Feed-in Tariffs Combined with Capital Subsidies

Abstract

Both feed-in tariffs (FITs) and capital subsidies have been widely employed to promote the adoption of renewable energy technologies. This chapter sheds light on the combined use of FITs and capital subsidies. The purpose is to clarify their optimal combinations to encourage households to adopt photovoltaic (PV) systems or to encourage firms to invest in PV generation. This study develops a microeconomic model embodying the idea of two-part tariffs. The most important findings concern the combination that maximizes social welfare for the residential sector: if FITs are applied to the total PV electricity generated, they should be set at the avoided cost per unit of PV electricity, and capital subsidies should be used to control the number of adopters; whereas, if FITs are applied to only surplus PV electricity, the previous principle is distorted to some extent. A similar result is obtained for the business sector. In the model for the business sector, the government aims to have a certain installed capacity of PV panels, whereas in the model for the residential sector, its aim is to have a certain number of households adopt PV systems. The problem of equity, that is, how to finance the cost of FITs and capital subsidies is also discussed.

Modified, with permission of Elesevier, from Yamamoto, Y., Feed-in tariffs combined with capital subsidies for promoting the adoption of residential photovoltaic systems, Energy Policy, 111, 312–320, Elsevier, 2017. I would like to thank Elsevier.

Appendix 1: Proof of the Lemma for the Social Welfare Maximization Problem

First, let us verify that for a given p, $\sum\nolimits_{{i \in\Theta _{p,c,g(p,c)} }} {\left[ {c(x_{i} + y_{i} ) - I_{i} } \right]}$ is maximized at p = c. The same reasoning may be applied here as in Sect. 5.4.3 (see also Fig. 5.2b). Suppose that the marginal household changes from i to j when p increases to p ₁, subject to r = c. Then, $\sum\nolimits_{{i \in\Theta _{p,c,g(p,c)} }} {\left[ {c(x_{i} + y_{i} ) - I_{i} } \right]}$ changes if and only if the marginal household’s surplus PV electricity increases, i.e., $x_{i} < y_{j}$. Otherwise, the set $\Theta _{p,c,g(p,c)}$ of adopters remains the same, and the sum does not change. Plugging p = c into $s = - px_{i} - cy_{i} + I_{i}$ from Eq. (5.5) yields $- cx_{i} - cy_{i} + I_{i} > - cx_{j} - cy_{j} + I_{j}$, or $c(x_{i} + y_{i} ) - I_{i} < c(x_{i} + y_{i} ) - I_{j}$ if $p_{1} < c$ and that $- cx_{i} - cy_{i} + I_{i} < - cx_{j} - cy_{j} + I_{j}$, or $c(x_{i} + y_{i} ) - I_{i} > c(x_{j} + y_{j} ) - I_{j}$ if $p_{1} > c$. Because the adopters, other than the marginal households i or j, are the same, $\sum\nolimits_{{i \in\Theta _{p,c,g(p,c)} }} {\left[ {c(x_{i} + y_{i} ) - I_{i} } \right]}$ is maximized at p = c.

Next, let us verify the second half of the lemma. Plugging p = 0 into $s = - px_{i} - cy_{i} + I_{i}$ and $s = - px_{j} - cy_{j} + I_{j}$ reveals that $\sum\nolimits_{{i \in\Theta _{p,c,g(p,c)} }} {(cy_{i} - I_{i} )}$ decreases if $x_{i} < x_{j}$. Hence, while $\sum\nolimits_{{i \in\Theta _{p,c,g(p,c)} }} {x_{i} }$ increases, it is not possible to state how $\sum\nolimits_{{i \in\Theta _{p,c,g(p,c)} }} {y_{i} }$ changes; this depends on the parameter values. Thus, changes in $\sum\nolimits_{{i \in\Theta _{p,c,g(p,c)} }} {b(x_{i} + y_{i} )}$ also depend on the parameter values.