The long-run efficiency of real-time electricity pricing.

• Author: Borenstein, Severin

Retail real-time pricing (RTP) of electricity--retail pricing that changes hourly to reflect the changing supply/demand balance--is very appealing to economists because it "sends the right price signals." Economic efficiency gains from RTP, however, are often confused with the short-term wealth transfers from producers to consumers that RTP can create. Abstracting from transfers, I focus on the long-run efficiency gains from adopting RTP in a competitive electricity market. Using simple simulations with realistic parameters, I demonstrate that the magnitude of efficiency gains from RTP is likely to be significant even if demand shows very little elasticity. I also show that "time-of-use" pricing, a simple peak and off-peak pricing system, is likely to capture a very small share of the efficiency gains that RTP offers.

1. INTRODUCTION

   Over the last few years, a great deal has been written about time-varying retail pricing of electricity. Many authors, myself included, have argued that real-time retail electricity pricing (RTP)--retail prices that change very frequently, e.g., hourly, to reflect changes in the market's supply/demand balance--is a critical component of an efficient restructured electricity market. During the California electricity crisis in 2000-2001, RTP boosters pointed out its value in reducing the ability of sellers to exercise market power. While nearly all economists have supported RTP conceptually, Ruff (2002) among others has argued that it is important to distinguish between RTP's long-run societal benefits and the short-run wealth transfers it might bring about. In particular, the reductions in market power primarily prevent a short-run wealth transfer from customers to generators, though the transfers can still be quite large.

   In this paper, I estimate the magnitude of the potential long-run societal gains from RTP, abstracting from market power issues and short-run wealth transfers in general. I do this by formulating a model of competitive electricity generation with demand and production costs based on actual data from U.S. markets. I solve computationally for the model's long-run competitive equilibrium, with the results indicating the amount of each possible type of capacity that would be built, the prices that would be charged to customers on RTP and on flat-rate service, and the total social surplus that would be generated by the system. The model also allows estimation of the transfers that would occur among customers if customers on RTP had demands that were (absent RTP) peakier or flatter than customers not on RTP.

   The estimates indicate that RTP would substantially reduce peak electricity production and thereby reduce the use of low-capital-cost/high-variable-cost peaker generation. The social gains from RTP for at least the largest customers in the system are estimated to far outweigh reasonable estimates of the metering cost. The magnitudes of the social gain are sensitive to the demand elasticity that is assumed, but the results indicate that even with quite small elasticities, the benefits are substantial.

   Section 2 presents the economic model that is the basis for simulations. Section 3 explains the data used in the simulations and the process used to compute long-run equilibria. The results of the simulations are presented and their implications discussed in Section 4. In section 5, I carry out a similar analysis on a much simpler pricing system, time-of-use (TOU) pricing, in which there are simple peak and off-peak periods, with the prices differing between periods, but being held constant for months or even years at a time. Section 6 discusses a number of factors that are omitted from the simulations and suggests how those factors are likely to affect the results. I conclude in Section 7.

2. LONG-RUN COMPETITION IN ELECTRICITY MARKETS

   The model that is the basis for the simulations is adapted from Borenstein and Holland (revised 2003, hereafter BH). (1) It assumes a simple competitive wholesale and retail market structure. The retail structure is identified only by the way in which it charges end-use customers for electricity, using a flat rate or RTP. The price(s) charged to each group allow the retailer to exactly break even on service to that group. As in BH, this reflects the outcome of competition among many retail providers, but it also could be interpreted as a single regulated retail provider that is required to exactly cover its costs and required not to cross-subsidize between flat-rate and RTP customers. Following BH, I assume for simplicity that retailers have no other transaction costs.

   I assume free-entry of generators of three different types. Generation exhibits no scale economies, with each generation unit having a capacity of one megawatt. The types of generation differ in their fixed and variable costs, higher fixed costs being associated with lower marginal cost of production. For generator type j, annual generator costs are modeled as a fixed cost plus variable costs that are linear in the number of megawatt-hours produced during the year, T[C.sub.j] = [F.sub.j] + [m.sub.j] x M[Wh.sub.j]. Startup costs and restrictions on ramping are not considered, an issue discussed in section 6. Parameters used for this and all other aspects of the simulations are discussed in the next section.

