Operations Research Forum


In the January-February 2016 issue of Operations Research Saed Alizamir, Francis de Vericourt, and Peng Sun write about feed-in-tariff policies for renewable energy technologies.  While new technologies may be ultimately be beneficial to their users and society at large they are often more costly and not well known in the market.  As the number of adopters increases, acquisition and operating costs usually decline, often sharply.  Potential adopters may be strategic in timing their adoption of the technology because they anticipate future cost reductions.  This strategic behavior slows down the overall adoption rate new technologies and delays their benefits.  Governments can play a role in speeding adoption of a new technology by subsidizing its adoption.  In the case of renewable energy technology feed-in-tariffs guarantee adopters of an energy generation technology prices for the energy generated.  This paper develops a theoretical model of technology diffusion and learning to derive properties of the optimal feed-in-tariff (FIT) schedule.

Currently it is common for the tariffs to be decreasing in time but in a way that is in sync with cost decreases so that the profitability of the investment remains constant.   In this paper, the authors are able to show that the optimal FIT policy is not constant in profitability.  The model explicitly allows for strategic behavior by investors who are aware of the technology and can profit from it yet may find it optimal to delay investment.  Such behavior creates two parameter regimes for the optimal FIT policy.  In the “no-delay” regime the FIT is non-increasing, while in the “delay” regime it is increasing. They also show that the problem of determining the optimal increasing FIT in the “delay” regime is mathematically intractable and thus forcing investors to not delay by implementing a constant profitability FIT policy, may be a pragmatic approach despite being theoretically suboptimal.


The editors received comments on this work from three experts.

Alfredo Garcia ( pdf Comments ) is a Professor of Industrial and Systems Engineering at the University of Florida.  He is an expert on dynamic games and mechanism design problems in electricity and communications networks.  He holds a PhD from the University of Michigan and has extensive experience in the electric power industry.

Johannes Schmidt ( pdf FITComments-SchmidtandSchmid ) is a Professor at the University of Natural Resources and Life Sciences in Vienna Austria.  He is a member of the Institute for Sustainable Economic Development and an expert on the economics of alternative energy technologies.

Erwin Schmid  is a Professor at the University of Natural Resources and Life Sciences in Vienna Austria. He is the Head of the Department of Economics and Social Sciences.  He is an expert on biophysical process modelling and land use economics

Author responses ( pdf Author Responses )


The commenters on this work highlight three important areas of concern when analyzing how to encourage the adoption of new energy technologies.  The first is the trajectory of the technology cost may not be monotonic.  This suggests that the time horizon being considered in the analysis is important because even if in the long run costs can be expected to decrease, in the short term there can be many surprises of large economic significance.  Second, the adoption of new technologies can have significant impact on prices for all power sources because changing supply is a slow process.  Third, because these investments have long pay back times and require considerable upfront investment, the predictability of the government behavior is important.

Technology Cost Dynamics

Schmid and Schmidt point out that the efficiency of individual investors (adopters) represented by the parameter θ in the paper is intended to include locational characteristics.  I.e. sunnier locations for photovoltaic.  For large scale installations if these differences are not accounted for in the land prices “there is a high incentive for investors to first use high yielding locations.”   The implication for the model is that “production costs may not be strictly decreasing as assumed in Proposition 1, because technological advances do [sic] not necessarily compensate for the decrease in high yielding locations.”  More generally Schmidt and Schmid are arguing that in the short term there can be production cost increases due to market forces even if in the long run grid parity is reached.

The authors respond that:

“Indeed, if the feed-in tariff is geographically uniform, large investors may be able to strategically choose the location of their investment, which could in turn temporarily increase production costs. Our model, however, focuses on predictable long-term effects and ignores short-term (or random) effects such as possible property price increases. This is because long-term effects have a more significant impact on the overall cost of renewable energy and hence FIT policies. For instance, we also ignore the sudden spike in solar panel prices in 2006-2007, caused by shortage of processed silicon, which led the production cost of solar electricity to temporarily deviate from the predicted exponential decay (see Bullis 2008 and de Véricourt and Munigowda 2012). Nevertheless, and despite these fluctuations, the global price of solar modules over the last three decades (as provided by the Department of Energy) suggests a close match to the exponential decay pattern assumed in our model.”

