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Report Contents Report#:EIA/DOE-0607(99)
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by Diffusion and Learning-by-Doing Technology Representations in NEMS
Diffusion and Learning-by-Doing Before they can provide widespread benefits, new technologies must pass through three phases: (1) invention—the development of a new technical idea; (2) innovation—the incorporation of the new idea into a commercial process for the first time, and (3) diffusion—the typically gradual process of adoption of the new product or process by potential users. Diffusion of technologies induces learning-by-doing for manufacturers and learning-by-using for consumers. These forces work in tandem in the market and are difficult, if not impossible, to separate. Learning relates cost reductions to cumulative capacity installed and is a surrogate for experience. Because invention and innovation cannot be projected reliably, they are incorporated in the National Energy Modeling System (NEMS) through the technology menu made available to consumers over time. Independent expert engineering judgments are used to develop the technology menus. Subsequent cost and performance improvements (evolutionary changes) are a function of the diffusion and adoption of technologies in the market. The relationship between technology diffusion and learning—i.e., cost and performance improvements—in NEMS is the focus of this paper. Background on Diffusion and Adoption The paradox of the very gradual diffusion of apparently cost-effective energy-conserving technologies—why the technology diffusion process is gradual and what factors cause this to be the case—has been examined in recent studies.1 The factors are grouped into (1) potential market failures, such as information problems, principal/agent slippage, and unobserved costs, and (2) non-market failures, such as private information costs, high discount rates, and heterogeneity among potential adopters. Two key adoption questions have been examined: what factors determine the rate of adoption of energy-conserving technologies, and what effects economic incentives and conventional regulations can have in encouraging technology adoption. Research has consistently shown that diffusion of new, economically superior technologies is never instantaneous. Typically, it follows an “S-shaped” (sigmoid) curve, with the adoption rate initially slow, then faster, then slower as saturation is approached.2 One commonly used model focuses on the spread of information regarding the existence and profitability of the innovation (the “epidemic model”). People are unlikely to use technologies they do not understand or are not aware of. If knowledge of existence and profitability are increasing functions of prevalence of use, then the use of a technology can be expected to spread like a disease: the probability that a non-user will adopt the technology in any time period will be an increasing function of the fraction of the population that has already adopted (been infected). The formulation can be characterized as follows: dSt/dt = a(C, P, ...) [St/Ut] * [1 - St/Ut] , where St = the stock of users who have adopted the technology by time t, Ut = the universe of potential users of the technology by time t, and a(C, P, ...) = the infectiousness of the disease (technology)—a parameter that depends on fuel prices (P), equipment costs (C), and possibly other factors. Notice that [St/Ut] is the probability of encountering an “infected” person and contracting the disease (adopting). The second factor, [1 - St/Ut], is the proportion of the population that is “healthy,” representing candidates for “infection” (adoption). Although a was specified as a constant in the original contagion formulation, Griliches established that diffusion is a function of economic returns to adoption. Mansfield showed that the rate of diffusion can depend on the size of the adopting firms, the perceived riskiness of the new technology, and the absolute size of the required investment.3 In such models, even if a technology is profitable for all firms, diffusion is gradual because it takes time for all firms to be “exposed.” David proposed that potential adopters are heterogeneous in their evaluation of cost-effectiveness, that is, they have a distribution of hurdle rates.4 Early adopters have the lowest hurdle rate and, by making early purchases of a new technology, enable a portion of the market to “learn” about the technology (learning-by-using) and manufacturers to reduce their production costs (learning-by-doing). The new cost reductions can then make the technology economical for an additional portion of the market, and the process is repeated until the market share stabilizes. Factors that slow the adoption of apparently superior technologies in the market are referred to as “market barriers.” Barriers that keep a market from behaving efficiently are termed “market failures.“ Other barriers are not failures, because they typically reflect hard-to-quantify costs that are incorporated by the market to develop an efficient equilibrium. The following barriers are market failures:
The following market barriers are not market failures:
