# The Staged Financing Selection Mechanism for Government to Maximize the Green Benefits of Start-Ups

Authors: Wenke Yang; Qianting Ma; Meile Tian; Lei Wang; Jianmin He
Journal: Mathematical Problems in Engineering
 (2021)

---

## Abstract

In this study, we investigate the most common forms of government grant in green start-ups, which are appropriation, interest-free bank loans, and tax subsidies. These mechanisms are used to mitigate the problem of higher research costs and sunk costs of start-ups on green innovation and help venture investors better monitor the business plan, asset use, and agency cost and regularly collect information of start-ups to retain the right to terminate financing projects and improve the efficiency of them. The aim of this work is to develop a theoretical model of the agency among the government, the venture capitalists who only pursue monetary income, the strategy investors who pursue strategic objectives and monetary income, and the entrepreneur who takes into account both the influence of different forms of government grant on entrepreneur financing at a different stage and the improved monitoring process of venture investors owe to the staged capital infusion of government. The model shows that the optimal staged financing decision is given when the first target of the government is to achieve social welfare optimization and the secondary goal of maximizing green benefits. Moreover, the model explains the optimal staged financing decision of venture investors and equity stake share in different rounds. Ultimately, we find the optimal staged financing portfolios for green start-ups to acquire venture investment, reduce the staged financing uncertainty, and help the government realize a national green innovation strategy.


---

## Body

## 1. Introduction

In the long run, accelerating green technology research and development (R&D) and transferring incubation have been the focus of innovation and entrepreneurship policy-making. However, with the rapid development of big data and cloud computing technology, more studies focus on the superficial phenomena and methods to accelerate green innovation efficiency and to help develop green start-ups in a short time. These studies, to some extent, improve the energy efficiency and ecological environment and solve the financing problems of green start-ups but also mean stringent follow-up production processes and standards, which makes the theoretical research relatively backward [1, 2]. To put it differently, green start-ups in the area of energy efficiency are different from other start-ups concerning financing needs and optimal staging of investments. Particularly, there are higher risks because of insufficient theoretical supports and proofs for local governments to issue green policy leads to investments, which is vital for start-ups to break the policy-induced constraint at lower cost and achieve the common aspiration [3, 4]. For example, we knew little about the internal mechanism of why there are higher research costs and sunk costs on green innovation than on general innovation research and how it would inhibit the enthusiasm of enterprises to develop green technology, transfer, and incubate green new products because of the popular creative destruction effect, “Schumpeter effect” [5].Obviously, the acquisition and efficient management of capital are more difficult for small enterprises in the process of technology development, product development, and technology transfer to the market, which have attracted wide attention from enterprises, governments, and the academic world still. For example, the external financing channels of small- and medium-sized enterprises (SMEs) in developing countries are mainly bank financing due to immature stock and venture capital markets [6], and thus high risky green start-ups would not survive. In contrast, capital resources in developed stock markets are more abundant, are more dependent on external finance, and have a greater innovation level [7]. Therefore, the sudden break of the external capital chain will have a devastating impact on the enterprise that is highly dependent on external finance. For instance, a large number of international private companies went bankrupt due to the financial crisis of 2008, and most venture investors turned to the gold market for safety, which led to a sharp decrease in R&D expenditure of start-ups and then greatly suppressed the green innovation drive [8].In this study, we establish the monitoring intensity function to show the existent asymmetric information in green innovation activities like transforming tangible assets into intangible assets and external financing process of small- and medium-sized enterprises after deriving three classic pieces of literature of Chemmanur et al. [9], Freeman [10], and Mina et al. [11] to some extent. Basically speaking, the problem of existent asymmetric information is relevant to the impact of institutional conditions on entrepreneurial motivation. Back et al. [12] consider the institutional voids which make start-ups often struggle to get enough finance. In particular, empirical evidence suggests that, under the condition of information asymmetry, even if entrepreneurs open external financing, it is difficult for them to obtain enough funds to achieve rapid growth. Even in nontransparent predatory government, start-ups are less affected by lower institutional quality in the short term, but the impact will continue to expand over time because start-ups are relatively independent due to their strong autonomy, resources, capabilities, and social network in the initial period [13].Besides, several authors have shown that internal factors such as human capital, market share, and financial capital and external factors such as social capital of enterprises have a heterogeneous effect on entrepreneurship under different institutional conditions [14–16]. Alam et al. [17] argue that the start-ups in the bank-based financial dominated systems are more dependent on external capital, while they are mainly dependent on internal R&D capital under the market-based financial dominated system. These institutional uncertainties undermine entrepreneurial action and create insurmountable obstacles to engage in productive business entrepreneurship, which is consistent with the North’s institutional theory [18–20]. To retain the right to terminate financing projects and improve the efficiency of start-ups, venture investors will monitor the business plan, asset use, and agency cost and regularly collect information as long as the institutional conditions have asymmetric information [21–23]. Concretely, Chemmanur et al. [9] have contributed to the research of the existent asymmetric information by focusing on the screening and monitoring procedures in the venture-capital-backed firms and the non-venture-capital-backed firms and illustrated the more obvious efficiency advantage and better product market performance of enterprises generated by venture capital backing. Thus, we combine strands of institutional theory with the resource-based view and reckon that institutional voids are existing in emerging markets of start-ups.In fact, the government grant can improve asymmetric information problems which tend to be most severe in the financing process of high risky start-ups [11]. As such, relying solely upon government subsidies can no longer meet the needs of emerging ICT innovations for large developing countries but can establish a dynamic relationship between the government and enterprise partners, upgrading it from the project level to the system level, and then forming sustainable partnerships between governments and enterprises is conducive to jointly explore market demands and deal with risks [24]. Urpelainen and Van de Graaf [25] document new evidence about the importance of the participation of government financing involved in stimulating innovation by using the case of the International Renewable Energy Agency (IRENA).The government mainly provides three forms of green subsidies: green appropriation, green product cost subsidies, and green tax incentives or green tax credits [26]. Green appropriation means that the government provides green start-up funds to entrepreneurs with scientific achievements, but the effects of this kind of direct subsidies rely on an ex ante screening mechanism [27–29]. Green product cost subsidies and green tax incentives are mainly to help small- and medium-sized enterprises to innovate their products, expand their scale of production, and have positive impacts on R&D activities. However, we do not consider the form of government equity investment, since such enterprises generally meet the requirements of national strategy, have high technology content and strong innovation ability, and are full of market potential, which is in contrast with start-ups [30].In this study, we reckon that the function of the government grant is related to the trend of world economic growth mode change which is pushed by natural resources turn to be pulled by the resources of knowledge and technology [31, 32]. The government grant, firstly, can address the market failure problem of underinvestment in the R&D financing process [33]. Secondly, it can also encourage small enterprises to increase their R&D activities for innovation [34]. Ideally, the government invokes an “additional effect” on the R&D activities; that is, the purpose of government subsidies is to lower the R&D cost of enterprises, encourage R&D activities, and promote knowledge spillover. More specifically, the small amount of grant for enterprise R&D will help enterprises finance, while excessive grant will crowd out investors for financing and hinder the development of start-ups [7, 35, 36].The model presented in this study includes three features which are important differences from those references cited: (i) We divided the subject of venture capital into strategic investors and venture investors according to the pecking order financing theory because strategic investors have stronger risk tolerance and weaker risk aversion characteristics than venture investors to obtain more equity, to achieve strategic goals, and to maximize expected returns, which are more conducive to the development of enterprise innovation activities [37–39]. (ii) Compared to the studies of Giudici and Paleari [40] and Hellmann and Puri [41], we take the cost of monitoring of venture capitalists into account during the stage of green R&D and green products expansion for further reproduction. (iii) Based on the availability of government grants, we also analyze the maximization of green benefits of financing and calculate the optimal social welfare of start-ups.The structure of the remainder of the study is as follows: Section2 introduces the methodology. Section 3 describes the optimal choice of government. Section 4 concludes the study.