      -Alizamir, De Vericourt, and Sun


Furthermore the authors point out that:

“land prices are more likely to increase due to large investors when the FIT program is close to maturity, and “efficient” land becomes scarce. (And even then, large producers comprise a small portion of the total FIT subscribers; for example, the majority of the solar PV capacity installed in Germany in 2010 belonged to private individuals and farmers.) We thus expect deviations in production cost (caused by land scarcity, etc.) to be stronger as the technology grows and gains significant market share. But this is also precisely the condition, under which the FIT programs should end, since the technology has then gained sufficient maturity for market forces to take over.”

      -Alizamir, De Vericourt, and Sun


The Spot Market

Both sets of commenters raise concerns that the model does not capture the impact of the new technology on the spot price for power. 

“I am not so confident as to the paper's relevance with respect to the analysis of FIT effects on bulk-power capacity expansion since details of the market design governing the determination of the spot price of electricity are largely omitted.”  -Garcia

In the paper the feed-in-tariff is set to guarantee a price for the power generated by the new technology.  So the cost of implementing the policy depends upon the spot market price for power.  If the new technology increases supply on the market the spot price will decrease yielding a social benefit but at the same time increasing the magnitude of the price support.

“If feed-in tariffs are paid directly by electricity consumers, as is the case in most implementations, depending on the magnitude of the merit order effect, two effects have to be taken into account: if changes in spot market prices are immediately handed on to end consumers, prices for electricity will decrease, while the costs for financing the feed-in tariff will increase with increasing penetration. This makes the determination of the cost parameter of the feed-in tariff endogenous to (P1). Considering pt only may therefore be too much of a simplification.”  -Schmid and Schmidt


The authors respond to this point as follows:

“Regarding the spot market price effect, first consider (P2) where the objective is to maximize social welfare until reaching grid parity. In this case, the growth of renewables stimulated by the FIT policy may indeed lead to reductions in spot market prices. In order to account for this effect, the government’s objective should be adjusted downward as the technology penetrates, which can be captured by inflating parameter β3 in our model. Note that in the current formulation, this parameter represents the development cost to the society for additional units of new installations. If these new installations impose an additional burden on the social planner (e.g., by driving down the spot market price and hence increasing the effective policy expenditures), then this impact can be captured by incorporating a higher β3. This approach, of course, only provides a first-order approximation since it assumes that the effect is linear in cumulated capacity. However, it endogenizes the essence of the market price effect by penalizing the social planner as the renewable technology grows.”

“In (P1), on the other hand, the objective is to minimize the policy expenditure for the government at early stages of the technology development in order to reach a specific capacity target. At these early stages where the technology is not mature and its commercialization is limited, the market share of the renewable energy is very small and hence, its impact on exiting technology mix and spot prices is not significant. In fact, if the influence of a particular renewable energy on the spot market price becomes significant, this can be interpreted as a signal that the technology has reached maturity, and the FIT policy should probably be terminated.”

     -Alizamir, De Vericourt, and Sun

Government Predictability

Garcia also asks about the ability of the government to commit:

“The assumption of ex-ante commitment by the government seems rather strong. In fact, the FIT reductions in Europe may be explained as resulting from opportunistic behavior by (the possibly newly elected) governments. If one relaxes the government’s ability to commit, the ability to strategically delay technology adoption is likely to become more valuable to investors and in a renegotiation-proof equilibrium, the government may have to maintain constant profitability to achieve the desired penetration target and deadline.

   - Garcia

The authors respond to this by saying that in their model the commitment is rather limited.

“We only use the notion of commitment in our model in the following sense: the existing contracts (commissioned in previous years) are not renegotiable, i.e., the government cannot renege on its existing obligations. We believe this is a very reasonable assumption and the governments can in general commit to their policies, especially in countries with proper rule of law. And beside the costs associated with breaching the law, governments and politicians that reneged on their commitments also bear potentially high reputation costs. The presence of exogenous costs such as these in a game theory setup typically justifies that agents can commit to their strategies.

In practice, Spain is the only example we know of where the government has attempted to deviate from its commitment (to the best of our knowledge). It seems that in doing so, the government has breached the country’s constitution as well as the international 1994 Energy Charter Treaty. Local authorities have brought the issue to the Spain constitutional court and the EU has opened a case against Spain in 2014.

Further, we assume governments are social-welfare maximizers, and hence, there is no rationale for any opportunistic behavior. (In this sense, our work makes a normative, not descriptive, contribution.) Therefore, from an analytical standpoint, a newly elected government does not find it optimal to default on the previous government’s obligations as long as its objective remains the same (maximizing social welfare). In other words, there is no reason for the new government to be opportunistic, and a rational government would follow the existing FIT schedules. This is why we do not need renegotiation-proof equilibrium.”  -Alizamir, De Vericourt, and Sun


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