Non-market failures typically represent internalized costs (barriers) that are used by a well-working, efficient economy to allocate resources optimally. Such barriers help to explain why the diffusion of energy conservation technologies is gradual. Government intervention to offset such barriers may decrease the efficiency of the market without providing compensating gains, and thus is not necessarily warranted. Although innovation (technical progress) and learning-by-doing may appear to be synonymous in this paper, they are not. However, they are related. Technical progress or innovation is commonly understood to mean the introduction of a new product or service into the market. Such products often, but not always, have greater efficiency and greater equipment cost than the alternatives for providing the same service. The cost per unit of output can be higher or lower for the new technology when both equipment and fuel costs are considered. For example, a SEER 18 central air conditioner costs about $900 more than a SEER 10 central air conditioner but is 80 percent more efficient. The total annual electricity cost savings from using a SEER 18 central air conditioner at today’s national average electricity price is about $110 per year. Thus, it would take roughly 8 years to recover the difference in equipment costs. An 8-year payback period has traditionally been unacceptable for U.S. residential or commercial investments, and very few 18 SEER units are sold. Consequently, although the SEER 18 central air conditioner unit represents a significant technical advance, the overall efficiency in residential/commercial cooling is not improved solely by the availability of the advanced SEER 18 technical achievement because of its negligible market adoption. In the context of this paper, we refer to technological progress as the combination of technical progress, adoption, and learning-by-doing. Because considerable technical progress, resulting in either cost reductions or efficiency improvements for existing technologies, occurs through adoption-stimulated manufacturing production experience (as well as research and development), learning is tied to both adoption and innovation. Technological progress in this paper measures the net technology impact on the market—that is, the combination of innovation, adoption of the more efficient technologies in the market, and learning (cost reductions and efficiency improvements induced by either manufacturing or consumer experience). Returns to adoption (another expression for learning-by-doing) are cost reductions due to manufacturing efficiencies and experience—usually taken as a function of cumulative capacity or the number of units built.6 Wright, for example, noted that the direct labor costs of manufacturing airframes declined by 20 percent for every doubling of cumulative capacity.7 Other authors have subsequently broadened the analysis of learning to other costs and shown that they also declined with experience. More recently, Hatch and Mowery have tied learning (in the semiconductor industry) to cumulative engineering resources devoted to implementing a new process on the manufacturing production line, not just cumulative production.8 Findings of recent studies indicate the following. There is always some loss of learning when a technology is transferred from research and development to the manufacturing production line. Global competition promotes global information and learning-by-doing (that is, production is local but learning is global). The more standardized (“commoditized”) a product is (like paper clips, radios, and gas turbines), the more likely it is that the product cycle time will be condensed and the more rapidly the learning-by-doing will occur.9 The more mature a technology, the more likely it is that learning will diffuse into the marketplace, because experts have time to move between firms. And finally, at the technological frontier, learning is limited to a small group of individuals or firms and disseminates more slowly to competing firms.10 Technology Representations in NEMS The National Energy Modeling System (NEMS)11 was developed by the Energy Information Administration (EIA) in 1993. NEMS is a large, regional, modularly designed, technology-rich, energy-economy model that solves for an annual equilibrium in U.S. energy markets. It is particularly well suited to address policy issues focusing on technological change. Technological decisionmaking in NEMS is tailored to the sector being modeled (e.g., utilities minimize costs subject to environmental constraints, whereas for residential markets cost is only one of a number of criteria used to choose appliances). Six of the major modules in NEMS (residential, commercial, transportation, refineries, electricity, and natural gas transmission and distribution) characterize technologies explicitly in the engineering sense, that is, with thermodynamic efficiency, specific fuel inputs and outputs, maximum capacity factors, unit capital costs, operations and maintenance (O&M) costs, physical lifetime, first year of commercial availability and installation, and maturity status (vintaged capital stock). The remaining NEMS modules (coal, oil, and gas production and industrial energy demand) represent technologies implicitly in the sense that technological change is embedded in other trend parameters that have been derived either through econometric methods or through engineering