## 2. The Model

The target of this section is to understand the financing strategy taken of green start-ups at different stages. Based on the financial growth cycle paradigm, we create a green staged financing model by achieving social welfare optimization and maximizing green benefits (note that we define the green benefits as the raised funds which are used as financing tools for green projects such as energy conservation, environmental protection and pollution prevention, resource conservation, and recycling).Briefly, we consider three issues: the optimal staged financing portfolio to maximize social welfare and green benefits [38, 42–44], the optimal staged financing portfolio for entrepreneur, and the optimal monitoring intensity for venture investors to reduce information asymmetry with the participation of government grant.


### 2.1. The Assumptions Based on the Existence of the Green Government Grant

The optimal level of monitoring is preferable to no intervention in a symmetric information environment, which means maximizing the value of the venture without monitoring cost.Consider that an entrepreneur who is financially constrained has a new green technology only in a risk-neutral world and fully competitive market with no discounting. The goal of these parties is to realize industrialization, commercialization, and marketization of new green technologies; and R&D takes place in the first stages0,T1, such as green conceptual product design, followed by the green product expansion reproduction period T1,T2 which is no grounds for terminating. Assume that minimum financing capital is available at each stage for start-ups. Hence, in this model, we divide two periods. Suppose that the entrepreneur has no capital in the state t=0 and seeks external financing. The external channels of financing of this stage include special appropriation funds K0G for green start-ups from government and venture investments K0V [31, 45, 46]. Due to the high risk of green R&D activities, we simply define the venture capitalists who solely pursue monetary income as VIs and the venture capitalists who pursue strategic objectives and monetary income as SIs. The venture investments K0V and K0S occur, respectively, from VIs and SIs. At the state of t=T2, the value of the asset of the start-up is A¯ in the case of success and A¯ in the case of failure. We define θ=A¯−A¯, and it measures the net impact of enterprises on SIs’ own assets. Besides, it means the complementary function on SIs’ own assets if θ>0 and substituted function if θ<0 [41]. Naturally, we have E homogeneous strategic investors with complementary function if θ>0, F homogeneous strategic investors with substituted function if θ<0, and H homogeneous VIs, so that there are E0+F0+H0 investors for the entrepreneur to select. Note that the entrepreneur is able to choose different portfolios in each financing stage. Thus, the entrepreneur is willing to sign contracts with mm=1,2,…,E0+F0+H0 investors and each of them invests capital k at the state of t=0. Moreover, the contract stipulates that the entrepreneur and the investor have only two choices: accept or reject. The total capitals from strategic investors are K0S=E0+F0k and VIs are K0V=H0k. Namely, the total raised capitals at the time t=0 are K0G=K0G+K0V+K0S, so the entrepreneur holds an equity stake that is equal to α0. In return, the entrepreneur will provide investors equity stakes α0Gi, i=S,V. However, the entrepreneur is the absolute decision-maker; thus, we assume that α0GV+α0GS<1/2α0G. Later, the period 0,T1 involves establishing new plants, purchase equipment, green technology incubation, employment expenditure, and other activities. Suppose that the green start-up follows the Cobb–Douglas production function YK,L=aKαL1−α; the factor of labor production L is simply decided by the efforts of the entrepreneur, while the factor of capital production K is decided by the number of capital investments [47]. α>0 corresponds to the elasticity coefficient of labor output and 1−α>0 corresponds to the elasticity coefficient of capital output. This simple specification ignores the effort cost of the entrepreneur as the sunk cost, for the assumption of the absolutely responsible entrepreneur.Besides, we assume that investors merely monitor the start-up to prevent entrepreneurs from opportunism, while the government only regulates the green appropriation funds it provides in this period (note that we have not considered the role of direct support for start-ups (e.g., through consultancy, networks)). Thus, VIs and SIs, respectively, determine the monitoring intensityξ0GVξ0GV>0 and ξ0GS, ξ0GV>0 (note that government regulation of green appropriation funds, to some extent, promotes the disclosure of financial information of green start-up, which significantly helps investors reduce the cost of monitoring and avoid unnecessary monitoring). Let μ be the maximum influence of monitoring intensity on the output value of the green start-up, and the value growth diminishes at the monitoring intensity ξ0GV=ξ0GV∗. So, we hypothesized that the output value of green start-up is positively correlated with monitoring intensity; namely,(1)fξ0G=bξ0G2+cξ0G+d.We also set that the start-up has the minimum output value of the enterprise regardless of whether or not it is monitored by investors; thus,fminξ0G=1.The output value of green start-up is as follows:(2)Yξ0G,L0,K0G=fξ0GYL0,K0G,where L0 is an exogenous model parameter, a captures productivity parameter, and YL0,K0G=aL1−αK0Gα denotes the original output value of green start-up.The investors’ wealth gain stems from their financing and monitoring activities (note that we use the production function to describe the process of capital appreciation at the period0,T1). Thus, according to the equity allocation plan in the contract, the wealth of VIs and SIs is equal to α0GVYξ0G,K0G and α0GSYξ0G,K0G, respectively.Based on the principal-agent theory [48], we assume that the green grant from the government has no effect on the cost of monitoring; thus, we use the effort cost function proposed by the compensation contract model to compute the cost of monitoring C0ξ0G,T1 (note that the capital and the cost of monitoring are fully deductible due to the high cost of Big Data) which can be expressed as(3)C0ξ0G,T1=C0ξ0GV,T1+C0ξ0GS,T1,C0ξ0GV,T1=12ξ0GVK0V2C0ξ0GS,T1=12ξ0GSK0S2.Taking into account a tax rateσ, we may now compute the total net profit πξ0G,K0G at the time of t=T1:(4)πξ0G,K0G=1−σYξ0G,K0G−C0ξ0G,T1−K0G.Then we are able to obtain the net profit of VIs and SIs:(5)πVξ0G,K0G=H0E0+F0+H0α0GVπξ0G,K0G,πSξ0G,K0G=E0+F0E0+F0+H0α0GSπξ0G,K0G,where H0/E0+F0+H0 and E0+F0/E0+F0+H0 denote the investment proportion between VIs and SIs, respectively.In the timeT1, to make the green product marketization, the government provides green product sales growth subsides η per item at this time. We assume that there are only two possible states in the times T1 and T2, that is, success and failure. Moreover, the VIs and SIs are myopic in the sense that they do not care about the information they obtained in the period of 0,T1 as long as the first stage is able to succeed. Then investors will decide whether to continue investing in this start-up. Besides, venture investments K1V and K1S occur from VIs and SIs. Thus, the total capital of T1 is(6)K1=K1V+K1S.Thus, the entrepreneur holds an equity stake that is equal toα1. In return, the entrepreneur will provide investors equity stakes α1i, i=S,V. However, the entrepreneur is the absolute decision-maker; thus, we assume that α1V+α1S<1/2α1.Besides, the fixed and variable costs of the green product are denoted as follows:(7)cfG=K0G+K1+C0ξ0G,T1,cvaG=τqG,CKG=cfG+cvaG,where qG represents sale quantity, cf captures the fixed cost of the green product, τ expresses unit variable cost, and cva denotes the variable cost of the green product.(8)π1G=pqG−1−ηCKG1−σ1−δ,where p captures retail price of the green product and δ represents tax refund rate of green product.Then we can obtain the net profit of VIs and SIs of timeT2 as follows:(9)π1GV=α1VpqG−1−ηCKG1−σ1−δ,π1GS=α1SpqG−1−ηCKG1−σ1−δ.Figure1 shows the staged financing process among government, VIs, and SIs between two subsequent R&D and expanded reproduction periods.Figure 1
The financing process with the green grant of government.


