Unraveling the Photovoltaic Technology Learning Curve by Incorporation of Input Price Changes and Scale Effects

Abstract

In a large number of energy models, the use of learning curves for estimating technological improvements has become popular. This is based on the assumption that technological development can be monitored by following cost development as a function of market size. However, recent data show that in some stages of photovoltaic technology (PV) production, the market price of PV modules stabilizes even though the cumulative capacity increases. This implies that no technological improvement takes place in these periods: the cost predicted by the learning curve in the PV study is lower than the market one. We propose that this bias results from ignoring the effects of input prices and scale effects, and that incorporating the input prices and scale effects into the learning curve theory is an important issue in making cost predictions more reliable. In this paper, a methodology is described to incorporate the scale and input-prices effect as the additional variables into the one factor learning curve, which leads to the definition of the multi-factor learning curve. This multi-factor learning curve is not only derived from economic theories, but also supported by an empirical study. The results clearly show that input prices and scale effects are to be included, and that, although market prices are stabilizing, learning is still taking place.

Full text

Unraveling the photovoltaic technology learning curve by incorporation of
input price changes and scale effects
C.F. Yu
1
, W.G.J.H.M. van Sark *, E.A. Alsema
Department of Science, Technology and Society, Copernicus Institute for Sustainable Development and Innovation, Utrecht University, Heidelberglaan 2,
3584 CS Utrecht, The Netherlands
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
2. The effect of scale, learning and input prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
2.1. Economies of scale, diseconomies of scale and returns-to-scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
2.2. Learning effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
2.3. Scale effects versus learning effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
2.4. Input prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
3. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
3.1. The relationships between learning, scale and input prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
3.2. The learning curve model in economic context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
3.3. The multi-factor learning curve model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
4. Input identification and research boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
4.1. Input identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
4.2. Research boundary and the MFLC model for PV production cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
5. Results and residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
5.1. Parameters and statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
5.2. The results of the multi-factor learning curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
5.2.1. Period 1976–1986 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
5.2.2. Period 1987–1997 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
5.2.3. Period 1998–2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
5.3. Sensitivity and uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
Renewable and Sustainable Energy Reviews 15 (2011) 324–337
ARTICLE INFO
Article history:
Received 9 July 2010
Accepted 9 July 2010
Keywords:
Multi-factor learning curve
Economies of scale
Input prices
PV cost
ABSTRACT
In a large number of energy models, the use of learning curves for estimating technological
improvements has become popular. This is based on the assumption that technological developme nt can
be monitored by following cost development as a function of market size. However, recent data show
that in some stages of photovoltaic technology (PV) production, the market price of PV modules
stabilizes even though the cumulative capacity increases. This implies that no technological
improvement takes place in these periods: the cost predicted by the learning curve in the PV study
is lower than the market one. We propose that this bias results from ignoring the effects of input prices
and scale effects, and that incorporating the input prices and scale effects into the learning curve theory
is an important issue in making cost predictions more reliable. In this paper, a methodology is described
to incorporate the scale and input-prices effect as the additional variables into the one factor learning
curve, which leads to the definition of the multi-facto r learning curve. This multi-factor learning curve is
not only derived from economic theories, but also supported by an empirical study. The results clearly
show that input prices and scale effects are to be included, and that, although market prices are
stabilizing, learning is still taking place.
ß2010 Elsevier Ltd. All rights reserved.
* Corresponding author.
E-mail address: w.g.j.h.m.vansark@uu.nl (W.G.J.H.M. van Sark).
1
Present address: Millennium Decision Technology Ltd., Floor 1, No. 19, Zhongxing 4th Ln., West Dist., Taichung City 40350, Taiwan.
Contents lists available at ScienceDirect
Renewable and Sustainable Energy Reviews
journal homepage: www.elsevier.com/locate/rser
1364-0321/$ – see front matter ß2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.rser.2010.09.001

6. A MFLC forecast for future PV cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
6.1. Short-term scenario MFLC-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
6.2. Short-term scenario with lower silicon prices in 2010 and 2011 (MFLC-2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
1. Introduction
Many governments in the world adopt strict energy policies to
reduce their fossil fuel consumption and decrease the greenhouse-
gas (GHG) emission level as to contribute to alleviating the global
warming problem. They provide economic incentives and increase
R&D budgets to promote renewable energies. In order to forecast
future global warming trends and GHG emission levels, experts
build up energy-environment-economy models to simulate those
impacts. These models, however, are extremely sensitive to the
assumptions about the improvement and deployment of new
technologies [1]. Technological change is commonly regarded as
the most important factor to estimate the trends of these new
technologies. Thus, the technological learning concept recently has
been widely applied in these models, and plays a key role in the
simulation processes incorporated within these models [2].
Generally, technological learning concepts are simulated
through the learning curve model, which explains the relationship
between cost decrease and output growth [3]. The learning curve
model is based on the observed fact that as experience with a
technology accumulates, as represented by cumulative production,
the performance of that technology, in terms of unit production
cost, improves [2]. The learning curve allows for the estimation of a
decrease in unit production costs as a result of an increase in
cumulative production. Explanations supporting learning curve
theory identify various types of learning, i.e., learning-by-doing,
learning-by-researching, learning-by-using and learning-by-inter-
acting. The Boston Consulting Group [4] mentions that ‘‘increasing
accumulated experience in the early stages of a technology is a
dominant strategy for both maximizing the profitability of firms
and the social benefits of technology-related public policy’’. As an
important implication of the learning curve, Gru
¨bler et al. [5] point
out that it is an essential bridge between innovation and integrated
assessment of climate change. It is clear that the learning curve
plays an important role in designing effective energy policies,
being a vital approach for simulating technical changes.
The learning curve describes the costs of a given technology
being changed through one factor, which is represented by
cumulative capacity or production of a certain technology [2,6].
It illustrates that when a new technology is brought in the market,
the cost per unit is initially high, but as cumulative output
increases, the cost per unit decreases in an orderly way [7]. This
type of learning curve is the so-called one-factor learning curve
(OFLC). The usual form to express the OFLC is by using a power
function [8]:
C¼C
i
Q
b
(1)
where Cis the cost per unit of production, installed capacity or
capital, C
i
is the cost of the first unit installed or produced, Qis the
cumulative capacity or output, bis the learning index or experience
index. The time step usually employed is 1 year, with Cand Qbeing
determined every year. By taking the logarithm on both sides, a
linear equation is obtained:
log C¼log C
i
blog Qþe(2)
in which
e
represents a residual term. This term
e
is added to a
regression equation in order to introduce all of the variation in cost
that cannot be explained by included independent variables (log C
i
,
blog Q)[9]. The so-called progress rate and learning rate can be
determined from Eq. (1) as follows:
Progress rate :Pr ¼2
b
;learning rate :Lr ¼12
b
(3)
These two equations are always used to express the percent
changes in cost as a result of doubling of cumulative capacity. For
example, a learning rate of 20% shows that after doubling of
cumulative capacity, the costs are decreased to 80% of their initial
level.
The OFLC, however, only describes the relationship between cost
changes and cumulative capacity. There is a problem of omitted
variable bias. Econometric theory argues that if an independent
variable, whose regression coefficient is nonzero, is excluded from
the model, the estimated values of all the regression coefficients
will be biased unless the excluded variable is uncorrelated with
other variables [9,10]. For example, if we only use the OFLC
(log C=logC
i
blog Q+
e
) to represent the learning effects and
ignore the independent variable learning-by-researching (KS)
whose regression coefficient
e
is nonzero, the total residual term
e
will be
e
+
a
log KS,with
a
the elasticity of learning-by-researching
or knowledge stock index. Thus, as also Nemet [6] indicated, the
cumulativecapacity is not the unique factorthat determines the cost
changes.
Since the OFLC ignores the effects of cumulative R&D expendi-
tures, incorporating the effects of knowledge acquired from other
sources, such as R&D or other industries, becomes an essentialissue.
Recently, the OFLC has been extended by integrating the knowledge
stock (KS) as an additional variable [11–13]:
C¼C
i
Q
b
KS

a
;log C¼log C
i
blog Qalog KS þe(4)
in which KS is defined as KS
t
=(1
h
)KS
t1
+RD
t
,
h
is the annual
depreciation rate, RD
t
represents R&D expenditures at time t, and
a
is the elasticity of learning-by-researching or knowledge stock
index. This extended equation is commonly denoted as the two-
factor learning curve (TFLC). The concept of the TFLC clearly
identifies knowledge stock as a variable of technological learning.
It explains that cost reduction occurs as resulting from learning-
by-doing and learning-by-researching combined [2].
Fig. 1 shows schematically the interactions between R&D and
production growth through learning-by-researching and learning-
by-doing leading to cost reduction. It depicts the direct and
[(Fig._1)TD$FIG]
Fig. 1. Relationships and feedbacks between R&D, production growth and
production cost.
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
325

