Research Article A Comparative Study of Renewable Energy

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2013, Article ID 368296, 9 pageshttp://dx.doi.org/10.1155/2013/368296

Research ArticleA Comparative Study of Renewable Energy IndustryRegulation on Feed-In Tariffs Based on Pricing Strategy ofValue Standard Method

Peng Sun

Institute of Industrial Economics, Jinan University, Guangzhou 510632, China

Correspondence should be addressed to Peng Sun; [email protected]

Received 16 July 2013; Accepted 27 August 2013

Academic Editor: X. Henry Wang

Copyright © 2013 Peng Sun. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Based on pricing strategy of value standard method, we establish a three-stage game model of energy production to compare thedifferences of optimal regulated price and social welfare under three regulation types of feed-in tariffs. We show that the optimalprice levels under three main regulation types are different. But the choice of regulation type does not impact the optimal socialwelfare. So policymakers with different preferences maymake regulation decisions in different ways.This successfully explains whymany regulation types exist in different countries. Moreover, although it is difficult to determine the optimal price by the valuestandard method in practice, the conclusions of this paper also provide a judgment criterion for other pricing strategies on how tochoose a suboptimal regulation type.

1. Introduction

Renewable energy sources (RES) are considered to be the bestsubstitution energy when we face increasing energy demandand higher environmental goals. The renewable energyindustry (REI) is immature yet because of the immaturity oftechnology, uncertainty of investment risk, and weakness ofmarket competition.Therefore, the related regulatory policieswill play a significant role in the rapid development of REI.

Feed-in tariffs (FITs) are the most widely used methodto stimulate rapid development of RES and are currentlyimplemented in 63 countries and regions worldwide [1–5].Compared with other regulatory policies (CBP, RO/RPS,RES-E, etc.), FITs are regarded as the most effective policyto attract venture capital, stimulate innovation, and buildmarket platform [6–10].

In this paper, we establish a three-stage game model ofenergy production to compare the differences of optimalregulated price and social welfare under three regulationtypes of feed-in tariffs. We show that the optimal pricelevels under three main regulation types are different. Theoptimal regulated price must correspond with regulationtype; otherwise the social welfare surely will lead to loss.

Policymakers with different preferencesmaymake regulationdecisions in different ways.That is why so many types of FITsare adopted in different countries.

The choice of regulation type and the price strategy arethe two core issues of FITs.The basic pricing methods of FITsinclude the cost-plus method (CPM) and the value standardmethod (VSM). CPM is similar to average-cost method,which equals to the cost plus a certain amount of investmentreturns. The advantage of CPM lies in the simplicity ofestimation and reasonableness of investment return. Butthis method cannot embody the whole value of emissionreductions, environmental effects, and social preferences[11]. The VSM tries to solve these problems. It takes intoaccount the negative externality (negative externality includeclimate, air and energy security, etc.) by the consumptionof traditional fossil energy and solves the market failureeffectively [2, 12]. This paper further employs the VSM.

In practice, there are many types of FIT policies. Ingeneral, they can be summarized as market-dependent andmarket-independent FITmodels [1]. And the advantages anddisadvantages of every type are analyzed in the existing liter-ature. But most scholars pay less attention on the comparisonof different types of FIT policies. When face with different

2 Journal of Applied Mathematics

market conditions, there is no common view of which type ofFIT policies is better than others. And there is no explanationwhy so many types of FIT policies exist in many differentcountries and regions in existing researches.

That is our writing motivation. In this paper, we providea theoretical basis on how to choose the level and type of reg-ulated price based on the pricing strategy of value standard.Based on three main types of FIT policies, we compare theiroptimal regulated price, government expenditure, and socialwelfare.

This paper is organized as follows. In Section 2, themodels of three main regulation types are established. Theanalysis of equilibrium solutions is presented in Section 3.In Section 4, numerical simulation and comparative anal-ysis are addressed, including regulated price, governmentexpenditure, and social welfare. The application conditionsof different types of FITs are also investigated. Concludingremarks are offered in the final section.

2. The Model

There are two firms,𝑅 and𝐷, in an industry. Firm𝑅 generateselectricity by renewable energy such as wind power, solarpower, and biomass power. Firm 𝐷 produces electricity byfossil energy such as coal, oil, and gas. For the negativeexternality of fossil energy consumption, public authoritiesneed to give a support price to the renewable energy firm𝑅 to achieve welfare maximization. In practical terms, thereare three main types of FIT prices: fixed price, constant-premium price, and variable-premium price. We will buildthree models, respectively, to compare the differences underthe three regulation types.