### 2.2. The Assumptions Based on the Absence of the Green Government Grant

Similarly, we now assume that the external financing channels of green start-ups of this stage come from venture investments only. For simplicity, we define that venture investmentsK0V and K0S occur from VIs and SIs. Thus, the total raised capital at time t=0 is K0=K0V+K0S, so the entrepreneur holds an equity stake that is equal to α0. In return, the entrepreneur will provide investors equity stakes α0i, i=S,V. However, the entrepreneur is the absolute decision-maker; thus, we assume that α0V+α0S<1/2α0. Likewise, the investors merely monitor the start-up to prevent entrepreneurs from opportunism. Therefore, VIs and SIs determine the monitoring intensity ξ0V0<ξ0GV<ξ0V and ξ0S, 0<ξ0GS<ξ0S, respectively (note that the green capital support of the government will improve the probability of investors to finance; however, the impact of the monitoring on the output value between venture investors and strategy investors remains steady). Then, we are able to rewrite equation (1) asfξ0=bξ02+cξ0+d. Thus, the output value can be rewritten as Yξ0,K0=fξ0YL0,K0. To put it in another way, the investors’ wealth gain stems from their financing and monitoring activities (also note that monitoring intensity of investors will be much higher without the green capital support of the government, for the reason of information asymmetry). Thus, according to the equity allocation plan in the contract, the wealth of VIs and SIs is equal to α0VYξ0,K0 and α0SYξ0,K0, respectively. Besides, the cost of monitoring is C0ξ0,T1=C0ξ0V,T1+C0ξ0S,T1, whereC0ξ0V,T1=1/2ξ0VK0V2C0ξ0S,T1=1/2ξ0SK0S2.In addition, we similarly compute the total net profitπξ0V,ξ0S,K0 at the time t=T1:(10)πξ0V,ξ0S,K0=1−σYξ0V,ξ0S,K0−C0ξ0,T1−K0.Then we can obtain the net profit of VIs and SIs:(11)πVξ0V,ξ0S,K0=H0E0+F0+H0α0Vπξ0V,ξ0S,K0,πSξ0V,ξ0S,K0=E0+F0E0+F0+H0α0Sπξ0V,ξ0S,K0,where H0/E0+F0+H0 and E0+F0/E0+F0+H0 denote the investment proportion between VIs and SIs, respectively.In the timeT1, to make the green product marketization, we assume that the VIs and SIs are myopic in the sense that they do not care about the information they obtained in the period of 0,T1 as long as the first stage was successful when they decide whether to continue investing on this start-up. Besides, venture investments K1V and K1S occur from VIs and SIs.Besides, the fixed and variable costs of the green product are denoted as follows:(12)cf=K0+K1+C0ξ0,T1+C1ξ1,T2,cva=τq,CK=cf+cva,where qG represents sale quantity, cf captures the fixed cost of the green product, τ expresses unit variable cost, and cva denotes the variable cost of the green product.(13)π1=pq−CK1−σ,where p captures retail price of the green product and δ represents tax refund rate of green product.Then we can obtain the net profit of VIs and SIs of timeT2 as follows:(14)π1V=α1VpqG−CKG1−σ,π1S=α1SpqG−CKG1−σ.Table1 presents the main notations to be used throughout this study.Table 1
Summary of notations.
GReceive government supportVIsVVenture capitalists who solely pursue monetary incomeSIsSVenture capitalists who pursue strategic objectives and monetary incomeKAmount of capitalρThe probability of venture investments occurrenceA¯The value of asset of the start-up in the case of successA¯The value of asset of the start-up in the case of failureθThe net impact of enterprises on SIs’ own assetsEAmount of homogeneous strategic investors with complementary function ifθ>0FAmount of homogeneous strategic investors with substituted function ifθ<0HAmount of homogeneous VIskAmount of capital invested of each investorαEquity ratioβThe elasticity coefficient of capital outputLThe factor of labor productionξThe monitoring intensityμThe maximum influence of monitoring intensity on the output value of the green start-upCξ,TThe cost of monitoringσThe tax rate for green start-upsπThe net profitηThe green product sales growth subsidesqThe sale quantitycfThe fixed cost of the green productτThe unit variable costcvaThe variable cost of the green productpThe retail price of the green productδThe tax refund rate of green productFigure2 shows the staged financing process between VIs and SIs in two subsequent R&D and expanded reproduction periods.Figure 2
The financing process without the green grant of the government.