indirect relationship between learning-by-doing and learning-by-
researching. With an increase of R&D investment, learning-by-
researching will be enhanced, which leads to falling cost directly.
An increase of R&D investment meanwhile improves the produc-
tion process, which enhances learning-by-doing as well. On the
other hand, the growth of output increases learning-by-doing,
which results in cost reduction directly. It supports, in the
meantime, the R&D investment that improves learning-by-
researching. The interactions of these factors finally lead to cost
reduction of a new technology.
Over the past decades a considerable number of studies have
been carried out on learning curve analysis, especially in emerging
energy technologies, e.g. [14–17], however, it must be noted that
many questions still remain unsolved. First of all, the learning
curve is not a theory, but an empirical research method, although
recently Wene [18] has developed a theoretical approach based on
cybernetic concepts. It cannot tackle or explain discontinuity
issues and ignores (changes in) data quality. The distributions of
the learning rates vary among different energy technologies; even
some negative estimations have been found; a recent update is
provided by Junginger et al. [3]. This variability is not only
observed among the different technologies, but also among the
same type of energy technologies. Recently, some studies pointed
out that the uncertainties in key parameters might be significant
[19,20].Fig. 2 shows the learning rate of PV for the period of 1976–
1990 is determined to be 19.4%, while for the period of 1991–2001,
it is determined to be 26.6%. Parente et al. [21] and Van Sark [22]
use the same time period data, but obtain different learning rates
for PV production as evidenced in Table 1: it is clear that all these
evidence illustrates one issue: the learning rate is not constant.
One cause of these observed changes in learning rates is that
mostly not production data are used but market prices. Market
prices do not always follow production cost, for various reasons.
They may be higher and sometimes also lower than production
cost. For example, shortages in production capacity will drive up
price while the production cost will remain unchanged or will even
decrease. Therefore changes in the market price will only reflect
production cost if they are viewed on time scales of 5 years and
more. Temporary market effects on price are likely to be an
important reason behind the discontinuity in the PV learning after
2002 when the PV industry had problems to keep abreast with the
rapidly expanding German market.
Schrattenholzer [23] argues that variations in learning rates are
being caused by using different data sets, time spans and
performance measures, and that experience depreciation is the
main reason behind negative learning rates, such as shown in Fig. 2
for the period 2002–2006. Jamasb [13] considers that the variability
can be explained by the stage of technological development or the
technology life cycle. Van Sark [22] indicatesthat when the first unit
cost, the data span, the inflation and the exchange rate are changed,
the learning rate willbe altered as well. It implies that smallchanges
in the learning rate lead to large differences in forecasting
technology development. Clearly, and also according to Wene
[15] and Neij et al.[24], the learning curve may not be an appropriate
way to estimate the cost of some technologies.
Aside from the discontinuity issue, as illustrated in Fig. 2, Hall
and Howell [7] indicate that the learning curve might become flat
over a short period. Swanson [19] indeed observes that the cost
trend of PV has been flat in recent years, even though the
cumulative capacity increases. Moreover, Fig. 2 shows that the
learning rate for the period of 2002–2006 is even negative: 2.6%.
This flatted or blunted learning curve represents that apparently
no learning effect is taking place during this short period. This
situation is namely ‘‘learning without doing’’ [25]. Pan and Ko
¨hler
[26] conclude that the learning curve may successfully describe the
cost reduction of a given technology at its emerging stage, but fails
to explain the cost changes at its mature stage.
Swanson [19] and Nemet [27] further suggest that a much
broader set of influences than experience alone is accounting for
the rapid cost reduction. The Boston Consulting Group [4] does not
purely refer to the relationship between labor productivity and
cumulative output in its report. It argues that there are several
reasons related to the cost reduction: learning effects, scale effects,
cost rationalization and technology improvement [4]. Hall and
Howell [7] consider that the sources of falling cost may include:
economies of scale, technological progress, input price changes,
internal efficiency and learning-by-doing. Of these factors, the
economies of scale may play an important role in cost reduction.
Cory et al. [28] and Ibenholt [29] also assert that cumulative
capacity is not the only element determining cost; other factors
such as R&D, economies of scale, input prices can change the costs
as well. Isoard and Soria [30] decompose the cost into a learning
and scale effect. They observe that learning effects are over-
estimated when the scale effect is not taken into account.
Moreover, So
¨derholm and Sundqvist [31] conclude that the role
of input prices has to be assessed in order to realize whether the
input prices change the cost over a time period. It is important to
note that the costs of a technology are changed by variables other
than cumulative capacity alone, perhaps most remarkably by input
prices and economies of scale [2,26,31]. Nemet [27] adopted an
alternative approach based on a traditional engineering analysis to
analyze technological change. Instead of cumulative output alone,
he decomposes the module cost of PV production into several
factors: raw material, plant and wafer size, average module cost,
and module efficiency, leading to a function Fin which all these
factors are introduced as variables:
DCost
t
¼DCost
t1
Fðh;size;yield;poly;sicost;siconsum;
waferÞ
in which
D
Cost
t
and
D
Cost
t1
is the total change in module cost at
time tand t1,
h
is the module efficiency, size represents the plant
size, yield is the proportion of functioning units available at the end
Table 1
Learning rates for PV technology development for different periods.
1981–1990 1991–2000 1981–2000
Parente et al. [21] 0.2 0.22 0.23
Van Sark [22] 0.16 0.29 0.18
[(Fig._2)TD$FIG]
Fig. 2. The PV learning curve in various time periods: 1976–1990, 1991–2001 and
2002–2006.Source: 1976–2001 [57]; 2002–2006 [19].
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
326

of the manufacturing process, poly represents the poly-crystalline
share, sicost represents the silicon cost, siconsum is the silicon
consumption, and wafer is the wafer size. The results of his model
show that these factors fail to explain most of the changes over the
period of 1975–1979, as 59% of the change is unexplained. It is
clear that his approach cannot give us a whole picture about scale
effects, input prices, and learning effects.
Apparently all these studies confirm one thing that incorporat-
ing the scale and input-prices effect at this moment is an inevitable
task. This paper therefore attempts to develop and validate a multi-
factor learning curve (MFLC), using PV technology development as
case. Having identified causes for cost reductions, a more accurate
forecast of future PV prices may be possible, using forecast of e.g.
input price development. We will demonstrate this as well.
This paper is organized as follows. The characteristics of and
differences between learning, scale and input-prices effect are
outlinedbriefly in Section 2. The methodologyis described in Section
3, in which two economic theories related to this study are
introduced. In Section 4, the input identification and the boundaries
of this study are discussed. A new modular model is built up to
express these various effects. In Section 5, the results of the MFLC
model comparedwith the OFLC model are depicted for the case of PV
technology development by dividing the analysis time period into
three parts. In Section 6, two scenarios are used to forecastthe future
prices of PV modules. Finally, conclusions are presented in Section 7.
2. The effect of scale, learning and input prices
It will be useful to make a distinction between two kinds of
effects: learning and scale. In economics terms, the scale effect can
be described either as economies of scale or returns-to-scale. Most
learningcurve studies only discussthe economies of scale and ignore
its counterpart: the diseconomies of scale [2,7,26,31].Economiesof
scale describe thatthe output of a given product can be doubled for
less than a doubling of cost; diseconomies of scale describe a
doubling of output requiring more than a doubling of cost. Returns-
to-scale is the rate at which output increases as inputs are increased
proportionally. It is always divided into three phases: increasing,
constant and decreasing returns-to-scale. The input prices affect the
production cost depending on the development of input prices. All
these factors are discussed in the following subsections.
2.1. Economies of scale, diseconomies of scale and returns-to-scale
In the last few decades, several papers have been devoted to the
study of the scale effect in PV technology, but the results vary
among these researches. The scale effect can be measured as (Size
t
/
Size
t1
)
f
where size represents the plant size, trepresents time
(year) and
w
represents the scaling factor [27]. The range of scaling
factors, as found in the literature, is shown in Table 2, and is
between 0.07 and 0.20. These numbers are obtained without
considering the learning, scale and input prices effects. Such large
variation results from differences in the time period, data source,
methodology, and purpose.
Economies of scale can be measured by a cost-output elasticity,
which is defined as the marginal cost being divided by average cost
[32]. If marginal cost is less than average cost, this is denoted as
economies of scale. The effects of economies of scale eventually
bring about a decreasing average unit cost as the output increases
[2,30]. Returns-to-scale is used as an alternative to describe the
scale effect. In terms of returns-to-scale, an increase of returns-to-
scale implies that output more than doubles when inputs are
doubled. It results from the larger scale of a production plant
allowing managers and workers to have a larger specialization in
their tasks. The complicated and large-scale equipment meanwhile
can be operated more effectively to increase productivity [33].
On the long run, a firm might change its input proportions as the
level of output changes. If the firm continues to grow, it may suffer
from the diseconomies of scale due to having difficulty in
management [33]. The marginal cost of diseconomies of scale is
larger than average cost [32]. Diseconomies of scale can be
described by decreasing returns-to-scale, which illustrates that
output is less than doubled when all inputs are doubled with large-
scale operation. It arises from the difficulties in organizing and
running a large-scale operation, so that it leads to decreases of
efficiency and productivity [33]. Finally, the diseconomies of scale
in the meantime take place instead of economies of scale. However,
there is a special case. When cost increases proportionally with
output, it is neither economies nor diseconomies of scale [32].Itis
commonly regarded as the constant returns-to-scale, which
explains that output doubles when all inputs are doubled.
2.2. Learning effects
As discussed above, it may be tempting to conclude that with the
economies of scale (increasing returns-to-scale), firms can achieve
their aim of cost reduction, but this need not be true. In fact, the
average cost of a new technology is relatively high at an initial low
level of output. At this stage, no economies of scale take place. With
learning, the cost of production for a firm can be reduced regardless
of the plant size [32]. Learning effects include learning-by-doing,
learning-by-researching, learning-by interacting, and learning-by-
using [3]. Of these effects, we mainlydescribe the following learning
effects as the others are not considered important here:
-
Learning-by-doing: Workers often take longer time to finish a
given task at the first few times they perform that task. As they
repeat doing the same task many times, their speed (or efficiency)
increases. Eventually, it improves the production processes and
accumulatesthe experience of the workers.Managers learn to plan
the production process more effectively through the organization
of the flow of all inputs. All this can be described by learning-by-
doing, and it always takes place at the production stage. When
managers and laborersgain experience with production, it leads to
cost reduction due to learning-by-doing [2,32,33].
-
Learning-by-researching: Increasing research investments
improve the innovation process. As a result, many specialized
tools are introduced into the design and production processes.
Learning-by-researching does not only take place at the
invention stage, but also can be observed at the diffusion and
saturation stages of a technology [2].
-
Learning-by-interacting: The interactions between the various
stakeholders, such as the suppliers of materials, transportation,
end-users and policy makers, enhance the diffusion of knowl-
edge. This can be called learning-by-interacting. It always takes
place at the large diffusion stage [5].
2.3. Scale effects versus learning effects
In Fig. 3 scale effects and learning effects are compared
schematically. Here, AC
1
represents the long-run average unit cost
curve. The economies of scale effects occur along the unit cost
curve, AC
1
. Due to economies of scale, the change in production
Table 2
The various scaling factors in PV technology between 1997 and 2003.
Scaling factor Reference
0.18 Gruber [54]
0.07 Bruton and Woodock [47]
0.20 Ghannam et al. [55]
0.12 Frantzis et al. [56]
0.09 Rohatgi [48]
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
327