2.1. Fixed Price Model for FIT Policy Design (𝐹 Tool). Fixedprice means that the regulated price is independent of themarket price (as shown in Figure 1). Under this type, therenewable energy firm (firm 𝑅) gains constant subsidies withno risk.

The profit function of firm 𝑅 is (the superscript “𝐹”of variables represents fixed price tool (𝐹 tool), similarlyhereinafter)

𝜋𝐹

𝑅= 𝑃𝐹

𝑄𝐹

𝑅− 𝑐𝑅(𝑄𝐹

𝑅)2

, (1)

where 𝑄𝐹𝑅is the electricity energy output of the renewable

energy firm, 𝑃𝐹is the regulated price which is irrelevantwith market price, 𝑐

𝑅is a constant and stands for the cost

coefficient, and 𝑐𝑅(𝑄𝐹

𝑅)2 is the total production cost which

means decreasing returns to scale. The price of the fossilenergy firm depends on market scale and electricity energyoutputs of both energy firms. We assume that there exists nodifference between the electricity energy products of the twoenergy firms. So the profit function of the fossil energy firm(firm𝐷) is

𝜋𝐹

𝐷= (𝛼 − 𝑄

𝐹

𝑅− 𝑄𝐹

𝐷)𝑄𝐹

𝐷− 𝑐𝐷(𝑄𝐹

𝐷)2

, (2)

where 𝛼 − 𝑄𝐹

𝑅− 𝑄𝐹

𝐷is the market price and 𝛼 > 0

is a constant and represents the market size. 𝑐𝐷(𝑄𝐹

𝐷)2 is

Fixed priceMarket price

P

t

Figure 1: Fixed price model for FIT policy design.

the total production cost of fossil energy firm. Consumersurplus contains two parts: the consumption of both firms’electricity energy subtracted by the negative externality fromconsuming fossil energy. That is,

CS𝐹 = [∫𝑄𝐹

𝐷+𝑄𝐹

𝑅

0

(𝛼 − 𝑄𝐹

𝐷− 𝑄𝐹

𝑅) 𝑑 (𝑄

𝐹

𝐷+ 𝑄𝐹

𝑅)

− (𝛼 − 𝑄𝐹

𝐺− 𝑄𝐹

𝑅) (𝑄𝐹

𝐷+ 𝑄𝐹

𝑅) ] − 𝛾(𝑘𝑄

𝐹

𝐷)2

=1

2(𝑄𝐹

𝐷+ 𝑄𝐹

𝑅)2

− 𝛾(𝑘𝑄𝐹

𝐷)2

,

(3)

where 𝑓(𝑄𝐷) = 𝛾(𝑘𝑄

𝐺

𝐷)2 is pollution damage function. It

is quadratic form of total pollutant emissions [13]. And wehave 𝜕𝑓(𝑄

𝐷)/𝜕𝑄𝐷> 0 and 𝜕2𝑓(𝑄

𝐷)/𝜕𝑄2

𝐷> 0, which mean

the negative externality of damage increases incrementallywith the increase of fossil energy consumption. 𝑘𝑄

𝐷is the

pollutant emissions when consuming fossil energy, 𝑘 ∈ [0, 1]is a constant and represents energy emission intensity. 𝛾 isthe pollution damage coefficient. The bigger 𝑘 and 𝛾 are, thehigher negative externality is and the lower consumer surplusis. Government expenditure function is

GE𝐹 = [𝑃𝐹 − (𝛼 − 𝑄𝐹𝑅− 𝑄𝐹

𝐷)]𝑄𝐹

𝑅. (4)

From (1)–(4), we get the social welfare function:

𝑊𝐹= 𝜋𝐹

𝑅+ 𝜋𝐹

𝐷+ CS𝐹 − GE𝐹

= 𝑃𝐹

𝑄𝐹

𝑅− (𝑐𝑅𝑄𝐹

𝑅)2

+ (𝛼 − 𝑄𝐹

𝑅− 𝑄𝐹

𝐷)𝑄𝐹

𝐷

− (𝑐𝐷𝑄𝐹

𝐷)2

+1

2(𝑄𝐹

𝐷+ 𝑄𝐹

𝑅)2

− 𝛾(𝑘𝑄𝐹

𝐷)2

− [𝑃𝐹

− (𝛼 − 𝑄𝐹

𝑅− 𝑄𝐹

𝐷)]𝑄𝐹

𝑅.