## 2.1. The Assumptions Based on the Existence of the Green Government Grant

The optimal level of monitoring is preferable to no intervention in a symmetric information environment, which means maximizing the value of the venture without monitoring cost.Consider that an entrepreneur who is financially constrained has a new green technology only in a risk-neutral world and fully competitive market with no discounting. The goal of these parties is to realize industrialization, commercialization, and marketization of new green technologies; and R&D takes place in the first stages0,T1, such as green conceptual product design, followed by the green product expansion reproduction period T1,T2 which is no grounds for terminating. Assume that minimum financing capital is available at each stage for start-ups. Hence, in this model, we divide two periods. Suppose that the entrepreneur has no capital in the state t=0 and seeks external financing. The external channels of financing of this stage include special appropriation funds K0G for green start-ups from government and venture investments K0V [31, 45, 46]. Due to the high risk of green R&D activities, we simply define the venture capitalists who solely pursue monetary income as VIs and the venture capitalists who pursue strategic objectives and monetary income as SIs. The venture investments K0V and K0S occur, respectively, from VIs and SIs. At the state of t=T2, the value of the asset of the start-up is A¯ in the case of success and A¯ in the case of failure. We define θ=A¯−A¯, and it measures the net impact of enterprises on SIs’ own assets. Besides, it means the complementary function on SIs’ own assets if θ>0 and substituted function if θ<0 [41]. Naturally, we have E homogeneous strategic investors with complementary function if θ>0, F homogeneous strategic investors with substituted function if θ<0, and H homogeneous VIs, so that there are E0+F0+H0 investors for the entrepreneur to select. Note that the entrepreneur is able to choose different portfolios in each financing stage. Thus, the entrepreneur is willing to sign contracts with mm=1,2,…,E0+F0+H0 investors and each of them invests capital k at the state of t=0. Moreover, the contract stipulates that the entrepreneur and the investor have only two choices: accept or reject. The total capitals from strategic investors are K0S=E0+F0k and VIs are K0V=H0k. Namely, the total raised capitals at the time t=0 are K0G=K0G+K0V+K0S, so the entrepreneur holds an equity stake that is equal to α0. In return, the entrepreneur will provide investors equity stakes α0Gi, i=S,V. However, the entrepreneur is the absolute decision-maker; thus, we assume that α0GV+α0GS<1/2α0G. Later, the period 0,T1 involves establishing new plants, purchase equipment, green technology incubation, employment expenditure, and other activities. Suppose that the green start-up follows the Cobb–Douglas production function YK,L=aKαL1−α; the factor of labor production L is simply decided by the efforts of the entrepreneur, while the factor of capital production K is decided by the number of capital investments [47]. α>0 corresponds to the elasticity coefficient of labor output and 1−α>0 corresponds to the elasticity coefficient of capital output. This simple specification ignores the effort cost of the entrepreneur as the sunk cost, for the assumption of the absolutely responsible entrepreneur.Besides, we assume that investors merely monitor the start-up to prevent entrepreneurs from opportunism, while the government only regulates the green appropriation funds it provides in this period (note that we have not considered the role of direct support for start-ups (e.g., through consultancy, networks)). Thus, VIs and SIs, respectively, determine the monitoring intensityξ0GVξ0GV>0 and ξ0GS, ξ0GV>0 (note that government regulation of green appropriation funds, to some extent, promotes the disclosure of financial information of green start-up, which significantly helps investors reduce the cost of monitoring and avoid unnecessary monitoring). Let μ be the maximum influence of monitoring intensity on the output value of the green start-up, and the value growth diminishes at the monitoring intensity ξ0GV=ξ0GV∗. So, we hypothesized that the output value of green start-up is positively correlated with monitoring intensity; namely,(1)fξ0G=bξ0G2+cξ0G+d.We also set that the start-up has the minimum output value of the enterprise regardless of whether or not it is monitored by investors; thus,fminξ0G=1.The output value of green start-up is as follows:(2)Yξ0G,L0,K0G=fξ0GYL0,K0G,where L0 is an exogenous model parameter, a captures productivity parameter, and YL0,K0G=aL1−αK0Gα denotes the original output value of green start-up.The investors’ wealth gain stems from their financing and monitoring activities (note that we use the production function to describe the process of capital appreciation at the period0,T1). Thus, according to the equity allocation plan in the contract, the wealth of VIs and SIs is equal to α0GVYξ0G,K0G and α0GSYξ0G,K0G, respectively.Based on the principal-agent theory [48], we assume that the green grant from the government has no effect on the cost of monitoring; thus, we use the effort cost function proposed by the compensation contract model to compute the cost of monitoring C0ξ0G,T1 (note that the capital and the cost of monitoring are fully deductible due to the high cost of Big Data) which can be expressed as(3)C0ξ0G,T1=C0ξ0GV,T1+C0ξ0GS,T1,C0ξ0GV,T1=12ξ0GVK0V2C0ξ0GS,T1=12ξ0GSK0S2.Taking into account a tax rateσ, we may now compute the total net profit πξ0G,K0G at the time of t=T1:(4)πξ0G,K0G=1−σYξ0G,K0G−C0ξ0G,T1−K0G.Then we are able to obtain the net profit of VIs and SIs:(5)πVξ0G,K0G=H0E0+F0+H0α0GVπξ0G,K0G,πSξ0G,K0G=E0+F0E0+F0+H0α0GSπξ0G,K0G,where H0/E0+F0+H0 and E0+F0/E0+F0+H0 denote the investment proportion between VIs and SIs, respectively.In the timeT1, to make the green product marketization, the government provides green product sales growth subsides η per item at this time. We assume that there are only two possible states in the times T1 and T2, that is, success and failure. Moreover, the VIs and SIs are myopic in the sense that they do not care about the information they obtained in the period of 0,T1 as long as the first stage is able to succeed. Then investors will decide whether to continue investing in this start-up. Besides, venture investments K1V and K1S occur from VIs and SIs. Thus, the total capital of T1 is(6)K1=K1V+K1S.Thus, the entrepreneur holds an equity stake that is equal toα1. In return, the entrepreneur will provide investors equity stakes α1i, i=S,V. However, the entrepreneur is the absolute decision-maker; thus, we assume that α1V+α1S<1/2α1.Besides, the fixed and variable costs of the green product are denoted as follows:(7)cfG=K0G+K1+C0ξ0G,T1,cvaG=τqG,CKG=cfG+cvaG,where qG represents sale quantity, cf captures the fixed cost of the green product, τ expresses unit variable cost, and cva denotes the variable cost of the green product.(8)π1G=pqG−1−ηCKG1−σ1−δ,where p captures retail price of the green product and δ represents tax refund rate of green product.Then we can obtain the net profit of VIs and SIs of timeT2 as follows:(9)π1GV=α1VpqG−1−ηCKG1−σ1−δ,π1GS=α1SpqG−1−ηCKG1−σ1−δ.Figure1 shows the staged financing process among government, VIs, and SIs between two subsequent R&D and expanded reproduction periods.Figure 1
The financing process with the green grant of government.