from Ato Balong AC
1
leads to lower cost. As a firm continues to
enlarge its plant size, an optimal scale of production eventually is
reached. At this stage, constant returns-to-scale takes place [30].
However, when the size of the plant is expanded further, the
change in production from Eto Falong AC
1
leads to higher cost due
to diseconomies of scale. In contrast to scale effects, the learning
effect shifts the whole average cost curve downward, from AC
1
to
AC
2
. The move from Aon AC
1
to Con AC
2
leads to lower cost due to
learning effects regardless of the current scale of production
[30,32]. Furthermore, an optimal scale of production qmay exist
between the economies and diseconomies of scale. It is clear that
economies of scale or returns-to-scale are a short-term effect,
while learning is a long-term effect [30,30].
2.4. Input prices
In general, inputs can be grouped into three categories: capital
(K), labor (L) and materials (M) (oil, water, copper, etc.). All firms
have to face a central problem: how to produce a given output at
minimum cost when the input prices increase?
The amount of inputs that the firms use will depend on the
prices of these inputs. On the short term, the plant size cannot be
changed [32]. With a growth of input prices, the firms in a short
period may keep the minimum cost by adjusting some input
proportions [33]. The silicon price, for example, increases rapidly in
recent years, but the price of labor rises very slowly. Firms may
reduce the labor and capital inputs to alleviate the impacts of
growing material prices. This is termed as the input substitution
effect [32,33].
On the long term, the firm adjusts all its inputs such that its cost
of production is as low as possible [33]. In the meantime, the firm
can change its plant size, design and phase out the old machinery
to enhance the efficiency and productivity. Thus the firm keeps the
cost of production as low as possible not only by adjusting the
input proportions, but also by enhancing the learning effect and
expanding the scale of operation to alleviate the impacts of
growing material prices. The point is that the firms have a greater
flexibility to change its inputs on the long term than on the short
term. Perloff [33] indicates that the more time firms have to adjust
their inputs, the more factors in production they can change.
Summarizing, on the short term, firms cannot change their
plant size and only use the adjustments of input proportions to
reduce the impacts of increasing input prices. On the long term, it
allows firms to change the plant size and buy new equipment to
improve the efficiency and productivity. In the meantime, it also
allows the firms to adjust all its inputs to keep the cost of
production as low as possible.
3. Methodology
Presently, only a few studies attempt to separate the effects of
scale and input prices from the learning effects. Most studies are still
using the OFLC to describe cost changes as a result of cumulative
output. Nemet [27], however, criticizes that ‘‘the learning curve
model relies on assumptions about weakly understood empirical
studies.’’ In addition, the linkages between cumulative capacity and
technological outcomes are not wellunderstood at thismoment. As a
result, an alternative approach based on a traditional engineering
analysis is adopted by Nemet [27] to analyze technological change.
Instead of cumulative output alone, he decomposed the module cost
of PV production into several factors: raw material, plant and wafer
size, average module cost, and module efficiency, leading to Eq. (5)
(Section 1). Nevertheless, 59% of the observed price changes remain
unexplained. Pan and Ko
¨hler [26] suggested another approach in
using a logistic curve to describe the technical changes. They adopt
life cycle theory to explain technological changes and integrate the
growth rate and R&D investment into the learning curve model to
find an expression for the scale of technological change Y
t
up to time
t:
Y
t
¼a
lo
þa
up
1þuexp bTð1þGÞ t
1þG

1=
u
(6)
in which
a
lo
represents the lower asymptote (saturation level),
a
up
represents the upper asymptote (initial level),
b
is the average
growth rate,
u
determines whether the maximum growth occurs
early or late,
t
represents the time of maximum growth, Tis the
time period, Gis the growth rate of R&D investment. Note that Y
t
is
also denoted as the degree of maturity for which
a
lo
<Y
t
<
a
up
.
This logistic curve model incorporates all phases of technology
development as used in life cycle theory. It also describes the life
span of energy technology on the long run. This logistic curve
includes the growth rate and R&D investment as the driving
variables, however it does not include scale effects and the changes
of input prices, as little is known about them.
3.1. The relationships between learning, scale and input prices
In the present research, rather than using the approach of
Nemet [27] and Pan and Ko
¨hler [26], we follow the approach by
So
¨derholm and Sundqvist [31] and Kahouli-Brahmi [34] to assess
the roles of learning-by-doing, learning-by-researching, input
prices and scale effects. We will show that using a TFLC is not
sufficient to explain cost reduction occurring as a result of
learning-by-doing and learning-by-researching: scale effects and
input price effects should be incorporated into the learning curve
model. The interaction diagram has to be expanded by incorpo-
rating the new variables. Fig. 4 presents the linkages and
interactions between R&D, learning-by-researching, production
[(Fig._4)TD$FIG]
Fig. 4. Relationships and feedbacks between R&D, production growth, economies of
scale, prices of input materials and production cost.
[(Fig._3)TD$FIG]
Fig. 3. Scale effects versus learning effects.
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
328

outputs, learning-by-doing, economies of scale, input prices, and
production cost. This diagram shows that the economies of scale
encourage large-scale production, which helps to enhance the R&D
investment and promotes learning-by-doing. R&D and production
output reduce production cost through enhancing the learning-by-
researching rate and learning-by-doing rate. The input prices
change the production cost depending on the development of
input prices. As the input prices rise (decline), it may increase
(decrease) the production cost. However, firms may adjust its input
proportions to alleviate the impact of increasing input prices over a
short period. In the long run, the learning effect and scale effect
help reducing the impacts of increasing input prices [32,33].
3.2. The learning curve model in economic context
Berndt [10] derives the one-factor learning curve from a Cobb-
Douglas production function under two assumptions. So
¨derholm
and Sundqvist [31] expand this equation by incorporating the R&D
variable to analyze the cost changes of a technology; this was
attempted first by Kouvaritakis et al. [35]. Before we develop our
model, economic theories involving cost minimization and the
Cobb-Douglas CD production function should be introduced and
explained briefly.
The theory of cost minimization relies on the assumption that a
company chooses inputs to the production process that minimize
the total cost of producing output. Usually, two factors are
considered, i.e., capital (K) and labor (L), and the third factor,
material inputs (M), is ignored [10,30,31]. Yet we, in this study,
consider three input elements, labor, capital and materials. As the
unit prices of labor (P
L
), capital (P
K
) and material (P
M
) are taken into
account, the cost minimization equation can be written as:
Minimize C
total
¼P
L
LþP
K
KþP
M
M(7)
This equation is then subject to a constraint equation that a
fixed output Q
x
is to be produced:
FðL;K;MÞ¼Q
x
(8)
where C
total
represents the total cost of a producing the fixed level
of output Q
x
.
Perloff [33] indicates that the production function describes the
relationship between the amount of inputs used and the maximum
quantity of output that can be produced. Here we only introduce
the Cobb-Douglas CD function, which normally is defined as:
Q
x
¼AL
d
1
K
d
2
M
d
3
(9)
in which
d
1
,
d
2
and
d
3
are the elasticity of labor, capital, and
materials, respectively (0 <
d
1
<1, 0 <
d
2
<1 and 0 <
d
3
<1), A
represents the technological change element which can be defined
as: A=Q
b
KS

a
. In order to solve the minimization or maximiza-
tion issues, the Lagrangian method is used with function
F
and
Lagrange multiplier
l
:
F¼P
L
LþP
K
KþP
M
MlðAL
d
1
K
d
2
M
d
3
Q
x
Þ(10)
By partial differentiation @
F
/@L=0, @
F
/@K=0, @
F
/@M=0,
and @
F
/@
l
= 0, we can obtain the following equations:
@F
@L¼P
L
lðd
1
AL
d
1
1
K
d
2
M
d
3
Þ¼0 (11)
@F
@K¼P
K
lðd
2
L
d
1
K
d
2
1
M
d
3
Þ¼0 (12)
@F
@M¼P
M
lðd
3
AL
d
1
K
d
2
M
d
3
1
Þ¼0 (13)
@F
@l ¼AL
d
1
K
d
2
M
d
3
Q
x
¼0 (14)
After some algebraic manipulation and dividing the total cost C
divided by the fixed output Q
x
, a new model can be obtained
[10,30,34]:
C
unit
¼aA
1=ð
d
1
þ
d
2
þ
d
3
Þ
Q
ð1ð
d
1
þ
d
2
þ
d
3
ÞÞ=ð
d
1
þ
d
2
þ
d
3
Þ
x
P
d
1
=ð
d
1
þ
d
2
þ
d
3
Þ
L
P
d
2
=ð
d
1
þ
d
2
þ
d
3
Þ
K
P
d
3
=ð
d
1
þ
d
2
þ
d
3
Þ
M
(15)
where C
unit
represents the average unit cost, the parameter ais
expressed as
a¼ð
d
1
þd
2
þd
3
Þðd
1
d
1
d
2
d
2
d
3
d
3
Þ
ð
d
1
þ
d
2
þ
d
3
Þ
(16)
and
d
1
+
d
2
+
d
3
represents the returns-to-scale parameter (r). After
substituting A=Q
b
KS

