta _{it}D\left( p^{r}_{t}\right) . \end{aligned}$$
(17)
Firms in competitive market do not have an incentive to discriminate a retail price depending on consumer demand size, because price discrimination will give arbitrage opportunities to other retailers. Finally, the wholesale electricity price at time
t is determined by the market clearing condition for the wholesale electricity market. The reformed system equilibrium denoted by
\((p^{r*},p^{w*}_{t},q^{*}_{it},e^{*})\forall i,t,\) is determined from Eqs. (
11), (
15)–(
17) and is equivalent to the social optimum equilibrium. In contrast to the default system, the retail electricity price is determined by the marginal cost pricing and a retailer has an appropriate incentive to increase retail service efforts, thus maximizing social welfare.