(5)

Journal of Applied Mathematics 3

CP priceMarket price

P

t

Figure 2: Constant-premium price model.

VP priceMarket price

P

t

Figure 3: Variable-premium price model.

2.2. Constant-Premium Price Model for FIT Policy Design (CPTool). If the government chooses a regulated price relevantto market price, there are two situations. One is constant-premium price (CP) (as shown in Figure 2); the other isvariable-premiumprice (VP) (Figure 3).Under the two types,the final profits will fluctuate with the market environment.So the regulated level will be different with the 𝐹 tools.

When the premium price is constant, we have the profitfunction of firm 𝑅:

𝜋CP𝑅= (𝛼 − 𝑄

CP𝑅− 𝑄

CP𝐷+ 𝜍)𝑄

CP𝑅− 𝑐𝑅(𝑄

CP𝑅)2

, (6)

where 𝜍 is the level of constant-premium price. The corre-sponding profit function of firm 𝐷 and government expen-diture function are

𝜋CP𝐷= (𝛼 − 𝑄

CP𝑅− 𝑄

CP𝐷)𝑄

CP𝐷− 𝑐𝐷(𝑄

CP𝐷)2

,

GECP= 𝜍𝑄

CP𝑅.

(7)

Similar to (5), the social welfare function is

𝑊CP= (𝛼 − 𝑄

CP𝑅− 𝑄

CP𝐷+ 𝜍)𝑄

CP𝑅− 𝑐𝑅(𝑄

CP𝑅)2

+ (𝛼 − 𝑄CP𝑅− 𝑄

CP𝐷)𝑄

CP𝐷− 𝑐𝐷(𝑄

CP𝐷)2

+1

2(𝑄

CP𝐷+ 𝑄

CP𝑅)2

− 𝛾(𝑘𝑄CP𝐷)2

− 𝜍𝑄CP𝑅.

(8)

2.3. Variable-Premium Price for FIT Policy Design (VP Tools).When the premium price is variable with the change ofmarket, the situation is complex. For convenience sake, wejust assume that the rate of change relative to market price isinvariable. Assume the rate of change relative to market priceis 𝜆. The profit function of firm 𝑅 is

𝜋VP𝑅= (1 + 𝜆) (𝛼 − 𝑄

VP𝑅− 𝑄

VP𝐷)𝑄

VP𝑅− 𝑐𝑅(𝑄

VP𝑅)2

. (9)

Correspondingly, the profit function of firm 𝐷 and govern-ment expenditure function are

𝜋VP𝐷= (𝛼 − 𝑄

VP𝑅− 𝑄

VP𝐷)𝑄

VP𝐷− 𝑐

VP𝐷(𝑄

VP𝐷)2

,

GEVP= 𝜆 (𝛼 − 𝑄

VP𝑅− 𝑄

VP𝐷)𝑄

VP𝑅.

(10)

And the social welfare function is

𝑊VP= (1 + 𝜆) (𝛼 − 𝑄

VP𝑅− 𝑄

VP𝐷)𝑄

VP𝑅− 𝑐𝑅(𝑄

VP𝑅)2

+ (𝛼 − 𝑄VP𝑅− 𝑄

VP𝐷)𝑄

VP𝐷− 𝑐

VP𝐷(𝑄

VP𝑅)2

+1

2(𝑄

VP𝐷+ 𝑄

VP𝑅)2

− 𝛾(𝑘𝑄VP𝐷)2

− 𝜆 (𝛼 − 𝑄VP𝑅− 𝑄

VP𝐷)𝑄

VP𝑅.

(11)

In order to ensure solution existence, we need to add anadditional assumption.

Assumption 1. Nomatter what kind of regulated tool type, theprecondition of government regulation is that the regulatoryprofit is bigger than the corresponding expenditure. That is,

(i) 𝛾(𝑘𝑄𝐹∗𝐷)2> [(𝑃

𝐹∗

− (𝛼 − 𝑄𝐹∗

𝑅− 𝑄𝐹∗

𝐷)]𝑄𝐹∗

𝑅> 0

in 𝐹 tool (the superscript “∗” of variables representsEquilibrium solution. Similarly hereinafter),

(ii) 𝛾(𝑘𝑄CP∗𝐷)2> 𝜍∗𝑄

CP∗𝑅

> 0 in CP tool;

(iii) 𝛾(𝑘𝑄VP∗𝐷)2> 𝜆∗(𝛼 − 𝑄

VP∗𝑅

− 𝑄VP∗𝐷)𝑄

VP∗𝑅

> 0 in VPtool.