a
into Eq. (15), a learning curve, in which
the cumulative capacity and R&D are incorporated, is obtained:
C
unit
¼aQ
b=ð
d
1
þ
d
2
þ
d
3
Þ
KS
a
=ð
d
1
þ
d
2
þ
d
3
Þ
Q
ð1ð
d
1
þ
d
2
þ
d
3
ÞÞ=ð
d
1
þ
d
2
þ
d
3
Þ
x
P
d
1
=ð
d
1
þ
d
2
þ
d
3
Þ
L
P
d
2
=ð
d
1
þ
d
2
þ
d
3
Þ
K
P
d
3
=ð
d
1
þ
d
2
þ
d
3
Þ
M
(17)
Eq. (17) is simplified using the following definitions [30,31]:
r¼X
n
i¼1
d
i
;a¼rY
n
i¼1
d
i
d
i
!
1=r
;
and P
d
1
=ð
d
1
þ
d
2
þ
d
3
Þ
L
P
d
2
=ð
d
1
þ
d
2
þ
d
3
Þ
K
P
d
3
=ð
d
1
þ
d
2
þ
d
3
Þ
M
¼Y
n
i¼1
P
d
i
i
!
1=r
This leads to
C
unit
¼aQ
b=r
KS
a
=r
Q
xð1rÞ=r
Y
n
i¼1
P
d
i
i
!
1=r
(18)
in which P
i
represents the prices of inputs required for producing
and operating the technologies, and
d
i
is the elasticity of the inputs.
Moreover, there are two assumptions related to this model
[2,10,30,31]:
(1)
The returns-to-scale parameter is taken constant (r= 1). Under
this assumption, the term involving the fixed output Q
x
, equals
1 and Eq. (18) can be rewritten as:
C
unit
¼aQ
b
KS
a
Y
n
i¼1
P
d
i
i
(19)
in which a¼Y
n
i¼1
d
i
d
i
!
1
;
(2)
The inflation of input prices is taken into account by using a
GDP (gross domestic product) price deflator [36], as it is the
most general price index that reflects inflation. The GDP
deflator is calculated as the ratio of the value of GDP in current
year prices and the value of GDP measured in base-year prices.
If we assume that the shares of the inputs in total production
costs are identical to the weights used for calculating the GDP
price deflator [10,30,31], it implies that C
unit

GDP price deflator ¼aQ
b
KS
a
Y
n
i¼1
P
d
i
and that the GDP price
deflator equals Y
n
i¼1
P
d
i
i
. The average unit cost C
unit
is changed
to C
inflation
unit
, which thus includes inflation. A simplified learning
curve model can be obtained:
C
inflation
unit
¼aQ
b
KS
a
(20)
Here, we can see that this equation is similar to the two-factor
learning curve. However, the problem is that the scale (Q
ð1rÞ=r
x
)and
input-prices (Y
n
i¼1
P
d
i
i
) effect are left out by these two assumptions.
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
329

3.3. The multi-factor learning curve model
The theory detailed above can be easily generalized. We
observe that when more input prices (P
1
,P
2
,P
3
,P
4
,...) and learning
variables (q
1
,q
2
,q
3
,q
4
,...) are added to the model, a general form,
termed multi-factor learning curve (MFLC), can be obtained:
C
unit
¼aQ
ð1rÞ=r
x
Y
m
i¼1
ðq
s
i
i
Þ
!
1=r
Y
n
i¼1
ðP
d
i
i
Þ
!
1=r
(21)
In this equation, the product Y
m
i¼1
ðq
s
i
i
Þ
1=r
represents the
technological changes, with the
s
i
the power of q
i
. These are
driven by e.g. R&D expenditures (knowledge stock KS), and
production expansion (Q), with associated PRs(PR
q
i
¼2
s
i
), which
can be derived from the terms 2
s
i
/r
. The product Y
n
i¼1
P
d
i
i

1
r
represents the impacts of input prices, and Q
x(1r)/r
represents
scale effects, which are changed by returns-to-scale. It can reflect
the economies and diseconomies of scale effects. Parameters nand
mrepresent the number of considered inputs and learning
variables, respectively.
4. Input identification and research boundaries
There are two main types of solar cells in production: crystalline
silicon and thin-film cells. Among them, crystalline silicon has the
largest share of the market, which is around 90% [19,37,38]. This is
expected to be continued for several years at least. Crystalline
silicon cells are produced either as single crystal or polycrystalline
cells. The single crystal cells are manufactured from silicon crystal
ingots. Until recently, most of the materials used for making the
silicon cells were left-over from the microelectronics industry. At
present, at least nine silicon producers are supplying high-purity
silicon to the photovoltaic industry [38].
4.1. Input identification
Swanson [19] indicates that many factors play a role in PV
production, but the most important elements are: factory (plant)
size, efficiency, silicon, and cellsize. Del Can
˜izo et al.[39] decompose
the cost of PV production into several factors: equipment, labor,
material, yield losses and a fixed part. Among these inputs, material
inputs have the largest share of the total cost, amounting to about
46% while labor accounts for 17%. In a study by Maycock [40],the
shares of material and labor cost are around 22–29% and 4–5%,
respectively. The basic raw material inputs for producing PV are
silicon and silver. Other materials (ethyl-vinyl acetate (EVA),
aluminum, other inputs and framing materials) are ignored since
they are less costlythan silicon and silver [27]. Here we chooseplant
size being the key factor for the scale effect, and silicon as well as
silver being the most essential material inputs.
The silicon price declined from $300/kg in 1975 to $25/kg in
2001 [6]. In recent years, the price has increased to the $40–$50
range for long-term contracts [19]. Subsequently, it has increased
to $83/kg in 2006 due to the shortage of silicon [41].Fig. 5 shows
the variation of silicon and silver price over the period 1976–2006.
As another important input, the silver price rose from $4.3/ounce
in 1976 to $20/ounce in 1980 due to the severe shortage of silver
supply [42]. It fell sharply from $20/ounce to $7/ounce within 2
years. Subsequently, the silver price fluctuated between $6/ounce
to $4/ounce. With the strong growth of the gold price, silver price
has increased to $11/ounce recently.
In the 1970s and 1980s, the average plant size of PV cell
manufacturing was around 1 MW [43]. Maycock [44] indicated
that Kyocera, the second largest producer of PV module in Japan,
had expanded its capacity to 2 MW in 1993. It planned to expand
its plant size to 4 MW in the next few years. In recent years,
Mitsubishi Electric expanded its plant size from 24 MW in 2002 to
35 MW in 2003 and increased to 50 MW in 2004 [45]. For 2007 it is
reported that the Japanese company Sanyo stated that they had
165 MW of capacity, and plans to increase its plant size to 350 MW
in 2008 [46]. We thus construct the historical development of plant
size as presented in Fig. 6.
4.2. Research boundary and the MFLC model for PV production cost
Although many economic studies have been performed on
labor, capital and other materials cost, little is known about the
historical data of these factors in PV production. In addition, little
R&D data can be obtained from the PV companies as well, due to
confidentially issues. Thus learning-by-researching, labor and
capital are omitted in this study, but these factors will be included
by introducing a remaining-factors term, see below. For the inputs,
only silicon and silver are chosen to be the input factors. The other
material inputs (glass, aluminum, etc.) are grouped into one ‘other’
factor (O). The cost minimization equation then is rewritten as:
Minimize C
total
¼P
Si
Si þP
Ag
Ag þP
O
O (22)
in which P
Si
,P
Ag
and P
O
represent the unit prices of silicon (Si),
silver (Ag) and other inputs (O), respectively. The Cobb-Douglas
function has to be rewritten by adding these inputs:
Q
x
¼ASi
d
3
Ag
d
4
O
d
5
(23)
[(Fig._6)TD$FIG]
Fig. 6. PV plant size (MW) from 1976 to 2006.Source:[43,45].
[(Fig._5)TD$FIG]
Fig. 5. Development of silicon and silver prices, 1976–2006.Source: (1) Silicon
prices: [43,45], (2) silver prices: [42].
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
330

where
d
3
,
d
4
, and
d
5
are the elasticity of silicon, silver and other
inputs, respectively.
After identifying the main factors, the cost minimization
equation (Eq. (22)) is subjected to the Cobb-Douglas function
(Eq. (23)). Then by using the method of Lagrange multiplier, Eq.
(10) is rewritten to yield:
F¼P
Si
Si þP
Ag
Ag þP
O
OlðASi
d
3
Ag
d
4
O
d
5
Q
x
Þ(24)
After partial differentiation @
F
/@Si = 0, @
F
/@Ag = 0,
@
F
/@O = 0, and @
F
/@
l
= 0 and dividing the total cost C
total
by
the fixed output Q
x
, we can obtain the following multi-factor
learning curve model:
C
unit
¼aQ
b=r
Q
ð1rÞ=r
x
ðP
d
3
Si
P
d
4
Ag
P
d
5
O
Þ
1=r
(25)
in which r=
d
3
+
d
4
+
d
5
is the returns-to-scale parameter, and a¼
rðd
d
3
3
d
d
4
4
d
d
5
5
Þ
1=r
is a constant term.
By taking the logarithm on both sides of Eq. (25), a linear form is
obtained:
log C
unit
¼log aþb
1
log Qþnlog Q
x
þd
Si
log P
Si
þd
Ag
log P
Ag
þd
O
log P
O
(26)
in which the coefficients are defined as:
log aRemaining-factors effect
b
1
=b(n+ 1) Learning-by-doing index
a
1
=
a
(n+ 1) Learning-by-researching index
n=(1r)/rScale index or the elasticity of plant size
d
Si
=
d
3
(n+ 1) Silicon price index
d
Ag
=
d
4
(n+ 1) Silver price index
d
O
=
d
5
(n+ 1) Other input-prices index
It is clear that Eq. (26) decomposes the unit cost of PV
production into four major parts: learning-by-doing, scale, input-
prices and remaining-factors effect:
(1)
Learning-by-doing: It is represented by the term b
1
log Q. The
coefficient b
1
is determined by the scale index n, which reflects
that leaning-by-doing is enhanced as the economies of scale
are taking place (r>1).
(2)
Scale effect: The scale effects are reflected by the term nlog Q
x
.
The returns-to-scale, in the model, does not only affect the
scale index, but also changes the elasticity of learning and input
prices. However, by setting returns-to-scale constant (r= 1),
the scale effect can be omitted from the model.
(3)
Input-price effect: The rest of Eq. (26) (
d
Si
log P
Si
+
d
Ag
log P
Ag
+
d
O
log P
O
) reflects all changes due to input prices. The input
prices are mainly changed by the elasticity of the inputs and the
returns-to-scale. The substitution effect also occurs between
these input factors. The term
d
O
log P
O
represents the other
input-prices effect. Since actual data of other inputs cannot
be obtained, this part is calculated by
d
O
log P
O
=logC
unit

