This study focuses on GCF, which belongs to the category of green finance. Therefore, we first review the literature on production and operation management considering green finance under deterministic scenario.

Some studies have analyzed green finance in conjunction with the green production behavior of firms. For instance, Lv, Fan and Lee examined the impact of green credit policy on firms’ green productivity using a double difference model and found that the implementation of green credit can significantly increase the green productivity of heavy polluters (Lv et al., 2023). Based on the context of transition insurance and green credit services, Liu et al. constructed a dynamic stochastic general equilibrium model covering the banking and insurance sectors, and they found that green credit incentives not only curb carbon emissions, but also increase the likelihood of producers’ energy transitions, which promotes low-carbon economic growth (Liu et al., 2023). Cui, Wang and Wang established an evolutionary game model including four players: government, financial institutions, enterprises and consumers, and used simulation methods to analyze the influence of each parameter on the changes and development of green financial market. The results show that the integrity of the green financial system has a positive impact on sustainable development and clean production (Cui et al., 2020). In addition, related studies have mainly focused on considering the impact of carbon emission caps brought about by green finance on enterprises’ operational decisions (Zhang and Xu, 2013; Feng et al., 2022; Lee and Yoon, 2022). At the same time, some studies have also treated carbon cap as a penalty mechanism for profit function, that is, if the enterprise exceeds the pre-established carbon emission cap in production and operation, it will get a certain profit penalty, and the expected profit of the enterprise will be reduced (An et al., 2021). As seen, the above literature has focused more on green production under green finance but has not considered possible investments in green technologies.

Other studies have considered both green production and green technology input decisions of firms under green finance policies. For example, Chen et al. integrated green credit policy with business decision-making and innovation behavior into a unified analytical framework to explore how to guide enterprises to carry out green production and low-carbon technological innovation (Chen et al., 2022). Wang and Wang suggested that upgrading industrial structure through green production and increasing investment in green innovation are the key influential paths to accelerate green transformation (Wang and Wang, 2023). Zhang studied the causal effect of green credit policy on green production and revisited the Porter hypothesis. By categorizing R&D into environmentally induced R&D and production R&D, it was found that green credit policy significantly increased green total factor productivity growth (Zhang, 2021). Tian et al. argued that green credit can guide the flow of funds from energy-consuming and highly polluting industries to technologically advanced emerging industry sectors, thus supporting the development of green industries and curbing emissions from polluting industries (Tian et al., 2022). Liu, Xia and Lee pointed out that green credit optimizes corporate debt financing by alleviating financing constraints, reducing debt costs and extending debt maturity structure, drives green technological innovation and encourages enterprises to carry out green production (Liu et al., 2024). In addition, relevant studies have analyzed carbon emission caps to green production and green technology investment, and they pointed out that with the support of green finance, enterprises can realize the unity of economic and environmental benefits through green production and increased investment in green technology (Bouchery et al., 2012; Yang et al., 2020; Li et al., 2022). All of the above studies are based on deterministic scenarios and do not consider the impact of uncertain environments on the production and operation management of enterprises.

The general fluctuation of business environment is an important factor affecting the operation and management of enterprises. Many researchers have discussed manufacturers’ operational decisions under uncertain environments.

Some studies have mostly explored the research on firms’ production and green technology input decision-making based on the uncertainty of economic policy, monetary policy, product supply. For instance, Zhang and Kong introduced the condition of economic policy uncertainty to explore the relationship between green credit policy and firms’ green technology inputs, and found that economic policy uncertainty is negatively related to firms’ green technology inputs (Zhang and Kong, 2022). Based on the background that manufacturers are subject to supply uncertainty and financial constraints, Wu and Shang established a Stackelberg game model to study the equilibrium green credit financing problem in a green supply chain with government subsidies and supply uncertainty, and analyzed how subsidy interest rates, supply uncertainty, and supply correlation affect the financing decision of equilibrium green credits as well as green products’ R&D investment decision (Wu and Shang, 2021a). In addition, some scholars explored the impact of green credit policy on corporate production and green technology innovation behavior from the perspectives of climate policy uncertainty environment and overall external uncertainty environment (Xu et al., 2021; Hoang, 2022; Du and Guo, 2023). The above-mentioned studies have paid more attention to the management of business production operations in various types of uncertain environments, but have ignored the demand uncertain environment that is directly related to the core business of a company.