This assumption ensures that the government gives therenewable energy firm a regulated price that is higher thanmarket price.

In conclusion, we have built a three-stage game modelthat includes three parties: the government, a renewableenergy firm, and a fossil energy firm. The timing of gamedecisions is given as follows: at the first stage, the governmentchooses the type and level of regulated price. Different regu-lation types will obtain different price levels. At the secondstage, the renewable energy firm decides its productionquantity of electricity. At the third stage, the fossil energy firmchooses electricity output.

3. Equilibrium Solution

The previous model is herein analyzed.We will use backwardinduction three times to solve three types of FIT policiesand compare their differences, including regulated price level,government expenditure, and social welfare.

3.1. Equilibrium Solution of 𝐹 Tool. By backward induction,the fossil energy firm is first considered. Taking derivative in(2) with respect to 𝑄𝐹

𝐷yields

𝑄𝐹

𝐷=

𝛼 − 𝑄𝐹

𝑅

2 (1 + 𝑐𝐷); (12)

and by (1), we get

𝑄𝐹

𝑅=𝑃𝐹

2𝑐𝑅

. (13)

So (12) can be changed to

𝑄𝐹

𝐷=

𝛼 − 𝑄𝐹

𝑅

2 (1 + 𝑐𝐷)=2𝛼𝑐𝑅− 𝑃𝐹

4𝑐𝑅(1 + 𝑐𝐷). (14)

And then through (1)–(4), we get the two firms’ profits,consumer surplus, and government expenditure:

𝜋𝐹

𝑅=

(𝑃𝐹

)

2

4𝑐𝑅

,

𝜋𝐹

𝐷=

(2𝛼𝑐𝑅− 𝑃𝐹

)

2

16𝑐2

𝑅(1 + 𝑐𝐷),

CS𝐹 = 12

[

[

2𝛼𝑐𝑅+ (1 + 2𝑐

𝐷) 𝑃𝐹

4𝑐𝑅(1 + 𝑐𝐷)

]

]

2

− 𝛾[

[

𝑘


)

4𝑐𝑅(1 + 𝑐𝐷)

]

]

2

,

GE𝐹 =[(4𝑐𝑅+ 2𝑐𝐷+ 4𝑐𝑅𝑐𝐷+ 1) 𝑃

𝐹

− 2𝛼𝑐𝑅(1 + 2𝑐

𝐷)] 𝑃𝐹

8𝑐2

𝑅(1 + 𝑐𝑅)

.

(15)

From (15), the social welfare is

𝑊𝐹=

(1 + 2𝑐𝐷) (2𝛼𝑐

𝑅− 𝑃𝐹

)

4𝑐𝑅(1 + 𝑐𝐷)

⋅𝑃𝐹

2𝑐𝑅

−

(𝑃𝐹

)

2

4𝑐𝑅

+


)

2

16𝑐2

𝑅(1 + 𝑐𝐷)+1

2

[

[

2𝛼𝑐𝑅+ (1 + 2𝑐

𝐷) 𝑃𝐹

4𝑐𝑅(1 + 𝑐𝐷)

]

]

2

− 𝛾[

[

𝑘


)

4𝑐𝑅(1 + 𝑐𝐷)

]

]

2

.

(16)

Taking derivative with respect to 𝑃𝐹 yields the optimal

regulated price

𝑃𝐹∗

=

2𝛼𝑐𝑅(2𝛾𝑘2+ 4𝑐2

𝐷+ 6𝑐𝐷+ 1)

2𝛾𝑘2 + 8𝑐𝑅(1 + 𝑐𝐷)2+ (4𝑐2

𝐷+ 6𝑐𝐷+ 1)

. (17)

As shown in (17), the optimal regulated price under 𝐹tool 𝑃𝐹∗ is also the final support price by the governmentwhich depends on the values of 𝛼, 𝑐

𝑅, 𝑐𝐷, 𝛾, and 𝑘.The impact

analysis of optimal price with the change of parameters willbe discussed in Section 4.

3.2. Equilibrium Solution of CP Tool. Following similar lines,we achieve equilibrium solution of CP tool. From (6)–(8), wehave

𝑄CP𝐷=

(1 + 2𝑐𝑅) 𝛼 − 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

,

𝑄CP𝑅=(1 + 2𝑐

𝐷) 𝛼 + 2 (1 + 𝑐

𝐷) 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

.