(log a+b
1
log Q+nlog Q
x
+
d
Si
log P
Si
+
d
Ag
log P
Ag
). It can be
regarded as the residual term in this research.
(4)
Remaining-factors effect: log ais the constant term in the MFLC
model which shows that when all the independent variables
(b
1
log Q,nlog Q
x
, etc.) in this model equal to zero, log aequals
to log C
unit
. It infers that not only are the costs determined by
learning-by-doing, scale and input-prices, but also by other
factors (such as learning-by-searching, subsidies, labor, etc.). In
this study, log arepresents the remaining-factors effect, which
reflects two types of factors: first, the factors have been
incorporated in this model, but left out from this study due to
lack of the historical data (such as labor, capital and R&D);
second, the factors have not been discussed in this study (such
as subsidies, taxes and O&M cost). Thus these factors are
grouped into the constant term log a. In a further study, these
factors should be incorporated into the research.
To summarize, the MFLC decomposes the cost into three major
effects: learning-by-doing,scale and input price effect.The elasticity
or indexes of the learning, scale and input prices are shaped by the
return-to-scales. The remaining-factors effect represents the effects
that are out of this research scope for various reasons discussed
above. Other material inputs are grouped into one factor
d
O
log P
O
,
which can be regarded as the residual term.
5. Results and residuals
In the following paragraphs, results of the simulations are
presented. The numbers and figures acquired by running the MFLC
model are interpreted by using the concepts described above. In
order to demonstrate the impacts of these effects on cost reduction,
the analysisand discussion is divided into three parts.In the first part
(Section 5.1), regression is carried out to obtain the values of the
variables discussed above. In the second part (Section 5.2), the
results are investigated by dividing the learning curve into three
time periods: (1) 1976–1986, (2) 1987–1997, and (3) 1998–2006.
Uncertainty and sensitivity issues are discussed in the last part,
Section 5.3.
5.1. Parameters and statistical analysis
The values of the variables from Eq. (26) are determined by
using multivariate regression [9]; here we used the regression
function available in Microsoft Excel on the data presented in Fig. 2
and Section 4.1. The base of the log numbers is 10. The results of the
regression are listed in Table 3; the fit to the data is shown in Fig. 7,
and compared to the OFLC fit.
For the complete data period 1976–2006, the scale index (n)is
0.062, which is less than 0.07 [47] and 0.09 [48] (see Table 2).
Compared with the OFLC model, the learning rate of this study is
13.5% (inferred from parameter b
1
and Eq. (3)), which is lower than
the OFLC one (19.5%). The positive index of silicon-price implies
that the effect of silicon increases with a rise of the silicon price.
The negative index of silver-price indicates that the effect of silver
is contrary to that of the silicon price. The larger returns-to-scale
(r>1) obtained from n=(1r)/ris 1.07, which shows that
economies of scale takes place in this simulation. The
d
O
computed
by this model is 0.853. Fig. 7 shows two fits, one with and one
without the other input effects included; there are only slight
differences. Of the coefficients, the standard errors of nand
d
Ag
are
49% and 35%, respectively. This indicates that there are some
uncertainties, which may exist in the historical data. One of the
uncertainties for the plant size might result from the various
expansion rates among countries. Both silver and silicon, but also
the PV unit prices, are average prices for each year, which may
bring some averaging uncertainties to this model.
Table 3
The values of the variables.
Parameter Value Standard error
log a1.058 0.112
b
1
0.210 0.028
n0.062 0.030
d
Si
0.285 0.050
d
Ag
0.138 0.048
d
O
0.853 0.031
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331

A measure of the goodness of the fit to the experimental data is
the coefficient of determination, R
2
. A value of R
2
close to one
usually shows an excellent overall fit, while a value near zero
shows a failure of the estimated regression. The R
2
of the regression
yielding the parameter values as given in Table 3 is 0.993, which
shows that the estimated regression equation fits the historical
data quite well. Compared with the OFLC, the R
2
of the MFLC is
better than that of the OFLC, whose R
2
is 0.9828. Moreover,
performing a Student t-test, it was found that the Student t-values
all are well above 1.96 (5% statistical significance level), which
implies that the values of the coefficients are statistically
significant. We therefore confidently will use the set of coefficients
shown in Table 3 in the following simulations.
5.2. The results of the multi-factor learning curve
In order to forecast future prices of PV modules, historical
simulation is of great importance. The regression results on the
above parameters were used to obtain the effects of remaining-
factors learning-by-doing, scale and input-prices. The final results
of these effects are shown in Fig. 8, with data in Tables 4–6, and
have been determined using the following equation:
C
unit
¼C
unit
log C
unit
ðlog aþb
1
log Qþnlog Q
x
þd
Si
log P
Si
þd
Ag
log P
Ag
þd
O
log P
O
Þ(27)
The overall effects were presented in Fig. 7. Note that of these
effects, learning-by-doing, remaining-factors and silicon-price
effect contribute the most to the cost reduction of PV. Here it
will be helpful to realize the interactions between these factors by
dividing the results into three time periods: (1) 1976–1986 (the
beginning stage); (2) 1987–1997 (the diffusion stage); (3) 1998–
2006 (the mature stage). We choose these periods for three
reasons. First, since most technologies just emerged from the
laboratory over the first period, the cumulative output was quite
low. The learning-by-doing effect plays a minor role in this period.
No economies of scale took place over this period. Second, the
market had already shifted from space satellite applications to
terrestrial ones. The economies of scale came in, but less
important. The learning-by-doing effect still played a minor role
in cost reduction at the second stage. Third, scale effect became
[(Fig._7)TD$FIG]
Fig. 7. The PV learning curve fitted to the OFLC and MFLC model (with and without
including other input effects) for the period 1976–2006.
Table 6
Summary of the MFLC results for time period, 1998–2006.
Factor Change Effects on
MFLC module
cost in 2006
price ($/Wp)
OFLC
($/Wp)
Remaining-factors 0.481
Learning 793.5–8070 MWp 1.081 2.764
Scale effect (plant size) 6–100 MW 0.463
Silicon price $19/kg–$83/kg 1.008
Silver price $5/ounce–
$11.62/ounce
0.239
Sum of factors 1.257 2.764
Others inputs (residual) 0.252 1.759
Actual change 1.005 1.005
[(Fig._8)TD$FIG]
Fig. 8. Breakdown of factors contributing to the unit cost.
Table 4
Summary of the MFLC results for time period, 1976–1986.
Factor Change Effects on
MFLC module
cost in 2006
price ($/Wp)
OFLC
($/Wp)
Remaining-factors 28.371
Learning 0.32–77.78MWp 8.170 50.67
Scale effect (plant size) 0.08–1MW 2.545
Silicon price $176/kg–$67/kg 18.470
Silver price $4.35/ounce–
$5.46/ounce
2.216
Sum of factors 55.341 50.67
Others inputs (residual) 2.404 7.075
Actual change 57.745 57.745
Table 5
Summary of the MFLC results for time period, 1987–1997.
Factor Change Effects on
MFLC module
cost in 2006
price ($/Wp)
OFLC
($/Wp)
Remaining-factors 2.548
Learning 98–662.53 MWp 0.256 4.620
Scale effect (plant size) 1.15–4 MW 0.234
Silicon price $60/kg–$21/kg 2.169
Silver price $7/ounce–
$4.87/ounce
0.441
Sum of factors 4.767 4.620
Others inputs (residual) 0.550 0.403
Actual change 4.217 4.217
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332