Regardless of how other uncertainties change, they ultimately need to be reflected through market demand. And the uncertainty of demand directly determines how companies make production plans, inventory strategies, and sales forecasts (Zhang et al., 2018; Zhang et al., 2022; Liao et al., 2019). Under such a setting, other studies have explored firms’ production and green technology input decisions in environments with uncertain demand information. Assuming that demand is uncertain and dependent on certain green investments, and that such uncertain demand obeys an associated probability distribution, Cohen, Lobel and Perakis extended the current understanding of the pricing newsvendor model, incorporated external influences from the government, and quantified how uncertainty in demand affects corporate production and green technology investment (Cohen et al., 2016). An et al. compared the optimal operational decisions and profit levels of both supply chain parties under green credit financing and commercial credit financing by considering a manufacturer with carbon emission limitations as well as financial constraints in a demand uncertainty scenario. They found that under relatively strict carbon emission policies, manufacturers can set appropriate green investment ranges and realize win-win situations with suppliers (An et al., 2021). Wang, Zou and Geng discussed green technology investment decisions in a decentralized supply chain under demand uncertainty, they found that providing corresponding incentives can optimize supply chain operation decisions and better guide retailers to participate in green technology investment (Wang et al., 2021). Wu and Shang established a Stackelberg game to study the information leakage and optimal green operation decision of supply chain under uncertain demand, the results showed that if suppliers disclose demand information, they will invest more in green product development (Wu and Shang, 2021b). The above literature considers the impact of green credit on firms under uncertain demand, but all of them are based on probability distributions to portray demand uncertainty. Unlike them, this paper considers describing the demand uncertainty environment through interval scenarios.

This paper studies a single-period revenue maximization problem for a financially constrained manufacturer who sells a class of products to the market. The problem entails the following assumptions:

• There is a two-stage decision-making process for the manufacture to maximize its revenue under uncertain demand. The first stage decision is choosing appropriate financing channel to obtain the loan for production, and the second is making decisions on production quantity q and green investment K.

Because of uncertain demand, we adopt a robust approach to find a green production and finance decision that minimizes the maximal deviation from the optimum under all possible scenarios. To identify the performance of a robust decision, a criterion called min-max regret is widely adopted which seeks a decision closing to the optimal one by bounding the magnitude of missed opportunities. More concretely, for a green production decision under a determined finance channel, which includes production quantity q and green investment K, the corresponding revenue under a scenario s is denoted as u q , K , s . The optimal revenue under that scenario is denoted as u s * . Then the regret of the decision q , K under scenario s can be calculated in Equation 1 as R q , K , s = u s * − u G q , K , s . (1)

Define the scenario maximizing the regret of decision q , K as its worst-case scenario s _w . The corresponding maximum regret of decision q , K is R max q , K = R q , K , s w = max s ∈ S R q , K , s . (2)

The following technical lemma is useful in analysis of the main result.

Lemma 1

For a given function f q = p − 1 + I c q + 1 + I T θ q , f T C = f 1 + I C θ p − 1 + I c .

Lemma 2

For any positive real number q ≥ 0 , f q = p − 1 + I c q + 1 + I T θ q takes its minimum value when q 0 = 1 + I T θ p − 1 + I c .

We omit the proof of Lemma one and 2, since they can be easily proved by quadratic-root formula and extremum principle.

Lemma 3

For any positive real numbers 0 ≤ q 1 ≤ q 2 , if q ∈ q 1 , q 2 , f q takes its maximum value when q = q 1 or q = q 2 .

Proof. f q = p − 1 + I c q + 1 + I T θ q is a hyperbolic function of q as shown in Figure 1. If q 0 ≤ q 1 , f q is an increasing function of q in its domain. The maximum value f max q = f q 2 . If q 0 ≥ q 2 , f q is a decreasing function of q in its domain, and the maximum value f max q = f q 1 . Otherwise q 1 < q 0 < q 2 , f max q = max f q 1 , f q 2 . In any cases, the maximum value of f q is acquired at either q = q 1 or q = q 2 . The lemma is proved.

Lemma 4

For given function g q = p − 1 + I c q   i f   q ≤ T C f q − 1 + I C θ   o t h e r w i s e with the domain q ∈ 0 , q 3 and q 3 > T C , then its maximum value can be calculated in Equation 3 as g max q = g max T C   i f   q 3 ≤ 1 + I C θ p − 1 + I c g max q 3   i f   q 3 > 1 + I C θ p − 1 + I c   i f   T C ≤ q 0 g max q 3   i f   T C > q 0 . (3)

Proof. Because p − 1 + I c T C = f T C − 1 + I C θ , g q is a continuous function of q . Besides, g q is a linear function of q in 0 , T C and a hyperbolic function of q in T C , q 3 , as shown in Figure 2.

If T C ≤ q 0 , g q takes its maximum value at q = T C or q = q 3 according to Lemma 3. Specially, when q 3 ≤ 1 + I C θ p − 1 + I c , f q 3 ≤ f 1 + I C θ p − 1 + I c = f T C , g max q = g max T C ; When q 3 > 1 + I C θ p − 1 + I c , f q 3 > f 1 + I C θ p − 1 + I c = f T C , g max q = g max q 3 ;

If T C > q 0 , g q is an increasing function of q and takes its maximum value at q = q 3 . The lemma is proved.