   Demand is modeled as constant elasticity, using a range of possible elasticities. Within any one simulation, demand is first assumed to have the same elasticity in all hours. I then consider the effect of demand elasticity varying positively or negatively with the level of demand. The level of demand in each hour is taken from the distribution based on the actual levels of demand in various US electricity regions, as explained in the following section. Cross-elasticities across hours are assumed to be zero, another issue discussed in section 6.

   Some proportion of customers, α, are on real-time pricing, and the remainder are on flat-rate service. I assume that all customers have identical demand up to a scale parameter. Thus, following BH, if the total demand in hour h is [D.sub.h]([p.sub.h]) and the flat-rate service customers are charged [bar.p] in every hour, the wholesale demand is

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

   In this case, demand is modeled as constant elasticity, [D.sub.h]([p.sub.h]) = [A.sub.h] x [p.sup.ζ.sub.h].

   Under these assumptions, for any set of installed baseload, mid-merit, and peaker capacity, [K.sub.b], [K.sub.m], [K.sub.p], there is a unique market-clearing wholesale price in each hour, provided that total installed capacity exceeds demand from flat-rate customers in every hour, [K.sub.b] + [K.sub.m] + [K.sub.p] > (1 - α) x [D.sub.h] ([bar.p]) ∀h. In the following section, I discuss the algorithm for finding the short-run equilibrium for any set of installed capacity and the long-run equilibrium allowing capacity to vary. In presenting the algorithm, I demonstrate that there is a unique long-run equilibrium.

   In addition to establishing long-run equilibria for any 0 = α ≤ 1, it will be important, as a baseline, to determine an equilibrium with no customers on RTP. The model above is not applicable to a market with no RTP customers, because without RTP there is no short-run demand elasticity, so in order to meet demand in all hours, sufficient capacity must be built so that the market always clears "on the supply side," i.e., at a price no greater than the marginal generation cost of the technology with the highest marginal cost. Such an organization requires some sort of additional wholesale payment to generation in order to assure that demand does not exceed supply in any period and, at the same time, that generators' revenues exceed their variable costs over a year by an amount sufficient to cover their fixed costs.

   It is straightforward to show that the annual capacity payment that assures sufficient generation and the optimal mix of generation is equal to the annual fixed costs of a unit of peaker capacity. To avoid distorting the mix of capacity, this payment is made to all units of capacity, regardless of type. (2) The payment is financed by increasing the price of the flat-rate electricity service until it generates sufficient revenue to cover the capacity payments. That is how simulation of the baseline flat-rate service is implemented in the following section. In contrast, in the RTP simulations no capacity payment is made; generators earn all revenues through energy sales.

3. DATA, MODEL DETAILS AND SOLUTION ALGORITHM

   The value of the simulation results depends on the realism of the underlying assumptions. In this section, I describe in detail the modeling of demand and supply, and then the algorithm for finding the long-run competitive equilibrium. I first present the details of the model, and then discuss the data used to parameterize the model.

   3.1 Demand, Supply and Equilibrium Modeling

   Within each hour, each customer's demand is modeled as constant elasticity. Each customer i is assumed to have a demand that is simply a fixed proportion, [γ.sub.i], of total demand. In the base simulations, I assume that total demand has the same elasticity in all hours, but this is later relaxed to allow elasticity to vary positively or negatively with the overall demand level.

   The aggregate demand function for hour h can be specified as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where elasticity may or may not vary by hour depending on the simulation run. For any share of demand on RTP, α, the demand from customers on RTP then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the demand function for customers on flat rate service is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The aggregate demand in the wholesale power market is then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

   Given an elasticity for a certain hour, [ζ.sub.h], and the assumption of constant-elasticity functional...