judgments. Learning-by-doing has been modeled in three ways in NEMS. Learning-By-Doing in the Oil and Gas Supply Module For the implicitly defined modules, such as the oil and gas module, time-dependent rates of change of key parameters that ultimately determine the cost of bringing new reserves into play are defined by improvements in such factors as cost per well, success rate, and the rate of increase of inferred reserves. Whenever technologies are represented implicitly in NEMS, learning-by-doing, innovation, and market penetration of advanced technologies are merged into one concept, which for simplicity we call “technological progress.” Horizontal drilling, improvements in reinjection technology, and improved computer applications (to interpret seismic data) are relatively recent technological innovations (technical progress) that have combined with increasing use (learning-by-using) and decreasing costs (learning-by-doing) to prompt further adoption and cost reductions. Net rates of improvement typically are estimated econometrically or derived through expert engineering judgement. The sensitivity of the solution is investigated and reported periodically in the Annual Energy Outlook. Below is one example of how the wellhead price of natural gas might change with a change of one standard deviation in the technological progress parameters. Shown in Figure 1 is the impact of slow and rapid technological progress cases, run both in standalone mode (without any interaction on demand) and integrated with full market responses to price changes. The impacts of the technological change implied by a difference of only one standard deviation are significant. Figure 1. Lower 48 Natural Gas Wellhead Prices in Three Cases, 1970-2020 [source] Technological Learning in the Residential, Commercial, and Transportation Modules In the NEMS building and transportation sectors, equipment choices are based on logit (or nested logit) models that can be derived from variations of the epidemic model described earlier. The production of end-use energy appliances tends to be standardized, and although the product cycles are typically longer than those associated with memory chips for computers, technological learning is short enough and investment small enough for learning to be characterized as a function of time instead of cumulative production experience (given stable fuel prices with some year-to-year perturbations). Technologies in the buildings sector can be classified as either mature, adolescent, or infant. Each classification identifies the rate of cost reductions or efficiency improvements that can occur over time. For mature or costly new technologies, the cost declines or efficiency improvements are either constant or slightly declining. The costs for adolescent technologies are gradually declining, because some adoption has occurred as a result of the heterogeneity of consumers, and their preferences result in additional cost or performance improvements. For infant but cost-effective technologies, the initial technology cost is low enough for significant early adoption and learning to take place, further reducing costs. The three options are illustrated in Figure 2. Figure 3 illustrates the actual projected cost declines for compact fluorescents, an adolescent technology in commercial lighting. Figure 2. Example of Learning: Buildings Sector Technologies [source] Figure 3. Capital Costs for Compact Fluorescent Lighting in the AEO98 Reference Case [source] Sources for the exogenous estimate of how much technological learning can take place in the buildings sector are based on engineering and market penetration estimates by A.D. Little.12 Exogenous estimates for technological learning in the transportation sector are based on work by Energy and Environmental Analysis, Inc., and others under contract to the U.S. Department of Energy. Two sets of time-dependent learning assumptions usually are provided. One set, for the reference case, assumes that the current market conditions will prevail into the future (reference case assumptions). Another set of cost and performance characteristics for advanced technologies is also developed by A.D. Little and assumes that additional sales will be generated through industry and government actions (possibly, increased research and development) that accelerate learning (the rapid technology case). Cost reductions through manufacturer learning associated with each market scenario are developed exogenously and translated to scenario-dependent and time-dependent paths of cost reductions. Learning in the Electricity Market Module The NEMS Electricity Market Module (EMM) is a large regional model of the U.S. generation market. The United States is divided into 13 NERC (National Electricity Reliability Council) regions or subregions, and each region is treated as a large single utility that optimally adds capacity and dispatches and prices electricity subject to market conditions (competitive or regulated) and environmental constraints for sulfur and nitrogen oxides (NOx) (Figure 4). Figure 4. Overview of the NEMS Electricity Market Module (EMM) [source] Currently, 5 of the 13 regions are assumed to be competitive and use marginal-cost pricing for generation (California, New York, New England, Mid-Atlantic Area Council, and Mid-America Interconnected