## 2.2. The Assumptions Based on the Absence of the Green Government Grant

Similarly, we now assume that the external financing channels of green start-ups of this stage come from venture investments only. For simplicity, we define that venture investmentsK0V and K0S occur from VIs and SIs. Thus, the total raised capital at time t=0 is K0=K0V+K0S, so the entrepreneur holds an equity stake that is equal to α0. In return, the entrepreneur will provide investors equity stakes α0i, i=S,V. However, the entrepreneur is the absolute decision-maker; thus, we assume that α0V+α0S<1/2α0. Likewise, the investors merely monitor the start-up to prevent entrepreneurs from opportunism. Therefore, VIs and SIs determine the monitoring intensity ξ0V0<ξ0GV<ξ0V and ξ0S, 0<ξ0GS<ξ0S, respectively (note that the green capital support of the government will improve the probability of investors to finance; however, the impact of the monitoring on the output value between venture investors and strategy investors remains steady). Then, we are able to rewrite equation (1) asfξ0=bξ02+cξ0+d. Thus, the output value can be rewritten as Yξ0,K0=fξ0YL0,K0. To put it in another way, the investors’ wealth gain stems from their financing and monitoring activities (also note that monitoring intensity of investors will be much higher without the green capital support of the government, for the reason of information asymmetry). Thus, according to the equity allocation plan in the contract, the wealth of VIs and SIs is equal to α0VYξ0,K0 and α0SYξ0,K0, respectively. Besides, the cost of monitoring is C0ξ0,T1=C0ξ0V,T1+C0ξ0S,T1, whereC0ξ0V,T1=1/2ξ0VK0V2C0ξ0S,T1=1/2ξ0SK0S2.In addition, we similarly compute the total net profitπξ0V,ξ0S,K0 at the time t=T1:(10)πξ0V,ξ0S,K0=1−σYξ0V,ξ0S,K0−C0ξ0,T1−K0.Then we can obtain the net profit of VIs and SIs:(11)πVξ0V,ξ0S,K0=H0E0+F0+H0α0Vπξ0V,ξ0S,K0,πSξ0V,ξ0S,K0=E0+F0E0+F0+H0α0Sπξ0V,ξ0S,K0,where H0/E0+F0+H0 and E0+F0/E0+F0+H0 denote the investment proportion between VIs and SIs, respectively.In the timeT1, to make the green product marketization, we assume that the VIs and SIs are myopic in the sense that they do not care about the information they obtained in the period of 0,T1 as long as the first stage was successful when they decide whether to continue investing on this start-up. Besides, venture investments K1V and K1S occur from VIs and SIs.Besides, the fixed and variable costs of the green product are denoted as follows:(12)cf=K0+K1+C0ξ0,T1+C1ξ1,T2,cva=τq,CK=cf+cva,where qG represents sale quantity, cf captures the fixed cost of the green product, τ expresses unit variable cost, and cva denotes the variable cost of the green product.(13)π1=pq−CK1−σ,where p captures retail price of the green product and δ represents tax refund rate of green product.Then we can obtain the net profit of VIs and SIs of timeT2 as follows:(14)π1V=α1VpqG−CKG1−σ,π1S=α1SpqG−CKG1−σ.Table1 presents the main notations to be used throughout this study.Table 1
Summary of notations.
GReceive government supportVIsVVenture capitalists who solely pursue monetary incomeSIsSVenture capitalists who pursue strategic objectives and monetary incomeKAmount of capitalρThe probability of venture investments occurrenceA¯The value of asset of the start-up in the case of successA¯The value of asset of the start-up in the case of failureθThe net impact of enterprises on SIs’ own assetsEAmount of homogeneous strategic investors with complementary function ifθ>0FAmount of homogeneous strategic investors with substituted function ifθ<0HAmount of homogeneous VIskAmount of capital invested of each investorαEquity ratioβThe elasticity coefficient of capital outputLThe factor of labor productionξThe monitoring intensityμThe maximum influence of monitoring intensity on the output value of the green start-upCξ,TThe cost of monitoringσThe tax rate for green start-upsπThe net profitηThe green product sales growth subsidesqThe sale quantitycfThe fixed cost of the green productτThe unit variable costcvaThe variable cost of the green productpThe retail price of the green productδThe tax refund rate of green productFigure2 shows the staged financing process between VIs and SIs in two subsequent R&D and expanded reproduction periods.Figure 2
The financing process without the green grant of the government.