significant in the third period. The learning-by-doing effect played
a key role in this period. In the following paragraphs, the
differences in the factors and residual in these three periods are
depicted by comparing with OFLC model.
5.2.1. Period 1976–1986
The PV market was still at the beginning stage. The actual price
of a PV module fell from $69/Wp in 1976 to $11/Wp in 1986. The
outputs and plant sizes were very small. Space satellite applica-
tions dominated market growth in this period [6,19]. Three factors,
i.e., remaining-factors, silicon price and learning, accounted for the
largest changes in cost. The factors scale and other inputs were of
less importance but played a role in this period.
Remaining-factors effect: Of the factors we identify, the declining
remaining-factors accounted for the largest changes (49%) in cost
(see Fig. 8 and Table 4). At this stage, most technologies just
emerged from the laboratory and tended to promote themselves
on the market before being commercialized. The public R&D and
governmental subsidies meanwhile helped the PV industry
shifting from the invention to the diffusion stage [27]. In the
mid-1970s, the birth of the terrestrial PV industry shifted the
market away from space applications [6,19]. Thus it is important to
note that the early development of PV production only focused on
research and innovation. Learning-by-researching was of much
importance during this period. It might be the major factor to
account for the falling of remaining-factors effect at this stage.
Learning effect: The learning effect during the first 2 years (see
Fig. 8) did not play a role to give a positive impact on cost reduction
since many technologies just emerged from the laboratory.
Subsequently, the learning effect came in to decrease the PV
module price, but it was not so important. It only accounted for
13.6% of the total reduction over this period.
Silicon-price effect: Silicon prices, at this stage, decreased from
$176/kg in 1976 to $67/kg in 1986, but still stood at a high level. It
contributed to the cost reduction by 32%.
Silver-price effect: The silver price first increased rapidly to $20/
ounce within 4 years. During this period, for decreasing the
production cost, firms adjusted their input proportions by shifting
away from silver to use other materials, known as the input
substitution effect [32,33]. After that, the price declined to the
normal level, around $5/ounce–$7/ounce range. Firms preferred to
use more silver for producing PV modules. It explains the cost
being increased by the silver-price effect.
Scale effect: All plants in this period were smaller than 1 MW.
The scale effects were not significant over this period. It only
accounted for 4.6% of the total reduction. Thus the scale index (n)
could be assumed as zero and the returns-to-scale would be
constant (r= 1). The model could therefore be simplified as:
log C
unit
¼log aþblog Qþd
3
log P
Si
þd
4
log P
Ag
þd
5
log P
O
(28)
This equation describes that the cost changes of PV in this period
were only dominated by remaining-factors (log a), learning effect
(blog Q) and input-prices: silicon and silver.
Compared with the OFLC model over this period, the residual
(other inputs) of the MFLC model in this period only accounted for
4.2%, which is smaller than the OFLC one (12.3%). These five factors
of the MFLC model together explained more than 96% of the change
in cost over this period, but OFLC only explained 88% of the total
change in cost.
5.2.2. Period 1987–1997
In this period, the costs of PV production slightly went up, but
the tendency still was to go down. The PV module price decreased
by 45%, from $9.4/Wp in 1987 to $5.2/Wp in 1997. The PV market
had turned to the diffusion stage. The cumulative output and plant
size increased steadily. Among these factors, remaining-factors
and silicon price contributed the most to cost reduction (see Fig. 8
and Table 5). Other factors still played a role at this stage, but less
important.
Remaining-factors effect: Compared to the first period, the
decreasing rate of remaining-factors fell to 2.7% per year, but it still
dominated the cost reduction. Compared to the period of 1976–
1986, the large decreases not only resulted from learning-by-
researching, but also from governmental subsidies [27]. Japan
launched a set of programs for supporting its PV industry since the
early 1970s [49]. Germany in 1991 introduced the feed-in law to
enlarge the renewable energy market [50]. USA and other
countries meanwhile had the same subsidy programs. It was
clear that the governmental subsides contributed the most to the
falling of remaining-factors effect over this period.
Learning effect: At this stage, the learning effect only contributes
a little (6%) for cost reduction. The cumulative output of PV
modules slightly increased from 98 MWp 1987 to 662.53 MWp.
This increase could not bring out a significant impact on PV cost
reduction.
Scale effect: Unlike the first period, the scale effect in this period
started to become important to give a positive impact on cost
reduction. The plant size was expanded from 1 MW to 4 MW.
However, it was too small to give a significant impact on cost
reduction, but it still played a role over this period.
Silicon-price effect: The prices of silicon declined by 65% in this
period that resulted in cost falling as well. Its contribution
accounted for 50% of the total reduction.
Silver-price effect: The silver price at this stage decreased by 30%.
Firms increased the use of silver instead of other expensive
materials. That might be one of the reasons that the cost of PV
production increased somewhat. Another reason is the effects of
other input-prices (see Fig. 8). In this period, the increase in capital
and labor to expand the plant size may result in the effects of other
input-prices rising a little in the period of 1990–1995.
5.2.3. Period 1998–2006
In this period, the PV production had already shifted from
diffusion stage to mature stage. Fig. 2 shows that the curve became
flat over 2002–2006 and the cost of PV production stopped falling.
The price of PV modules was slightly decreased by 22%. Compared
to the first two periods, of these factors, learning effect, scale effect
and remaining-factors contributed the most to cost reduction.
Silicon-price effect, in contrast to the past, played a different role in
this period. As we observed earlier capacity shortages among solar
cell and module manufacturers are likely to be partially responsi-
ble for the increase in module prices after 2002, but it is very
difficult to quantify this effect. The quick expansion of the PV
market after 2002 led also to steep increases in the price of high-
purity silicon. If we analyze this period under the assumption that
the market price did nonetheless reflect production cost we may
observe that compared to the first two periods, the contribution of
learning effect, scale effect and remaining-factors contributed the
most to cost reduction. The silicon-price effect, in contrast to the
past, played a different role in this period.
Learning effect: Only looking at the OFLC figure, we might
simply infer that no learning effect is taking place at this stage. The
fact, however, was that the learning effects obtained by running
the MFLC model were still present as in the other periods. The
decreasing rate of learning effect over this period was around 3%
per year. It accounted for the largest part of cost reduction at this
stage (see Table 6 and Fig. 8).
Scale effect: Aside from learning effect, the scale effect is of large
importance due to the rapid expansion of plant size from 6 MW in
1998 to around 100 MW in 2006. The decreasing rate of scale
effects was 11.6% per year. The economies of scale played a
significant role in this period. With the expansion of plan size in the
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333

future, the contribution of scale effect will be much more
important than the past.
Silicon-price effect: The silicon prices in this period boosted
quickly from $24/kg in 1998 to $83/kg in 2006 due to shortage of
silicon. Until now, the spot market price even is over $300/kg.
Consequently, it caused the rise of production cost. Table 6 shows
that the increased silicon-price effect almost neutralized the
decreased learning effect.
Silver-price effect: As the Silver Institute [42] mentioned, the
silver price increased by 110%, up to $11/ounce in 2006. This
caused the firms adjusting the proportions of input materials to
avoid the lost. As a result, decreasing the use of silver leads to a
reduction in the cost of PV production.
Remaining-factors effect: The effect of remaining-factors, at this
stage, became smaller. It played a role in cost reduction, but of less
importance than before.
Overall, in this period only the silicon effect gave a negative
impact on cost reduction. It lead to an increase of the cost of PV
production. The rest of the effects, learning, scale, remaining-
factors and silver-price effects, still gave a positive impact on cost
reduction leading to a reduction of the cost of PV production, but
these effects were counteracted by the increase of the silicon effect
(learning effect + scale effect + remaining-factors effect + silver
effect–silicon effect). The overall effects in this period were much
smaller than in earlier periods. As a result, it caused the PV module
price to decrease slightly. The MFLC shows that the rising silicon
price weakened the learning effect. The module price stopped
falling, while the cumulative output still increased.
To summarize, through the above investigation, we demon-
strate that the cost reduction of PV production actually is explained
by a set of effects, rather than by learning-by-doing alone. Once the
expansion of plant size and the growth of input prices take place to
change the cost of PV production over a short period, the OFLC
model cannot reflect these effects and gives us a wrong impression,
i.e., no learning effect is taking place over this time period. It
certainly causes one major issue, that in the long-term forecasting
the estimations of the OFLC are less reliable due to lack of scale,
input-prices and other effects. Furthermore, in this historical
analysis, we find that the assumption of the shares of the inputs in
total production costs being identical to the weights used for
calculating the GDP price deflator in order to leave out the input-
prices effect is a very weak hypothesis. The silicon-price effect, for
example, in this study does play an important role over the period
of 1976–2006, especially in recent years. It cannot be omitted from
the model.
5.3. Sensitivity and uncertainty
In this section uncertainty in four factors is addressed:
cumulative output, plant size, silicon price and silver price. The
sensitivity of the model is tested by considering an increase and a
decrease of 80% in each of the four factors. The model is most
sensitive to uncertainty in two variables: cumulative output and
silicon price, which is indicated in Fig. 9. The plant size is of
moderate importance at this moment. If the plant size will
continue to increase, the scale effect will become much more
significant. Since the standard error for plant size index and silver-
price index are relatively high, 49% and 35%, respectively (see Table
3), it indicates that there are some uncertainties existing in the
historical data. The sensitivity analysis here for plant size and silver
price therefore is less reliable.
With converting the learning curve into linear form (logarithm),
the stochastic error term or residual term must be present in a
regression equation, since the real-world costs are not exactly the
same as the estimated costs. The residuals represented by
d
5
log P
O
in the MFLC model may result from three sources: (1) other minor
influences on estimation of cost that are omitted from the equation
(such as the input of glass); (2) cross-countries data are not easily
obtained and in some cases, having the data is impossible. Since
the labor cost, investment and O&M may easily vary among
countries, global data for these factors does not exist. For example,
the labor cost in China is much lower than that in Japan. In
addition, the prices of silicon and plant size (1976–2001) are
acquired from the figures of Nemet’s study [43]. Since the
expansion rates of the plant size are different among the countries,
finding the global data is not easy. These may enlarge the
uncertainties of the results; (3) all attempts to generalize human
behavior must contain at least some amount of unpredictable
variation.
6. A MFLC forecast for future PV cost
Having now available a fit to the historical data, in which the
influence of several factors now is clear, it is possible to forecast PV
cost development, based on expert data or opinion. For example,
forecasts of silicon price can be used in combination with plant size
developments. In this section we briefly explore two scenarios, as
an illustration how the MFLC could be used in a more reliable
prediction of future cost than the OFLC.
Like many studies of future PV cost estimations, Van der Zwaan
and Rabl [51] apply a progress ratio of 0.80 to estimate that the
cumulative PV production has to be increased to 148 GW in order
to reach a break-even cost of $1/Wp. The current cumulative
production is about 8070 MWp [45]. Maycock [52] predicts that
the world PV module production will increase from 955 MW/year
in 2004 to 4000 MW/year in 2010. The unit cost will reach $2/W.
Swanson [19] forecasts that assuming the growth of the market at
30% per year, a price of $1.56/W is obtained in 2012. However, all
these estimations are based on the OFLC model and ignore the
rising input-prices effect and economies of scale effect. For a better
understanding of the interactions between these factors in our
MFLC model, two short term scenarios with various silicon prices
are carried out, scenario MFLC-1 and MFLC-2.
Before turning to the simulation, the input data of this scenario
have to be set up. Rogol [41] makes a forecast on PV future
development over the time period of 2007–2011. First of all, he
believes that with the growth of the new suppliers in China, more
silicon supply will come on line than was estimated before. He also
estimates the average of both indirect and direct sales, to be $103/
kg in 2007 and $109/kg in 2008, but the price will drop to $97/kg in
[(Fig._9)TD$FIG]
Fig. 9. Sensitivity of the MFLC model to a variation of four factors.
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
334

