Thomas-Olivier Leautier - Imperfect Markets and Imperfect Regulation: An Introduction to the Microeconomics and Political Economy of Power Markets

Load duration curve for France in 2009. All half hours of a given year are represented on the horizontal axis, demand is represented on the vertical axis. The load duration curve represents demand for every half hour, ordered from the highest to the lowest.

Inverse demand curves for different half hours of the year. In Europe, the left-most curve corresponds to a summer morning, the right-most to a winter evening.

Gross consumer surplus and marginal gross consumer surplus (left panel) and net surplus and marginal net surplus (right panel).

Demand curves and supply curve for a single-generation technology.

Short-term net surplus and marginal short-term net surplus (left panel) and operating profit and marginal operating profit (right panel) for any on-peak hour.

Pricing structure. Hours are represented on the horizontal axis, prices on the vertical axis. For most hours, price is equal to the variable cost c. On-peak, price rises above the variable cost. The operating margin is equal to the fixed cost.

Demand curves if demand is perfectly inelastic (left panel) and partially elastic (right panel). On the left panel, in every hour, demand does not vary with price. When demand is lower than installed capacity K, it can be entirely served. When demand exceeds installed capacity K, it must be reduced through involuntary curtailment. The price is then set at the VoLL: inverse demand is a horizontal line at the VoLL. On the right panel, demand is slightly reduced as price increases, up to the VoLL.

Price structure when no customer is price responsive (left panel) and when a fraction of customers is price responsive, and curtailment occurs (right panel). When no customer responds to price, the SO starts curtailing customers when demand (at the variable cost of production) is equal to installed capacity and sets the price at the VoLL. When a fraction of customers respond to prices, the price rises on peak, as in section 2.1. If the price rises to the VoLL, the SO starts curtailing constant-price customers and sets the price at the VoLL.

Screening curves for three generation technologies: nuclear, CCGT, and OCGT. Hours are represented on the x-axis, and the y-axis presents the total annual cost of producing 1 MW during a strip of any number of hours.

Optimal usage of a nuclear power plant (left panel) and an open-cycle gas turbine (right panel).

Supply curve for three technologies.

Determination of the optimal generation mix combining the screening curves and the load-duration curve.

Projected evolution of the residual demand curve (also called net load) for a typical day in California from 2013 to 2020. Residual demand is significantly reduced between hours 8 and 17 hours. It then increases rapidly between hours 17 and 20, requiring a significant ramp-up capability.

Functions v(pR, ), (0, ), and (1, ) if demand and uncertainty are represented by the exponential specification presented in section 2.7.

Actual and fitted demand.

Perfectly competitive and Cournot outputs and prices. The perfectly competitive output is such that the value of the marginal unit, which is the price, is equal to the variable cost of production of that unit (which is constant in the figure). The Cournot output is such that the revenue generated by the last unit produced, which is the price minus the revenue reduction on all units, is equal to the variable cost of production of that unit. The Cournot price is the value of the last unit produced, which is higher than the competitive price.

Strategic capacity reduction.

Equilibrium capacity if the price cap is always reached on-peak, for . The capacity-maximizing cap is , and p = 3.9. Equilibrium capacities for different values of the cap are , and bKC(p) = 6.2. Source: Lautier (2018).

Equilibrium capacity (left scale) and expected net surplus (right scale) if the price cap is always reached on-peak, for . The surplus-maximizing cap is p* = 3.6, higher than the capacity-maximizing cap , and close to the highest admissible cap p = 3.9. Source: Lautier (2018).

Hotelling equilibrium retail price when suppliers cannot discriminate among customers.