## 3. Staging Optimal Decision among Government, Entrepreneur, and Investors

### 3.1. The Optimal Choice for Government Based on the Data Simulation

To achieve the government strategic goals of green development, we will first consider what happens whether or not the green government grant is made with the start-up in each stage. In this case, we investigate the government optimal choices to maximize the green benefitsGP1 from the first-stage conditions:(15)GP1=πξ0G,K0G−πξ0,K0.The remaining constraint is a bound on the utilities of government. The green benefits of the start-up must satisfy the relation(16)GP1=πξ0G,K0G−πξ0,K0>0.Apparently, the green benefits of the analysis are highly relevant to the intensity of monitoring, so the problem is(17)maxGP1=maxπξ0G,K0G−πξ0,K0.Proposition 1.
Green benefits increase asξ0GV increases first, and then, from the monitoring intensity of ξ0GV∗, green benefits decrease as ξ0GV increases. There only exist venture investors with the monitoring intensity of ξ0GV∗, and thus, the function of monitoring intensity is represented as follows:(18)fGVξ0GV=b1ξ0GV2+c1ξ0GV+d1,where b1, c1, and d1 are constants, b1<0, and c1>0. Besides, since fGV0=1 at a given monitoring intensity ξ0GV=0, which denotes that the monitoring is not considered in the production process, we obtain that d1=1, and the output value of the green start-up is as follows:(19)Yξ0GV,K0GV=fGVξ0GVYL0,K0GV.The total net profit at the timet=T1 is as follows:(20)πξ0GV,K0GV=1−σYξ0GV,K0GV−C0ξ0GV,T1−K0GV.Thus, the problem can be rewritten as follows:(21)maxπξ0GV,K0GV−πξ0V,K0V,where the monitoring intensities ξ0GV and ξ0V are the venture investors’ choice variable. Specifically, we assume that the maximum influence of monitoring intensity on an output value of the green start-ups only depends on the venture investors. Meanwhile, there is no effect on the monitoring intensity of venture investors whether government exists. To obtain the optimal analytic solution, we thus suppose ξ0GV=ξ0V. Then, ξ0GV∗,μ denotes the efficient choices.Let∂GP1V/∂ξ0GV=0, and then we can obtain the optimal analytic solution as follows:(22)ξ0GV∗=−c2b.To determine whether the solution is a minimum or a maximum, we take the second derivative of equation (A.5), and we have these equations for force here.(23)∂GP1V∂ξ0GV=1−σaL1−α2b1ξ0GV+c1K0G+K0Vα−12K0GV2,(24)∂GP1V∂ξ0V=1−σ−aL1−α2b1ξ0V+c1K0Vα+12K0GV2,(25)∂GP1V∂2ξ0GV=2ab11−σL1−αK0G+K0Vα<0,(26)∂GP1V∂2ξ0V=−2ab11−σL1−αK0Vα>0.According to equations (23)–(26), we can learn that green benefits monotonically increase with the rising of monitoring intensity 0,ξ0GV∗ and then with ξ0GV∗ growing and GP1V decreasing. Meanwhile, green benefits monotonically decrease with the rising of monitoring intensity 0,ξ0V∗ and then with ξ0V∗ growing and GP1V increasing.Additionally, we clearly presented the impacts of the monitoring intensity on the green benefits in Figure3. This figure also depicts the optimal monitoring intensity and green benefits do exist, which means the desire of the government.Figure3 shows the impacts of the monitoring intensity on the green benefits (a=550; L=1; α=0.3 [49]; b=−1; c=3; K0=10; K1=100).Figure 3
The green benefits when monitored by venture investors only.Proposition 2.
Green benefits increase asξ0GS increases first, and then, from the monitoring intensity of ξ0GS∗, green benefits decrease as ξ0GS increases. There only exist strategy investors with the monitoring intensity of ξ0GS∗, and thus, the function of monitoring intensity can be expressed as follows:(27)fGSξ0GS=b2ξ0GS2+c2ξ0GS+d2.Similarly, we can acquire the same results of Proposition1. Thus, we only presented the impacts of the monitoring intensity on the green benefits in Figure 4 (note that the actual monitoring intensity of venture investors is usually different from strategy investors; however, the impacts of monitoring on green benefits are the same).Figure4 shows the impacts of the monitoring intensity on the green benefits (a=550; L=1; α=0.3; b=−1; c=3; K0=10; K1=100).Figure 4
The green benefits when monitored by strategy investors only.Proposition 3.
There both exist venture investors and strategic investors with the monitoring intensities ofξ0GS∗ and ξ0GV∗, and thus, we obtain the monitoring intensity function:(28)maxfGVξ0GV,fGSξ0GS=maxb1ξ0GV2+c1ξ0GV+d1,b2ξ0GS2+c2ξ0GS+d2,(29)maxfGVξ0GV,fGSξ0GS=Zξ0GV,ξ0GSs.t.Zξ0GV,ξ0GS≥fGVξ0GVZξ0GV,ξ0GS≥fGSξ0GSξ0GV≥ξ0GS>0d1=d2=1.Then, the objective function can be reexpressed as follows:(30)fGSξ0GS,ξ0GV−−c2b≥−c2b−ξ0GS,fGVξ0GV,ξ0GV−−c2b<−c2b−ξ0GS.To calculate the optimal green benefits, the output value of the green start-up becomes(31)fGSξ0GSYL0,K0G,ξ0GV−−c2b≥−c2b−ξ0GS,fGVξ0GVYL0,K0G,ξ0GV−−c2b<−c2b−ξ0GS.Thus, the total net profit at the timet=T1 is as follows:(32)πξ0GV,ξ0GS,K0G=1−σfGSξ0GSYL0,K0G−C0ξ0GV,T1−C0ξ0GS,T1−K0G,ξ0GV−−c2b≥−c2b−ξ0GS,fGVξ0GVYL0,K0G−C0ξ0GV,T1−C0ξ0GS,T1−K0G,ξ0GV−−c2b<−c2b−ξ0GS,πξ0V,ξ0S,K0=1−σfSξ0SYL0,K0−C0ξ0V,T1−C0ξ0S,T1−K0,ξ0V−−c2b≥−c2b−ξ0S,fVξ0VYL0,K0−C0ξ0V,T1−C0ξ0S,T1−K0,ξ0V−−c2b<−c2b−ξ0S.Therefore, the problem must be of the following form:(33)maxπξ0GV,ξ0GS,K0G−πξ0V,ξ0S,K0.To directly show the relationship between green benefits and the monitoring intensity, we presented the impacts of the monitoring intensity on the green benefits in Figure5.Figure5 shows the impacts of the monitoring intensity on the green benefits (a=550; L=1; α=0.3; b=−1; c=3; K0=10; K1=100, K2=100).As is shown in Figure5, we can learn that green benefits GP1 decrease first and then increase with monitoring at the point of ξ0GV∗, where ξ0GV=ξ0V and ξ0GS=ξ0S. Clearly, the government thus may be willing to improve and promote the monitoring intensity of venture investors and strategic investors to maximize the green benefits at the point of ξ0GV∗. Besides, the results also imply that making an optimal investment portfolio is not the decisive factor in maximizing green benefits, which means that the monitoring intensity of investors should be drawn attention to realize optimal social welfare. In the Appendix, we examine it at the proof of Proposition 3.Figure 5
The green benefits when monitored by strategy investors and venture investors simultaneously.Proposition 4.
Then, we consider the optimal choices of government to maximize the green benefitsGP2 at the time T2; we assume that qG=λq, ξ0GV=ξ1GV, ξ0GS=ξ1GS, ξ0V=ξ1V, and ξ0S=ξ1S, where λ>1, and thus, the problem can be expressed in the following form:(34)GP2=π1G−π1>0.The remaining constraint is a bound on the utilities of society. To realize optimal social welfare, we maximize the total net profits:(35)maximizeπξ0GV,ξ0GS,K0G,maximizeπ1G.In the Appendix, we thus examine it at the proof of Proposition4. For pλ−1q>K0G, we can understand that the optimal green benefits happen when ξ1V=maxξ1V and ξ1GV=0 and when ξ1S=maxξ1S and ξ1GS=0 in the meantime.