2011. With more silicon production, Rogol [41] also foresees that
the world production of PV module will increase to 4 GW in 2007,
6.3 GW in 2008, 10.9 MW in 2009, 17.2 MW in 2010, and 22.7 GW
in 2011.
At the same time, the Japanese company Sanyo stated that they
had 165 MW of capacity in 2007, and plans to increase its plant size
to 350 MW in 2008 [45]. Trina, a Chinese company, claims that
they had 150 MW of capacity in 2008 and will expand to 350 MW
in 2008 as well. Both Solland and EverQ plan to raise their capacity
to 600 MW by 2010. E-Ton is aiming at building a 500 MW plant in
2009. Sunpower declares that they plan to expand its plant to
875 MW in 2011.
The Silver Institute [42] points out that the silver price increases
from $4.6/ounce in 2002 to $13.39/ounce in 2007 and the current
average price is around $17.52/ounce (May 2008). The average rate
of increase between 2002 and 2008 is 24.97%. For the future,
Klapwijk [53] predicts that silver price will fall to the $13/ounce–
$16/ounce range. Thus this study assumes the future price will
decrease to $13/ounce in 2011. The average decreasing rate
between 2009 and 2011 will be around 9.46%.
All data used for a short-term scenario are listed in Table 7. This
scenario is referred to as scenario MFLC-1.
6.1. Short-term scenario MFLC-1
The results of this scenario compared with the OFLC model are
shown in Table 8. In the period of 2007–2011, the PV production
has already shifted to a mature stage. The expansion of the PV
market is still ongoing. The plant size will increase to over
800 MW. The world cumulative output of PV production will rise to
69 GW in 2011. The scenario shows that learning and scale effect
will account for most of the reduction in cost. Other factors will
play a role in this period, but less important.
Learning effect: In this period, the cumulative output increases
rapidly. The improvement of the production process and labor
efficiency, the introduction of new equipment and production
methods, and the changes in the organization enhance the learning
rate. All these lead to the fact that the learning effect contributes
the most to cost reduction.
Scale effect: With the increases of plant size, the scale effect is of
much more significance in this period than the past. The economies
of scale, at this stage, ensure the firms to gain the benefits from the
larger specialization of workers and managers. In addition, it also
helps to enhance the learning-by-doing rate. In the future, its role
in cost reduction will be of importance.
Silicon-price effect: Rogol [41] predicts that the silicon price will
first increase to $109/kg due to shortage of silicon, but, with more
silicon suppliers in China, the price will decrease to $97/kg.
Comparing this with the past, it still stands at a high level. In
contrast to the learning and scale effect, the silicon-price effect
increases the cost, thus yielding a negative impact on costreduction.
Silver-price effect: Silver-price effect in this period still plays a
minor role since silver prices are relatively stable. It allows the
firms to adjust the proportions of input materials slightly to
overcome the impact of silver-price effect.
Remaining-factors effect: The remaining-factors effect plays an
entirely different role in this period, it slightly increases by 9% in
2011. Together with the silicon-price effect, it increases the cost of
PV production to give a negative impact on cost reduction.
Overall, the expansion of plant size leads to the fact that the
economies of scale are becoming much more important than before.
Economies of scale enhance the learning-by-doing effect. Silver-
price effect meanwhile plays a role, but less important. The high
prices of silicon as well as remaining-factors effect, however,
increase the cost of production to give a negative impact on cost
reduction,thus weakening the cost decreasesdue to the learning and
scale effect. As a result, the overall effect is an upward shift of the
average cost curve. The multi-factor learning curve can reflect all
these effects sufficiently. Thus the price of PV modules will decrease
from $3.047/Wp in 2007 to $1.881/Wp in 2011. Fig. 10 shows that
the prices forecasted by the MFLC will not follow the OFLC trajectory
anymore, but are shifted upwards.
6.2. Short-term scenario with lower silicon prices in 2010 and 2011
(MFLC-2)
Since Swanson [19] mentions that the price recently has
increased to the $40–$50 range for long-term contracts, Rogol [41]
Table 7
The data are used in scenario MFLC-1, 2007–2011.
Year Cumulative capacity (MWp) Plant size (MW) Silicon price ($/kg) Silver price ($/ounce)
2007 12,070 165 103 13.39
2008 18,370 350 109 17.52
2009 29,270 500 106 14.5
2010 46,470 600 101 13.1
2011 69,170 875 97 13.0
[(Fig._10)TD$FIG]
Fig. 10. The PV learning curve extrapolated to 2011 using the MFLC model for two
scenarios, MFLC-1 and MFLC-2, compared to the OFLC.
Table 8
Summary of the MFLC-1 scenario results for time period, 2007–2011.
Factor Change Effects on
MFLC module
cost in 2006
price ($/Wp)
OFLC
($/Wp)
Remaining-factors 0.592
Learning 12–69GW 1.570 0.963
Scale effect (plant size) 165–875 MW 0.383
Silicon price $103/kg–$97/kg 0.270
Silver price $13.39/ounce–
$13/ounce
0.075
Sum of factors 1.166 0.963
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335

might overestimate the future silicon prices. In an alternative
second scenario (MFLC-2), we assume that the silicon price may
decrease from $106/kg in 2009 to $70/kg in 2010 and to $50/kg in
2011, while all other data as stated in Table 7 remain the same.
Fig. 10 shows the effect on the learning curve. Of the effects,
only the silicon-price effect decreases slightly due to the assumed
decreases of silicon prices in 2010 and 2011, but together with the
remaining-factors effect, it still gives a negative impact on cost
reduction. The learning-by-doing and scale effect still play the key
roles in cost reduction over this period. Silver-price effect plays a
role as above, but less important.
The overall result on the learning curve using this lower silicon
price scenario is shown in Fig. 10 (MFLC-2). Since the silicon prices
decrease from $106/kg in 2009 to $70/kg in 2010 and to $50/kg in
2011, the silicon effect falls which leads the cost of PV production
to decrease from $3.047/Wp in 2007 to $1.556/Wp in 2011. The
learning-by-doing and scale effect still play the key roles in cost
reduction over this period. Silver-price effect plays a role as above,
but less important. Compared to the prices in 2010 and 2011 for
the first scenario MFLC-1, the price of PV module reduces by $0.21
in 2010 and $0.244 in 2011. It proves that the input-prices play an
important role in cost reduction. Compared with the OFLC, the
MFLC model reflects the changes of silicon prices, which lead to the
falling of cost in 2010 and 2011.
7. Conclusion
This study was motivated by the fact that the one factor
learning curve ignores some factors and uncertainties, which are
vital in driving cost reduction. As recent cost data evidences, the
market price of PV modules stabilizes as the cumulative output
increases, which would imply that no technological improvement
takes place in these periods. In order to address this issue, the
paper has described a methodology, named the multi-factor
learning curve, to incorporate the scale and input-prices effect as
the additional variables into the one factor learning curve. The
multi-factor learning curve is not only derived from the economic
theories, but also supported by an empirical study, for the case of
PV technology development.
The results of this research challenge the credibility of the one
factor learning curve. They confirm that a learning curve actually
represents a combined effect on cost reduction, rather than
learning by doing alone. At the technology emerging stage, the
learning effect plays a minor role in cost reduction. No economies
of scale take place at this stage. The factors that drive the cost
decline in case of PV technology development are silicon price and
other factors (such as learning-by-researching, subsidies from
government). At the diffusion stage, the economies of scale effect
starts to play a role in cost reduction, but it is not so important. The
learning effect also accounts only to a small extent to cost
reduction. The other factors and input-prices effect still play an
important role in cost reduction at this stage. At the mature stage,
learning and scale effect instead of input prices and other factors
contribute the most to cost reduction.
We have shown that the one factor learning curve may
successfully describe the cost reduction at the technology emerging
stage, but failsto explain the changes in cost at themature stage. The
OFLC cannot reflect the cost changes caused by the growth ofinput-
prices. As a consequence, the costs estimated by the OFLC are lower
than the market ones. The MFLC reflects all these changes
sufficiently to present a reliable result for cost reduction.
In addition, the results also verify the assertion by Isoard and
Soria [30], and Pindyck and Rubinfeld [32] that economies of scale
play an important role in a large scale production due to the larger
scale of a production plant allowing managers and workers to have
a larger specialization in their tasks. We also find that the
assumption about the shares of the inputs in total production costs
being identical to the weights used for calculating the GDP price
deflator is a weak hypothesis. Our results reveal that the silicon-
price effect does play an essential role in cost changes. The input-
prices effect should not be eliminated from the model.
Compared with the one factor learning curve, the MFLC model
solves the discontinuity issue,which exists in the one factor learning
curve. Furthermore, the MFLC modelhas a better capability than the
OFLC in forecasting future cost since the cost production is not only
determined by cumulative output alone, but also by scale, input-
prices and other factors. As a result, the reliability of the estimated
costs has been improved by the MFLC model. The MFLC model, in
addition, is not only restricted for use in the PV technology case
study, but it can easily be used for other technologies (such as wind
power and biomass), e.g.data on steel price development could help
to elucidate wind turbine cost development.
However, some issues related to the research still remain
unsolved. First, since many factors such as labor, investment and
learning-by-researching are omitted from this study, the effects of
remaining-factors contributing to the cost reduction are not very
clear. In addition, this model cannot tackle the issue of lack of
representation of institutional structures (such as subsidies). In
future studies, we recommend two issues to be investigated: the
first issue is that some factors which have been incorporated in to
the MFLC model are left out from this study due to the absence of
historical data (such as labor, capital, and learning-by-research-
ing). Thus, seeking reliable historical data is required. The second
issue is that some factors that are not discussed in this study
should be investigated as to how to incorporate them into the
MFLC model. For example, the effect of feed-in law should be
investigated to incorporate into this model.
References
[1] Nakicenovic N. Special Report on Emission Scenarios. Cambridge, U.K.: Cam-
bridge University Press; 2000.
[2] Kahouli-Brahmi S. Technological learning in energy-environment-economy
modeling: a survey. Energy Policy 2008;36:138–62.
[3] Junginger M, Faaij A, Van Sark W, editors. Technological Learning in the Energy
Sector, Lessons for Policy, Industry and Science. Cheltenham, UK: Edward Elgar
Publishing; 2010.
[4] Boston Consulting Group. Perspectives on Experience; 1972.
[5] Gru
¨bler A, Nakicenovic N, Victor DG. Dynamics of energy technologies and
global change. Energy Policy 1999;27:247–80.
[6] Nemet GF. Beyond the learning curve: factors influencing cost reductions in
photovoltaics. Energy Policy 2006;34:3218–32.
[7] Hall G, Howell S. The experience curve from the economist’s perspective.
Strategic Management Journal 1985;6:197–212.
[8] Argote L, Epple D. Learning curves in manufacturing. Science 1990;247:920–4.
[9] Studenmund AH. Using Econometrics: A Practical Guide. Reading, MA, U.S.A.:
Addison Wesley; 2001.
[10] Berndt ER. The Practice of Econometrics: Classicaland Contemporary. Reading,
MA, U.S.A.: Addison-Wesley; 1991.
[11] Klaassen G, Asami M, Larsen K, Sundqvist T. The impact of R&D on innovation
for wind energy in Denmark, Germany and the United Kingdom. Ecological
Economics 2005;54:227–40.
[12] Kobos PH, Erickson JD, Drennen TE. Technological learning and renewable
energy costs: implications for US renewable energy policy. Energy Policy
2006;34:1658.
[13] Jamasb T. Technical change theory and learning curves: patterns of progress in
electricity generation technologies. Energy Journal 2006;28:51–71.
[14] McDonald A, Schrattenholzer L. Learning rates for energy technologies. Energy
Policy 2001;29:255–61.
[15] Wene C. Experience Curves for Energy Technology Policy. Paris, France: OECD/
IEA; 2000.
[16] Neij L. Use of experience curves to analyse the prospects for diffusion and
adoption of renewable energy technology. Energy Policy 1997;25:1099–107.
[17] Ferioli F, Schoots K, Van der Zwaan BCC. Use and limitations of learning curves
for energy technology policy: a component-learning hypothesis. Energy Policy
2009;37:2525–35.
[18] Wene C. Energy technology learning through deployment in competitive
markets. The Engineering Economist 2008;53:340–64.
[19] Swanson RM. A vision for crystalline silicon photovoltaics. Progress in Photo-
voltaics Research and Applications 2006;14:443–53.
[20] Van Sark WGJHM, Alsema EA, Junginger HM, De Moor HHC, Schaeffer GJ.
Accuracy of progress ratios determined from experience curves: the case of
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
336