Network). Those 5 regions have instituted legislation toward market pricing. The 8 other regions are assumed to continue with cost-of-service pricing in the reference case. Key regional inputs to the EMM include end-use electricity demand and associated load profiles, delivered fuel prices and availability, the current and future menu and cost and performance characteristics (efficiency, maximum capacity factor, capital and O&M costs, etc.) of available generation units with their date of initial installation, the risk factor associated with investments in new capacity, degree of maturity, environmental and fuel-use regulations, and the degree of market structure. Some of the key features of the EMM follow. Capacity expansion planning using a multi-year horizon is formulated as a dynamic linear program to optimally dispatch current and future technologies to minimize costs across all time slices. The solution is adjusted to reallocate a portion of the new generation capacity to those technologies that were marginally unattractive, to account for the heterogeneity of electric utilities within a region. Annual electricity demand is divided into 27 time segments per year for planning purposes, and demand for dispatch is divided into 108 time segments. Local and Federal environmental regulations are treated endogenously. Traditional cogeneration (combined heat and power systems primarily for own use) is represented in the demand sectors (industrial and commercial), refinery sector, and the oil and gas supply sector. Twenty-six technologies are explicitly represented: 15 fossil-fueled, 1 nuclear, and 10 renewable. Most importantly, technology costs are adjusted to reflect learning with market penetration—learning-by-doing—as described below. Important additional features of the utility capacity expansion module include an adjustment for technological optimism,13 the adjustment of discount rates for risk and uncertainty, the use of “reduced costs” to reallocate some of the planned capacity to technologies that are almost competitive, and the use of either adaptive14 or rational15 expectations. Technological optimism is defined as the difference between initial engineering estimates and final first-of-a-kind costs. New technology costs are uncertain because all components are not known with certainty. Some designs may be novel or untested for large-scale plants. Initial capital costs tend to be underestimated. As more of the engineering design becomes definitive, costs become more certain and tend to increase. First commercial plants tend to be manufactured inefficiently and to require design modifications and adjustments. After the first few units, normal learning takes place and costs decline at a more gradual pace (Figure 5). Learning-by-doing is the process by which the market gains operational and manufacturing experience. Figure 5. Technological Learning [source] In NEMS, the cumulative capacity or number of full-sized plants constructed is used as a surrogate for experience. The use of this modeling feature allows for the analysis of market “lock-out”and “lock-in.” Preventing the lock-out of new technologies that have high (uncompetitive) initial costs but are expected to have much lower costs after learning-by-doing occurs is the goal of technology deployment programs. This modeling feature allows the simulation of policies that affect technologies in the early stages of commercialization and represents the effects of learning on cost reduction. Electricity Technology Adjustment and Characterization The basic steps in the adjustment algorithm (Figure 6) are as follows:
Figure 6. Electricity Technology Adjustment and Characterization [source]
Learning-by-doing, as shown in Figure 5, is characterized in three piecewise nonlinear curves for overnight costs:17 early rapid learning (units 1-5), normal learning (units 6-40), and extended learning (units 41 and beyond). The standard capacity of a unit is a function of the technology. For example, the standard size for a fuel cell is 10 megawatts, and the standard size for a gas combined-cycle unit is 400 megawatts (see Table 1). Overnight costs are a function of cumulative capacity, where capacity is measured in numbers of standard-sized units. The functional form18 has the nonlinear form: OC(C) = a * C-b , where C is the cumulative capacity in numbers of standard-sized units. The progress ratio (pr) is defined by speed of learning (e.g., how much costs decline for every doubling of capacity). In NEMS, the percentage reduction in capital cost for every doubling of cumulative capacity (f) is an exogenous parameter input for each technology. Consequently, the progress ratio and the NEMS input f are related by pr = 2-b = (1 - f) . We can solve for b in terms of f. Once b is solved, a can be found from initial conditions. Thus, once the rates of learning (f) are known for each interval, the corresponding parameters (a and b) of the nonlinear function are known. The overnight costs can be computed for any amount of experience (cumulative number of units built). Table 1. AEO99 Cost and Performance Characteristics for New Generating Technologies The Market Adjustment Algorithm Technologies in the EMM are defined as “competitive” when the annualized cost of the capital plus operating and maintenance costs of a technology are