## 3.1. The Optimal Choice for Government Based on the Data Simulation

To achieve the government strategic goals of green development, we will first consider what happens whether or not the green government grant is made with the start-up in each stage. In this case, we investigate the government optimal choices to maximize the green benefitsGP1 from the first-stage conditions:(15)GP1=πξ0G,K0G−πξ0,K0.The remaining constraint is a bound on the utilities of government. The green benefits of the start-up must satisfy the relation(16)GP1=πξ0G,K0G−πξ0,K0>0.Apparently, the green benefits of the analysis are highly relevant to the intensity of monitoring, so the problem is(17)maxGP1=maxπξ0G,K0G−πξ0,K0.Proposition 1.
Green benefits increase asξ0GV increases first, and then, from the monitoring intensity of ξ0GV∗, green benefits decrease as ξ0GV increases. There only exist venture investors with the monitoring intensity of ξ0GV∗, and thus, the function of monitoring intensity is represented as follows:(18)fGVξ0GV=b1ξ0GV2+c1ξ0GV+d1,where b1, c1, and d1 are constants, b1<0, and c1>0. Besides, since fGV0=1 at a given monitoring intensity ξ0GV=0, which denotes that the monitoring is not considered in the production process, we obtain that d1=1, and the output value of the green start-up is as follows:(19)Yξ0GV,K0GV=fGVξ0GVYL0,K0GV.The total net profit at the timet=T1 is as follows:(20)πξ0GV,K0GV=1−σYξ0GV,K0GV−C0ξ0GV,T1−K0GV.Thus, the problem can be rewritten as follows:(21)maxπξ0GV,K0GV−πξ0V,K0V,where the monitoring intensities ξ0GV and ξ0V are the venture investors’ choice variable. Specifically, we assume that the maximum influence of monitoring intensity on an output value of the green start-ups only depends on the venture investors. Meanwhile, there is no effect on the monitoring intensity of venture investors whether government exists. To obtain the optimal analytic solution, we thus suppose ξ0GV=ξ0V. Then, ξ0GV∗,μ denotes the efficient choices.Let∂GP1V/∂ξ0GV=0, and then we can obtain the optimal analytic solution as follows:(22)ξ0GV∗=−c2b.To determine whether the solution is a minimum or a maximum, we take the second derivative of equation (A.5), and we have these equations for force here.(23)∂GP1V∂ξ0GV=1−σaL1−α2b1ξ0GV+c1K0G+K0Vα−12K0GV2,(24)∂GP1V∂ξ0V=1−σ−aL1−α2b1ξ0V+c1K0Vα+12K0GV2,(25)∂GP1V∂2ξ0GV=2ab11−σL1−αK0G+K0Vα<0,(26)∂GP1V∂2ξ0V=−2ab11−σL1−αK0Vα>0.According to equations (23)–(26), we can learn that green benefits monotonically increase with the rising of monitoring intensity 0,ξ0GV∗ and then with ξ0GV∗ growing and GP1V decreasing. Meanwhile, green benefits monotonically decrease with the rising of monitoring intensity 0,ξ0V∗ and then with ξ0V∗ growing and GP1V increasing.Additionally, we clearly presented the impacts of the monitoring intensity on the green benefits in Figure3. This figure also depicts the optimal monitoring intensity and green benefits do exist, which means the desire of the government.Figure3 shows the impacts of the monitoring intensity on the green benefits (a=550; L=1; α=0.3 [49]; b=−1; c=3; K0=10; K1=100).Figure 3
The green benefits when monitored by venture investors only.Proposition 2.
Green benefits increase asξ0GS increases first, and then, from the monitoring intensity of ξ0GS∗, green benefits decrease as ξ0GS increases. There only exist strategy investors with the monitoring intensity of ξ0GS∗, and thus, the function of monitoring intensity can be expressed as follows:(27)fGSξ0GS=b2ξ0GS2+c2ξ0GS+d2.Similarly, we can acquire the same results of Proposition1. Thus, we only presented the impacts of the monitoring intensity on the green benefits in Figure 4 (note that the actual monitoring intensity of venture investors is usually different from strategy investors; however, the impacts of monitoring on green benefits are the same).Figure4 shows the impacts of the monitoring intensity on the green benefits (a=550; L=1; α=0.3; b=−1; c=3; K0=10; K1=100).Figure 4
The green benefits when monitored by strategy investors only.Proposition 3.