(18)

And the profits, consumer surplus, and government expendi-ture are

𝜋CP𝑅= (1 + 𝑐

𝑅) [(1 + 2𝑐

𝐷) 𝛼 + 2 (1 + 𝑐

𝐷) 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

]

2

,

𝜋CP𝐷= (1 + 𝑐

𝐷) [

(1 + 2𝑐𝑅) 𝛼 − 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

]

2

,

CSCP = 12[2 (1 + 𝑐

𝐷+ 𝑐𝑅) 𝛼 + (1 + 2𝑐

𝐷) 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

]

2

− 𝛾[𝑘(1 + 2𝑐

𝑅) 𝛼 − 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

]

2

,

GECP= 𝜍 ⋅

(1 + 2𝑐𝐷) 𝛼 + 2 (1 + 𝑐

𝐷) 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

.

(19)



𝑊CP= (1 + 𝑐

𝐷) [

(1 + 2𝑐𝑅) 𝛼 − 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

]

2

+ (1 + 𝑐𝑅) [(1 + 2𝑐

𝐷) 𝛼 + 2 (1 + 𝑐

𝐷) 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

]

2

+1

2[2 (1 + 𝑐

𝐷+ 𝑐𝑅) 𝛼 + (1 + 2𝑐

𝐷) 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

]

2

− 𝛾[𝑘(1 + 2𝑐

𝑅) 𝛼 − 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

]

2

− 𝜍 ⋅(1 + 2𝑐

𝐷) 𝛼 + 2 (1 + 𝑐

𝐷) 𝜍

4 (1 + 𝑐𝑅) (1 + 𝑐

𝐷) − 1

.

(20)

Taking derivative with respect to 𝜍 yields the optimal pre-mium level

𝜍∗=

𝛼 [2𝛾𝑘2(1 + 2𝑐

𝑅) − 2𝑐𝑅+ 4𝑐2

𝐷+ 6𝑐𝐷+ 1]

2𝛾𝑘2 + 8𝑐𝑅(1 + 𝑐𝐷)2+ (4𝑐2

𝐷+ 6𝑐𝐷+ 1)

. (21)

Comparingwith (17), the optimal constant premium level𝜍∗ in (21) and 𝑃𝐹∗ of 𝐹 tool have the same denominator butdifferent numerators. The final regulated price of CP tool isequal to market price plus premium level, that is, 𝛼 − 𝑄CP∗

𝑅−

𝑄CP∗𝐷

+ 𝜍∗. It will be analyzed in detail in Section 4.

3.3. Equilibrium Solution of VP Tool. From (9)–(11), we have

𝑄VP𝐷=

(1 + 𝜆 + 2𝑐𝑅) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

,

𝑄VP𝑅=

(1 + 𝜆) (1 + 2𝑐𝐷) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

.

(22)

And the profits, consumer surplus, and government expendi-ture are

𝜋VP𝑅= (1 + 𝑐

𝑅) [

(1 + 2𝑐𝐷) (1 + 𝜆) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

]

2

,

𝜋VP𝐷= (1 + 𝑐

𝐷) [

(1 + 𝜆 + 2𝑐𝑅) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

]

2

,

CSVP = 2{[(1 + 𝜆) (1 + 𝑐𝐷) + 𝑐𝑅] 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

}

2

− 𝛾[𝑘(1 + 𝜆 + 2𝑐

𝑅) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

]

2

,

GEVP=

𝜆 (1 + 2𝑐𝐷) (1 + 𝜆 + 2𝑐

𝑅) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

⋅(1 + 𝜆) (1 + 2𝑐𝐷) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

.

(23)


𝑊VP=

(1 + 2𝑐𝐷) (1 + 𝜆 + 2𝑐

𝑅) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

⋅(1 + 𝜆) (1 + 2𝑐𝐷) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

− 𝑐𝑅[

(1 + 2𝑐𝐷) (1 + 𝜆) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

]

2

+ (1 + 𝑐𝐷) [

(1 + 𝜆 + 2𝑐𝑅) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

]

2

+ 2{[(1 + 𝜆) (1 + 𝑐𝐷) + 𝑐𝑅] 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

}

2

− 𝛾[𝑘(1 + 𝜆 + 2𝑐

𝑅) 𝛼

4 (1 + 𝑐𝑅+ 𝜆) (1 + 𝑐

𝐷) − (1 + 𝜆)

]

2

.