crystalline silicon photovoltaic module technology development. Progress in
Photovoltaics Research and Applications 2008;16:441–53.
[21] Parente V, Goldemberg J, Zilles R. Comments on experience curves for PV
modules. Progress in Photovoltaics Research and Applications 2002;10:571–4.
[22] Van Sark WGJHM. Introducing errors in progress ratios determined from
experience curves. Technological Forecasting and Social Change 2008;
75:405–15.
[23] Schrattenholzer L, Analysis of past learning rates; ECS contribution progress
report TEEM; 1998.
[24] Neij L, Dannemand Andersen P, Durstewitz M. The Use of Experience Curves
for Assessing Energy Policy Programmes; 2003.
[25] Seebregts AJ, Kram T, Schaeffer GJ, Stoffer A, Kypreos S, Barreto L, Messner S,
Schrattenholzer L. Endogenous Technological Change in Energy System Mod-
els: Synthesis of Experience with ERIS, MARKAL, and MESSAGE; 1999.
[26] Pan H, Ko
¨hler J. Technological change in energy systems: learning curves,
logistic curves and input–output coefficients. Ecological Economics 2007;
63:749–58.
[27] Nemet GF. How well does learning-by-doing explain cost reductions in a
carbon-free energy technology. Nota di Lavora 2006;143.
[28] Cory KS, Bernow S, Dougherty W, Kartha S, Williams E. Analysis of Wind
Turbine Cost Reductions: The Role of Research and Development and Cumu-
lative Production; 1999.
[29] Ibenholt K. Explaining learning curves for wind power. Energy Policy 2002;
30:1181–9.
[30] Isoard S, Soria A. Technical change dynamics: evidence from the emerging
renewable energy technologies. Energy Economics 2001;23:619–36.
[31] So
¨derholm P, Sundqvist T. Empirical challenges in the use of learning curves
for assessing the economic prospects of renewable energy technologies.
Renewable Energy 2007;32:2559–78.
[32] Pindyck RS, Rubinfeld DL. Microeconomics, 5th ed., Upper Saddle River, NJ,
U.S.A.: Prentice Hall; 2001.
[33] Perloff JM. Microeconomics, 3rd ed., Reading, MA, U.S.A.: Addison Wesley;
2004.
[34] Kahouli-Brahmi S. Testing for the presence of some features of increasing
returns to adoption factors in energy system dynamics: an analysis via the
learning curve approach. Ecological Economics 2009;68:1195–212.
[35] Kouvaritakis N, Soria A, Isoard S. Modelling energy technology dynamics:
methodology for adaptive expectations model with learning-by-doing and
learning-by-searching. International Journal of Global Energy Issues
2000;14:104–15.
[36] Levac
ˇic
ˇR. Macroeconomics: The Static and Dynamic Analysis of a Monetary
Economy. London, U.K.: Macmillan Press; 1977.
[37] Andrews J, Jelley N. Energy Science: Principles, Technologies and Impacts.
Oxford, U.K.: Oxford University Press; 2007.
[38] Van Sark WGJHM, Brandsen GW, Fleuster M, Hekkert MP. Analysis of the
silicon market: will thin films profit? Energy Policy 2007;35:3121.
[39] Del Can
˜izo C, Del Coso G, Sinke WC. Crystalline silicon solar module technolo-
gy: towards the 1
s
per watt-peak goal, CrystalClear Integrated Project.
Progress in Photovoltaics Research and Applications 2009;17:199–209.
[40] Maycock P. Cost reduction in PV manufacturing, impact on grid-connected and
building-integrated markets. Solar Energy Materials and Solar Cells 1997;
47:37–45.
[41] Rogol M. Even bigger things in a small package: Rogol’s monthly market
commentary. Photon International 2007 (March);98–100.
[42] Silver Institute. Historical Silver Prices from 1975 to 2007. Comex Spot
Settlement 2008.
[43] Nemet GF. Policy and Innovation in Low-Carbon Energy Technologies; 2007.
[44] Maycock P. International photovoltaic markets: developments and trends
forecast to 2010. Renewable Energy 1995;6:469.
[45] Photon International Magazine, 2003 (July, p. 42); 2005 (January, p. 42); 2006
(April, p. 30, 42); 2006 (September, p. 139); 2007 (November, pp. 13, 29, 52,
87); 2007 (December, p. 115).
[46] Photon International 2007 (December) 91–95.
[47] Bruton TM, Woodock JM, Multi-megawatt upscaling of silicon and thin film
solar cell and module manufacturing, MUSICFM, Technical Report CT94; 1997.
[48] Rohatgi, A. Road to cost-effective crystalline silicon photovoltaics, in Proceed-
ings Third World Conference on Photovoltaic Energy Conversion, Osaka, Japan,
pp. 829–834.
[49] Sande
´n BA, Azar C. Near-term technology policies for long-term climate
targets—economy wide versus technology specific approaches. Energy Policy
2005;33:1557–76.
[50] Mitchell C, Bauknecht D, Connor PM. Effectiveness through risk reduction: a
comparison of the renewable obligation in England and Wales and the feed-in
system in Germany. Energy Policy 2006;34:297–305.
[51] Van der Zwaan B, Rabl A. Prospects for PV: a learning curve analysis. Solar
Energy 2003;74:19–31.
[52] Maycock P. PV review: world solar PV market continues explosive growth.
ReFOCUS 2005;6:18–22.
[53] Klapwijk P. The Silver Market in 2007. The Silver Institute; 2008.
[54] Gruber H. Trade policy and learning by doing: the case of semiconductors.
Research Policy 1996;25:723–39.
[55] Ghannam M, Sivoththaman S, Poortmans J, Szlufcik J, Nijs J, Mertens R, et al.
Trends in industrial silicon solar cell processes. Solar Energy 1997;59:101–10.
[56] Frantzis L, Jones E, Wood LCM, Wormser P. Opportunities for Cost Reductions
in Photovoltaic Modules, in Proceedings 16th European Photovoltaic Solar
Energy Conference, Glasgow, UK, 2000. pp. 2100–2103.
[57] Strategies Unlimited, Photovoltaic Five-Year Market Forecast 2002–2007, PM-
52; 2003.
C.F. Yu et al. / Renewable and Sustainable Energy Reviews 15 (2011) 324–337
337