There both exist venture investors and strategic investors with the monitoring intensities ofξ0GS∗ and ξ0GV∗, and thus, we obtain the monitoring intensity function:(28)maxfGVξ0GV,fGSξ0GS=maxb1ξ0GV2+c1ξ0GV+d1,b2ξ0GS2+c2ξ0GS+d2,(29)maxfGVξ0GV,fGSξ0GS=Zξ0GV,ξ0GSs.t.Zξ0GV,ξ0GS≥fGVξ0GVZξ0GV,ξ0GS≥fGSξ0GSξ0GV≥ξ0GS>0d1=d2=1.Then, the objective function can be reexpressed as follows:(30)fGSξ0GS,ξ0GV−−c2b≥−c2b−ξ0GS,fGVξ0GV,ξ0GV−−c2b<−c2b−ξ0GS.To calculate the optimal green benefits, the output value of the green start-up becomes(31)fGSξ0GSYL0,K0G,ξ0GV−−c2b≥−c2b−ξ0GS,fGVξ0GVYL0,K0G,ξ0GV−−c2b<−c2b−ξ0GS.Thus, the total net profit at the timet=T1 is as follows:(32)πξ0GV,ξ0GS,K0G=1−σfGSξ0GSYL0,K0G−C0ξ0GV,T1−C0ξ0GS,T1−K0G,ξ0GV−−c2b≥−c2b−ξ0GS,fGVξ0GVYL0,K0G−C0ξ0GV,T1−C0ξ0GS,T1−K0G,ξ0GV−−c2b<−c2b−ξ0GS,πξ0V,ξ0S,K0=1−σfSξ0SYL0,K0−C0ξ0V,T1−C0ξ0S,T1−K0,ξ0V−−c2b≥−c2b−ξ0S,fVξ0VYL0,K0−C0ξ0V,T1−C0ξ0S,T1−K0,ξ0V−−c2b<−c2b−ξ0S.Therefore, the problem must be of the following form:(33)maxπξ0GV,ξ0GS,K0G−πξ0V,ξ0S,K0.To directly show the relationship between green benefits and the monitoring intensity, we presented the impacts of the monitoring intensity on the green benefits in Figure5.Figure5 shows the impacts of the monitoring intensity on the green benefits (a=550; L=1; α=0.3; b=−1; c=3; K0=10; K1=100, K2=100).As is shown in Figure5, we can learn that green benefits GP1 decrease first and then increase with monitoring at the point of ξ0GV∗, where ξ0GV=ξ0V and ξ0GS=ξ0S. Clearly, the government thus may be willing to improve and promote the monitoring intensity of venture investors and strategic investors to maximize the green benefits at the point of ξ0GV∗. Besides, the results also imply that making an optimal investment portfolio is not the decisive factor in maximizing green benefits, which means that the monitoring intensity of investors should be drawn attention to realize optimal social welfare. In the Appendix, we examine it at the proof of Proposition 3.Figure 5
The green benefits when monitored by strategy investors and venture investors simultaneously.Proposition 4.
Then, we consider the optimal choices of government to maximize the green benefitsGP2 at the time T2; we assume that qG=λq, ξ0GV=ξ1GV, ξ0GS=ξ1GS, ξ0V=ξ1V, and ξ0S=ξ1S, where λ>1, and thus, the problem can be expressed in the following form:(34)GP2=π1G−π1>0.The remaining constraint is a bound on the utilities of society. To realize optimal social welfare, we maximize the total net profits:(35)maximizeπξ0GV,ξ0GS,K0G,maximizeπ1G.In the Appendix, we thus examine it at the proof of Proposition4. For pλ−1q>K0G, we can understand that the optimal green benefits happen when ξ1V=maxξ1V and ξ1GV=0 and when ξ1S=maxξ1S and ξ1GS=0 in the meantime.


## 4. Conclusions

In this study, we establish a theoretical model based on the financing selection mechanism of green start-ups under government grants and investigate the subject of venture capital into strategic investors and venture investors according to the pecking order financing theory. We restrict the equity control of investors and take the cost of monitoring of venture investors into account during the stage of green R&D and green products expansion for reproduction combining data simulation with empirical data to show the entire financing process of green start-ups with the help of the government to achieve green benefits, to reduce the staged financing uncertainty, and to help government realize national green innovation strategy. Our findings are as follows: Firstly, expanding the scale of green start-ups with the help of government grants is indispensable to the development of sustainable economic. Secondly, moderate monitoring intensity is beneficial to enhance green benefits. Specifically, the impact of monitoring intensity on green benefits exists in an inverted u-shaped relationship. Thirdly, both venture investors and strategic investors have the same influence on green benefits through monitoring intensity.



---

*Source: 9921355-2021-06-17.xml*