(24)

Taking derivative with respect to 𝜆 yields the optimal pre-mium rate

𝜆∗=

2𝛾𝑘2(1 + 2𝑐

𝑅) + 4𝑐

2

𝐷+ 6𝑐𝐷+ 1 − 2𝑐

𝑅

4𝑐𝑅(1 + 𝑐𝐷) (1 + 2𝑐

𝐷) − 2𝛾𝑘2 − (4𝑐

2

𝐷+ 6𝑐𝐷+ 1)

. (25)

Comparingwith (17) and (21), the difference of (25) is thatthe optimal variable premium rate 𝜆∗ is not relative to themarket scale𝛼. 𝜆∗ just depends on the value of 𝑐

𝑅, 𝑐𝐷, 𝛾, and 𝑘.

And note that 𝜆∗ has the same numerator as 𝜍∗ in (21) except𝛼. The final regulated price is (1 + 𝜆∗)(𝛼 − 𝑄VP∗

𝑅− 𝑄

VP∗𝐷).

4. Numerical Simulation andComparative Analysis

In Section 3, we obtained the optimal regulated price underthree types of regulation tools. Because the expressions ofoptimal prices are complex, we compare the differences underthe three regulation types by numerical simulation. We willgive assignment to the parameters and obtain the path ofnumerical solution when the parameters change. All theprogram setting and graphic processing will be achieved byMATLAB 7.0.

4.1.The Comparison of Regulated Price. The level of regulatedprice reflects the government’s support intensity for therenewable energy firm. The higher the regulated price is,the more quickly the REI develops and achieves energysubstitution. So we compare the optimal regulated price ofthree tools firstly. For the sake of convenience in analysis, wejust consider the changes of two parameters 𝛼 (market scale)and 𝑐𝑅(cost coefficient of renewable firm). Other parameters

will be set constant. Under the condition of Assumption 1, westipulate that 𝑐

𝐷= 1, 𝛾 = 100, and 𝑘 = 0.1.

4.1.1.The Change ofMarket Scale 𝛼. Wewill consider the pathof regulated price when market scale 𝛼 lies in the interval of[5, 15] and with 𝑐

𝑅= 2.


5 6 7 8 9 10 11 12 13 14 152

4

6

8

10

12

14

Market scale

Regu

lated

pric

e

P(F)P(CP)P(VP)

Figure 4: Three tools comparison of regulated price under thechange of market scale 𝛼.

As shown in Figure 4, with the increase of market scale,the regulated price will increase under the three kinds ofregulated price. Because when themarket scale is larger, moreelectricity output by the fossil energy firm will be producedandmore greenhouse gas (GHGs) will be discharged. It needshigher support price to renewable energy firm to achievewelfare maximization.

In addition, the optimal regulated price of VP tool ishigher than the other tools. And the regulated price of 𝐹 toolis the lowest. It reflects that the FITs tool of variable-premiumprice has the highest support intensity and REI will achievedevelopment quickly.

Why do the three tools display different regulated prices?One possible reason is the risk difference. Under the fixedregulated price, the subsidy level of unit output is constant.The renewable energy firm will obtain stable profits anddoes not need to worry about the fluctuation of marketprice. So a relatively low regulated price will achieve welfaremaximization. And under the CP and VP tools, the profitsof the renewable energy firm fluctuate with market price.So the firm has to undertake the market risk when demandcontracts. The VP tool has the biggest risk and need to thehighest regulated price.

4.1.2. The Change of Cost Coefficient of Renewable EnergyFirm 𝑐

𝑅. The cost coefficient 𝑐

𝑅reflects the production

efficiency of the renewable energy firm. The lower 𝑐𝑅is, the

higher production efficiency is. With the development ofREI, production efficiency shows an increasing trend. So weconsider the path of regulated price when cost coefficient 𝑐

𝑅

in the interval of [3, 1] and with 𝛼 = 10.As shown in Figure 5, with the decrease of cost coefficient

𝑐𝑅, different regulated tools show very different paths. The

price of 𝐹 tool decreases gradually, and the price of VP toolincreases. The price of CP tool increases inapparently. Whydifferent tools display different price paths? We show thatthe impact of improved production efficiency to regulatedprice has two opposite effects: (i) the optimal regulatedprice design must balance two parts of efficiency loss. One

5678

8.59

10111213

Cost coefficient of renewable energy firm

Regu

lated

pric

e

11.21.41.61.822.22.42.62.83

P(F)P(CP)P(VP)