low enough to be adopted in the optimal capacity expansion planning decision. For example, on a cost per kilowatthour basis, gas combined-cycle plants in the 2000-2010 time frame typically are expected to cost about $0.04 per kilowatthour, are competitive, and are selected in the planning process; solar photovoltaic systems typically are expected to cost more than $0.25 per kilowatthour, are not competitive, and are not selected in the planning process. The recalculation of market shares after the Capacity Expansion Model has solved for the optimal expansion plan is designed to account for heterogeneity of utilities within the NERC regions. The recalculation of market shares is based on the levelized fixed costs (capital plus fixed O&M) of the selected new generation capacity and the costs of the marginally uncompetitive technologies. The fixed costs of each technology are checked to determine whether they were within 20 percent of being competitive. For those technologies that are within 20 percent of being competitive, each market share is reallocated according to a logit function. More precisely, we define Fi = the levelized costs of capital cost plus fixed O&M for technology i, and Ri = the “reduced cost” for technology i in the optimal solution. The solution to a linear programming model produces “reduced costs” for every variable in the optimal solution. The reduced cost represents how much the cost of that technology must be reduced to become economically attractive. The reduced cost for a “basic” variable in a linear programming formulation, a technology that was selected by the program, will be zero in the NEMS formulation. Those that were not selected will be positive. Next we compute the following ratio for each technology and check to see whether it is less than or equal to 1.2. Ratioi = Fi/|(Fi - Ri)| , where we check to be sure that |Fi - Ri| > 0 (i.e., the absolute value of the difference, Fi - Ri, is greater than zero). For all technologies that satisfy the condition that costs are within 20 percent of being competitive (ratioi # 1.2), we allocate new capacity shares according to the following logit function: Si
= (ratioi)- The
larger the exponent Figure 7 illustrates market lock-out (and lock-in) for four technologies. For simplicity of discussion, we assume that a standard-sized plant is 200 megawatts (composed of one or multiple generation units at a single site), and that all plants use the same fuel inputs. To simplify the illustration, we also assume that the efficiencies and other inputs are the same. In this case, assuming no subsidization, the mature technology for the “next unit” (unit 1 on the horizontal axis), would always “win” the market. Because the other “unit 1” technologies are not economical in comparison with the mature technology, they are not built, and learning-by-doing does not occur for them—market lock-out. Figure 7. Lock-Out Example [source] Assuming that the three highest-cost technologies were somehow subsidized until they became competitive with the original lowest-cost technology, Figure 8 illustrates the minimum subsidy each would require until sufficient learning-by-doing was accomplished for the technology to penetrate the market on its own.19 Of course, to do a more complete analysis, all the costs and benefits, including efficiency, co-products, and environmental considerations, would have to be included. To illustrate the importance and impact of learning-by-doing in the EMM, Figure 9 shows the cost paths for gas combined-cycle and biomass generation from two recent EIA analyses—the Annual Energy Outlook 1999 (AEO99) and Impacts of the Kyoto Protocol on U.S. Energy Markets and Economic Activity (Kyoto Protocol).20 Figure 8. Implied Subsidy Cost, Undiscounted [source] Figure 9. Learning in AEO99 and in the Kyoto Protocol 1990-7% Case [source] Given the severe fuel price impacts of the Kyoto Protocol 1990-7% case, which projects a “carbon price” of $348 per ton of carbon in 2010, biomass generation capacity21 is rapidly adopted (about 7 additional gigawatts), and costs decline by about 35 percent within a span of a few years as a result of about 7 gigawatts of cumulative adoption and resulting learning between 2005 and 2008. The gas combined-cycle technology still is projected to be adopted heavily in both cases (more than 25 gigawatts of new capacity between 2005 and 2008), because it is economical in both cases, and there is little difference in the learning path between the two cases. Tables
1 and 2 summarize the major generation technologies and
characteristics assumed for AEO99. Normally, either the
current capital cost (dollars per kilowatt) if the technology is
mature, or the cost of the fifth unit (nth-of-a-kind) if
the technology is in the early phases of adoption, is input to the
model. To determine the first-of-a-kind cost, note that the
fifth-of-a-kind22 represents
about 2.5 doublings of capacity. If 10 percent is the cost
reduction for each doubling of capacity, then the first-of-a-kind
cost, without applying any technological optimism factor, is 26.9
percent higher than the fifth-of-a-kind. Applying the optimism
factor to the first-of-a-kind cost results in the ultimate
first-of-a-kind cost. For example, the fifth-of-a-kind cost of a
biomass generation plant is $1,448 per kilowatt (in 1997 dollars).
