Fixed and Variable Costs

Theory and Practice in Electricity

C. Harris

• Publisher: Palgrave Macmillan
• Year: 2014
• Print ISBN:
  9781137384799
• eBook ISBN:
  9781137370891
• Topic: Business
• Subtopic: Accounting
• Index: Business

Fixed and Marginal Costs in Electricity Markets lays out clear cost methodologies for understanding marginal price structures, further cementing electricity's role as an asset class with fixed and variable costs.

CHAPTER 1

Introduction

The politics, economics, and design and operation of and in power markets are highly dependent on the definition of fixed and variable costs, and yet the prevailing definitions remain unsatisfactory to the extent of driving outcomes far from the optimum.

This book pays attention to the definition of fixed, marginal, and variable costs that are most useful to policymakers and market actors. Through the development of the definition, we find that power stations form a useful archetype and metaphor in the wider canon of fixed and variable costs, which began with bridges and canals and more latterly include a variety of items such as airline seats and entry tickets.

The three practical aims of this book are to support

    1.  Capital and operating decisions for power plants

    2.  Plant and demand characterization for optimal power market design

    3.  Short, medium, and long term planning of security of supply

Our model will show that it is the whole cost vector that is most important, and while division into fixed and variable can make costs easy to understand, and modeling commonly must allocate total cost between these two, such modeling must always recognize the variability of fixed costs. We will also see that the division between variable and fixed costs breaks down further when we relax the hard capacity constraint and further still when we add stochastic factors to our models.

We will see a central theme is the use of the current plan for production and consumption as the key reference point, as distinct from no production and consumption as the reference point.

Where a deeper study of welfare, utility, cost of risk, and surplus is required, we refer the reader to the sister text “utility and welfare, theory and practice in electricity,” which for short we call the “sister text on welfare” (Harris 2015, forthcoming). Similarly for capacity, peak load pricing, and the use of derivatives we refer to the sister text “peak load and capacity pricing—theory and practice in electricity,” which for short we call the “sister text on capacity” (Harris, 2014).

1.1   Nomenclature

There is a broad consistency of nomenclature in the literature.

The key terms are:

B—fixed costs, also β

b—variable costs, also β, γ

C—total or generic costs

Q—capacity or volume

λ—probability or percentage utilization

N—total number (sub-periods, units, etc.)

P—price, also probability

Π—profit

u—a shock in price or volume

To facilitate comparison with original material, where the work of specific authors is worked through, we use their original nomenclature.

1.2   Taxonomy of Costs

There is little consistency in the terminology of costs, largely due to the genuine difficulty of separating the entire cost base of a complex operation into three words—marginal, variable, and fixed. Here we create a taxonomy that intends to map the terminology used by the authors to a consistent framework.

    1.  Marginal costs: These costs are at the margin, that is, for a small increment extra relative to the current plan, and average costs refer to the total cost of the category in question (variable, inescapable, etc.) divided by the relevant denominator (capacity, energy, etc.).

    2.  Myopic marginal/variable costs: The “myopic” terminology follows Arrow (1964). The myopic marginal cost is the cost that is incurred within a short period of time from an increment of activity over and above the cost that would have been incurred without the increment. Whether or not future costs and revenues are impacted by the activity of payment are not recognized. This definition does not accommodate uncertainty, for example, that we may become unable to pay the money.¹ As far as possible we treat the production variation increment in the context of a deterministic level of production. Aware of the oxymoron of having a variable cost for a deterministic production schedule, the increment necessarily tends to zero. In the extreme, myopic marginal costs are zero.

    3.  Short run marginal/variable costs (SRMC): Myopic marginal cost is the narrowest definition. SRMC is commonly known as “variable costs” where ambiguity is unlikely, and normally where returns to scale are constant. These are the costs that are incurred (accrued) from an increment of production, this time recognizing the inevitable or likely spend or loss of net (i.e., including revenue effects) cash flow that will be incurred in the near future as a result of the increment. For “lumpy” investments the cost increase that is made inevitable by production is commonly not included in SRMC. SRMCs and indeed all marginal costs can be asymmetric,² in that the increase in cost for an increase in load is not necessarily equal to the decrease in cost for a decrease in load. A subcategory of SRMCs is the costs that are required for the first increment of production (i.e., a finite spend required to produce the first infinitesimal amount). Short run fixed operating costs are one of the family of fixed costs, which we will work through in more detail.

    4.  Fixed capital costs: Within this we include all costs that would be paid, other than spend on physical items that might be unaffected by plant operation or revaluation of the plant. This is mainly debt repayment according to the contractual terms.

    5.  Variable capital: This reflects the fact that plant value changes (plus or minus) over time relative to expectation, as a result of the variable pace of technology developments, costs of fuels, taxes and regulatory interventions, and other factors. For forward planning, the plant should be valued at the market replacement value, not the historic cost.

    6.  Fixed operational costs: That is the noncapital costs that are required according to initially planned operation but independent of actual operation. This includes expectation of those taxes and decommissioning and other liabilities that must be accrued for according to the planned plant life. This includes, for example, staff costs and maintenance of civil structures.

    7.  Inescapable costs: These are costs that cannot be avoided. In this book we include all liabilities in this category. The practical modeling requirement is that there must be a way to discharge liabilities even when the asset value has fallen below the level at which shareholders and creditors receive anything. This is best modeled as an insurance contract.

    8.  (Fully loaded) long run costs (LRCs or LRMCs at the margin): These costs are also called levelized costs for new build, and include all costs that are incurred over investment timeframes. This can be divided variously, for example, as fixed costs for zero load plus average variable costs, or capacity cost (or “development cost” as termed by Boiteux, 1949), measured in £/kW/year plus the SRMCs measured in £/MWh.

    9.  Shadow costs: These costs represent the marginal cost of a constraint. So if plant output is limited to Q, the marginal cost of the constraint is the increase in cost, or loss of profit, for a small increase in constraint.

CHAPTER 2

Equilibrium and Other Core Assumptions

In taking a formal analytical approach to practical problems we must lay out the framework in which our plant operates. We begin with the simplest possible model, with assumptions made explicit, and gradually relax those assumptions that have a critical impact on the modeling.

2.1 Equilibrium and Rational Expectations

We assume long term equilibrium as the starting point before we include trends such as resource depletion. In this equilibrium, the state of the world at the beginning of the next period/epoch is the same as at the beginning of the last one. In particular, the demand will be the same and the government continues (so that there is no “one shot game” by the government in the first period). Using the metaphor of the bridge, if we need a bridge in the first period then we need one in the second, and government actions (on toll regulation etc.) in the second period will be consistent with those in the first.

Rational expectations rely on the equilibrium foundation. Each rational actor will make rational assumptions on the states of the world in future and the behaviors of other actors. So, for example, if the state has ever abrogated an actual or implied contract with a firm or nation, then the rational expectation is that abrogation will be repeated according to expedience.

This joint framework has significant impact on the game theory related to costs. In taking a long term equilibrium view of the world there is simply no such thing as a “one shot game.” Any game that is played must result in some form of equilibrium, such as a viable private sector or s...

Table of contents

• Cover
• Title
• 1 Introduction
• 2 Equilibrium and Other Core Assumptions
• 3 Modeling with Hard Constraints
• 4 Modeling with Soft Constraints
• 5 The Treatment of Change
• 6 The Characterization of Consumption
• 7 Summary
• Notes
• References
• Index
• Author Index