Figure 5: Three tools comparison on regulated price under thechange of cost coefficient of renewable energy Firm 𝑐

𝑅.

is the negative externality by the fossil energy firm; theother is low production efficiency of the renewable energyfirm. With the improvement of production efficiency, thegovernment has the trends to support the renewable energyfirm more and increase the regulated price. This effect canbe defined as relative efficiency effect (REE). (ii) On theother hand, the government has to pay the cost of regulatedprice. And the higher production efficiency is, the moreprofits the renewable energy firm makes. So the governmenthas a motivation to lower the support price and reduceexpenditure. It can be defined as efficiency improvementeffect (EIE). The final change of regulated price depends onthe two opposite effects. We find that EIE is bigger than REEunder the 𝐹 tool. So the regulated price drops off gradually.And the regulated price increases gradually under theVP toolbecause EIE is smaller than REE. Under the CP tool, EIE isclose to REE. So the regulated price changes a little.

4.2.The Comparison of Government Expenditure. In practice,government expenditure of REI regulation is also a significantconsideration. Noticeably, social welfare is the uppermostconcern by the public and economists, but how to maximizethe social welfare with the lowest expenditure is the favoritesubject by government, especially when the government facesa budget constraint. So we will compare the governmentexpenditure of the three regulation tools when parameterschange.

As shown in Figures 6 and 7, government expenditureis always the lowest under the 𝐹 tool and the highest underthe VP tool. With the increase of market scale, governmentexpenditure will rise under the three kinds of regulatedprice. Because the bigger market scale is, the more electricityoutputs of the two firms and the higher expenditure are.And with the decrease of cost coefficient 𝑐

𝑅, government

expenditure also increases. The reason is that EIE is alwaysless than REE. So the lower cost coefficient is, the higherexpenditure is.

But the changes in range under the three tools are verydifferent.The 𝐹 tool is the most stable whatever the change of


5 6 7 8 9 10 11 12 13 14 150

2

4

6

8

10

12

Gov

ernm

ent e

xpen

ditu

re

Market scale

GE(F)GE(CP)GE(VP)

Figure 6: Three tools comparison on government expenditureunder the change of market scale 𝛼.

11.21.41.61.822.22.42.62.830

5

10

15

20

25

Cost coefficient of renewable energy firm

Gov

ernm

ent e

xpen

ditu

re

GE(F)GE(CP)GE(VP)

Figure 7: Three tools comparison on government expenditureunder the change of cost coefficient of renewable energy firm 𝑐

𝑅.

𝛼 or 𝑐𝑅and VP tool’s fluctuation is the biggest. This reflects

that the expenditure of 𝐹 tool is low and stable and thegovernment need not concern with the problem of budgetconstraint when the situation of market and/or firm changes.But under the VP/CP tool, the government has to considerthe changes of expenditures in the future.

4.3. The Comparison of Social Welfare. The comparison ofsocial welfare is herein analyzed. As shown in Figure 8,unpredictably, the welfare under the three regulation toolsare exactly the same no matter how the parameters change(we just display the figure of social welfare with the changeof market scale 𝛼, and the results of other parameters’change are the same). And with the increase of market scale,social welfare will improve. These results reveal that differentchoices of regulation tools do not impact the social welfarebut just influence the optimal regulated price and governmentexpenditure.

5 6 7 8 9 10 11 12 13 14 1505

10152025303540

Market scale

Welf

are

W(VP)

W(F)W(CP)

Figure 8: Three tools comparison on welfare under the change ofmarket scale 𝛼.

Formally, we present the following proposition.

Proposition 2. The choice of regulation type of FITs doesnot impact the optimal social welfare. But different tools mayobtain very different optimal regulated price and governmentexpenditure. The regulated price of F tool is the lowest and sois the government expenditure. Under the VP tool, we obtainthe highest regulated price and government expenditure. Bothregulated price and government expenditure under the CP toolare in the middle of three tools.

Remarks. From the previous analysis, we show that regula-tion tool does not impact the social welfare. So the problemis that what is the standard for the government in choosingthe regulation type in practice?Maybe governments with dif-ferent preferences will make decisions in different ways. Highsupport price inevitably accompanies with high volatility andhigh government expenditure. So the governmentmustmakea choice between the two aspects.