The optimism factor assigned to biomass is 1.19, which implies
that there are some significant uncertainties related to biomass
material handling and processing. The true first-of-a-kind cost is
1.19 Table 2. AEO Technological Optimism and Learning Factors for New Generating Technologies Issues Associated with the EMM Implementation The rate of learning-by-doing in the EMM hinges critically on three parameters: (1) the rate at which cost reductions occur with production, (2) the definition of standard unit size, and (3) how much “learning” actually can take place when the vendor is, for all intent and purposes, building plants in the same year. The problem encountered with learning for electricity generation is that a significant portion of installed costs are site-specific, and most equipment installations retain a certain level of customization; hence, learning-by-doing can be divided between advances in the technology and advances in the installation. For example, some European experts assert that learning for wind turbine technology has undoubtedly slowed to about 2 to 8 percent for every doubling of worldwide capacity for the best wind sites,23 and 4 to 6 percent has recently been recommended.24 Considerable learning remains with respect to siting wind turbines in more difficult terrain and in lower quality wind resource areas. On the other hand, gas combined-cycle systems—which are the most modular, turnkey systems available, with the fewest customization requirements—reflect learning through modularization and system integration to boost efficiency and reduce total installation costs. The extent to which further learning can progress in each of these areas (technology and siting) remains a difficult, technology-specific issue. It is unclear how much learning can be achieved from simultaneous construction of large-scale electricity generation equipment. Typically, it takes some time (often years or decades)25 before accrued operational experience is fed back to the manufacturer. There may be a limit to the maximum “learning” that can be achieved in one year. Further, the manufacturer is often obliged to make adjustments on existing equipment to meet the contractual operational specifications. Thus, the first quoted cost is often larger than the bid, and the equipment is often customized. Learning-by-doing
(for manufacturers) and learning-by-using (for consumers) have
been shown by numerous authors to be important determinants of the
rate of adoption of new technologies. Manufacturing learning
reduces the cost of equipment production and makes the equipment
more economical for adoption. Increased consumer learning
(familiarity with and use of a product) can increase the
likelihood that more of the technology will be adopted. These
forces work in tandem in the market and are difficult, if not
impossible, to separate. In NEMS, the two learning concepts are
integrated and implemented in combination. However, because
technologies and their adoption are represented somewhat
differently in the various NEMS modules, based on the markets they
represent, the treatment of technological learning in NEMS also
differs by sector. Despite the uncertainties and difficulties of
representing technological learning, its importance for the
effective analysis of proposed technology policies is undeniable,
and it must be represented in the modeling framework. The National Energy Modeling System (NEMS) was developed by the Energy Information Administration (EIA) in 1993. NEMS is a large, regional, modularly designed, technology-rich, energy-economy model that solves for annual equilibrium in U.S. energy markets. It is particularly well suited to address policy issues focusing on technological change. The Integrating Module (Figure A1) controls communications in NEMS through a common shared data structure. As an oversimplified representation of the equilibration process, the demand modules can be viewed as receiving fuel prices by end use and returning the quantity of each fuel demanded. Technology choice is determined within each sector and is not part of the equilibration process.26 The oil and gas supply modules receive the demand for each fuel and the associated prices and provide a supply curve based on drilling investments, drilling activity, and reserve additions. Coal supply curves are based on labor productivity. Figure A1. Structure of the National Energy Modeling System [source] The conversion modules27 are the most complex and the largest models within NEMS. The electricity module receives the delivered prices of fossil fuels, the demand for electricity, the current generation mix available, and environmental policies and regulations to determine the least-cost dispatch of plants, fuel consumption to generate electricity, and electricity prices. The electricity capacity expansion submodule uses the same information as the electricity dispatch module, along with the menu of technologies available for construction, expected fuel prices, and electricity demand and determines the least-cost plan that meets all identified environmental constraints. The NEMS representation of energy markets focuses on four important interrelationships: (1) interactions among the energy supply, conversion, and consumption sectors; (2) interactions between the domestic energy system and the general domestic economy; (3) interactions between the U.S. energy system and world energy markets for oil, liquefied natural gas, and coal (and gas and electricity trade within North America); and (4) the interaction between current production and consumption decisions and expectations about the future.
|
/ (
(ratioj)-
) .
is in the logit formulation, the more the region resembles a
homogeneous single utility that optimizes capacity expansion
plans. The choice of 
=11
as an exponent means that a relatively small share of new capacity
will be given to marginally uncompetitive technologies with fixed
annualized costs approaching 20 percent above the current market. Ratioi
could have been calculated on the basis of both annualized fixed
costs plus variable O&M and fuels costs; however, such a
calculation would have added significant complexity (and more
assumptions) to the computation, because the variable costs are a
function of the actual generation, which are unknown for the
marginally uncompetitive technologies.
1.2691, or 52 percent above the mature fifth-of-a-kind cost.
Learning rates are estimated and input for each technology and
each learning interval (Table 2).