If policymakers are concerned more with the rapid buthigh volatile development of REI and face a loose expenditureconstraint; they will choose the VP tool. With the changeof market situation and/or firm efficiency, the governmentmust undertake the risk of high and unstable expenditureat the same time. If the government wants to give a stablesupport price to the renewable energy firm whatever the firmefficiency or if the firm does not want change in the regulatedprice frequently, thenmaybe theCP tool is a good choice. Andif the government expects a low and controllable expenditureto achieve a healthy and steady development of REI, the𝐹 toolabsolutely is a good choice.

In practice, different countries and different renewableindustries choose different regulation types. In initial stagesof regulation, fixed price tool (𝐹) is the most often adoptedmethod in many countries, such as China and many Euro-pean countries (Ireland, Switzerland, Austria, France, Ger-many, and so on). Why? Because this tool is very easy to


W

W∗

I II III

PCP∗

PF∗

PVP∗ P

WCP

WVP

WF

Figure 9: The comparison of three welfare functions.

handle and implement. And the character of stability and lowrisk becomes the main reason of prudent policymakers.

But with the diversified development of regulation tools,many countries begin to adopt more flexible instruments,such as Spain, Italy, Denmark, the Czech Republic, and Esto-nia, which had brought in the constant-premium price (CPtool).The Netherlands has introduced varied premium price.Precisely because different tools display different advan-tages and disadvantages, policymakers of different countrieschoose to change the regulation type or not.

4.4. The Choice of FIT Tools under Other Pricing Strategies.Asmentioned previously, different regulation tools obtain thesame optimal social welfare under different optimal prices.According to Proposition 2, we draw a diagram about thesocial welfare and regulated price (shown in Figure 9). Theoptimal prices under different regulation tools are basedon the pricing strategy of value standard method whichconsiders the common social welfare. Although it is not easyto determine exactly in practice, the previous conclusion alsoprovides a judgment criterion when applying to other pricingstrategies and help policymakers to choose a suboptimalproject when they cannot obtain the optimal solution.

There are three areas in Figure 9: I, II, and III. The socialwelfare under the 𝐹 tool is the highest in area I, CP tool inII, and VP tool in III. The optimal prices are 𝑃𝐹∗, 𝑃CP∗, and𝑃VP∗, respectively, under the three FIT types. The optimal

social welfare is 𝑊∗ no matter which regulation tools wereapplied. And we know that 𝑃𝐹∗ < 𝑃

CP∗< 𝑃

VP∗. So whenpolicymakers cannot determine the regulated price exactly byusing the pricing strategy of value standard method and haveto apply other pricing strategies (cost-plus method, e.g.), 𝐹tool of FITs may be a good choice if the practical regulatedprice is relatively low. Because the lower price is, the morelikely price falls into area I. Correspondingly, CP tool is betterif the regulated price is modest. And if the regulated priceis relatively high, VP tool will be a better choice. The wrongchoice of regulation types (e.g., policymaker chooses VP toolwhen the regulated price is low) will lead to a deadweightwelfare loss.

5. Conclusion

This paper establishes a three-stage game model including arenewable energy firm, a fossil energy firm, and the govern-ment to analyze the regulation effects of different FIT types.We find that the different regulation tools obtain differentoptimal price levels. The optimal price is the lowest underthe 𝐹 tool and the highest under the VP tool, which could beexplained by risk differences. But if the regulated prices are allset appropriately under different tools, we show that the socialwelfares are the same under the three tools of FITs.The choiceof regulation type does not impact the welfare. So we highlyemphasize that government preference plays a crucial role inthe choice of FIT types. If the government expects a rapid buthigh volatile development of REI, it will choose the variableprice tool which has the highest and most unstable optimalregulated price. If the government does not want to changethe regulated price frequently no matter how high the firmefficiency is, the constant price tool is a good choice. And ifthe government expects a healthy and steady development ofREI under low and controllable expenditure, fixed price toolabsolutely is a good choice.

We also point out that if policymakers cannot determinethe exact regulated price in practice, the analysis of this paperalso can help them to choose a suboptimal project. Thatmeans that the pricing strategy of value standard method isnot only a method of optimal regulated price design whichcould solve the market failure perfectly, but also a judgmentcriterion for other pricing strategies.

How to apply the proper regulation tool to achieve boththe rapid development of REI and improvement of socialwelfare is the issue of common concern both in theoreticaland practical fields. The conclusions of this paper providea theoretical basis on how to choose the level and typeof regulated price based on the pricing strategy of valuestandard. The optimal regulated price must correspond withregulation type; otherwise the social welfare surelywill lead toloss. Moreover, this paper successfully explains that the threetools of FITs all exist in different countries.

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper.

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