We first analysis the optimal production and green investment decisions of GCF under a deterministic scenario s. Denote the optimal production and green investment decisions with the maximal revenue under scenario s as q s * , K s * , and the corresponding revenue can be calculated in Equation 4 as u s * = u * q s * , K s * , s = p ⁡ min d s , q s * − 1 + I c q s * + K s * . (4)

Note that the optimal production quantity cannot exceeds the demand under scenario s, i.e., q s * ≤ d s , otherwise it would lead to wasted production and green investment. Hence, u s * = p q s * − 1 + I c q s * + K s * . (5)

Consider the carbon emission constraint C − θ K s * q s * ≤ T , if q s * ≤ T C , any green investment is unnecessary because the carbon emissions do not exceed the cap. Then K s * = 0 , and u s * = p − 1 + I c q s . * (6)

Otherwise q s * > T C , according to Equation 5, u G , s * is a monotonic decreasing function of K s * . The carbon emission constraint implies that K s * ≥ C θ − T θ q s * . In order to achieve a maximum revenue, K s * = C θ − T θ q s * , and u s * = p − 1 + I c q s * + 1 + I T θ q s * − 1 + I C θ = f q s * − 1 + I C θ . (7)

In conclusion, according to Equations 6, 7, u s * = g q s * = p − 1 + I c q s *   i f   q s * ≤ T C f q s * − 1 + I C θ   o t h e r w i s e . (8)

Because the optimal production quantity q s * depends on the demand d s , we have following two lemmas to derive the optimal revenue under demand d s .

Lemma 5

When T C ≤ q 0 , u s * = p − 1 + I c d s   i f   d s ≤ T C p − 1 + I c T C   i f   T C < d s ≤ 1 + I C θ p − 1 + I c . f d s − 1 + I C θ   o t h e r w i s e (9)

Proof. According to Equation 8, if the demand under scenario s is d s ≤ T C , which implies q s * ≤ T C , u s * = p − 1 + I c q s * . Because q s * ≤ d s ≤ T C , u s * gets its maximum value when the optimal production quantity is q s * = d s , and u s * = p − 1 + I c d s . (10)

Otherwise d s > T C . Because u s * = g q s * with the domain q ∈ 0 , d s , according to Lemma 4, u s * gets its maximum value when q s * = T C if d s ≤ 1 + I C θ p − 1 + I c , or q s * = d s if d s > 1 + I C θ p − 1 + I c . Therefore, when d s > T C , u s * = g T C = p − 1 + I c T C   i f   T C < d s ≤ 1 + I C θ p − 1 + I c . g d s = f d s − 1 + I C θ   o t h e r w i s e (11)

According to Equations 10, 11, the lemma is proved.

Lemma 6

When T C > q 0 , u s * = p − 1 + I c d s   i f   d s ≤ T C . f d s − 1 + I C θ   o t h e r w i s e (12)

Proof. If the demand under scenario s is d s ≤ T C , u s * = p − 1 + I c q s * . Because q s * ≤ d s ≤ T C , u s * gets its maximum value when the optimal production quantity is q s * = d s , and u s * = p − 1 + I c d s . (13)

Otherwise d s > T C , according to Lemma 4, u s * = g d s = f d s − 1 + I C θ . (14)

According to Equations 13, 14, the lemma is proved.

The relationship between u s * and d s * is illustrated in Figure 3. We can get the following lemma.

Lemma 7

The optimal revenue u s * is a continuous and non-decreasing function of d s .

Based on the above analysis, we can determine the optimal production and green investment decisions of GCF under deterministic scenario s as follows:

Theorem 1

The optimal production and green investment decisions of GCF under deterministic scenario s can be calculated in Equation 15 as q s * , K s * = d s , 0   i f   d s ≤ T C T C , 0   i f   T   C < d s ≤ 1 + I C θ p − 1 + I c d s , C θ − T θ d s   i f     d s > 1 + I C θ p − 1 + I c   i f T C ≤ q 0 d s , 0   i f   d s ≤ T C d s , C θ − T θ d s   i f   d s > T C   i f   T C > q 0 . (15)

While for the uncertain environments where the demand is uncertain but lies in an interval d _ , d ¯ , the revenue of any decision q , K under scenario s is u q , K , s = p ⁡ min d s , q − 1 + I c q + K . (16)

Similar as that pointed out in Section 4, u q , K , s is also a decreasing function of K, and takes its maximum value when K = 0 if q ≤ T C , or K = C θ − T θ q if q > T C . We can naturally get the green investment decision once the production decision is determined. To simplify the expression, we only consider the production decision q. Hence, u q , s = p ⁡ min d s , q − 1 + I c q   i f   q ≤ T C p ⁡ min d s , q − 1 + I c q + C θ − T θ q   o t h e r w i s e . (17)

Because we cannot learn the exact value of d s in advance under uncertain environment, we derive the maximum regret of the production decision q under GCF based on whether q ≤ d s or q > d s .

Lemma 8

When q ≤ d s , the maximum regret can be calculated in Equation 18 as R max ⁡ , 1 q = u s ¯ * − g q . (18) and.

1) if T C > q 0 or T C ≤ q 0 and q > 1 + I C θ p − 1 + I c , R max ⁡ , 1 q decreases with q ;

Proof. According to Equation 17 when q ≤ d s , u 1 q , s = g q = p − 1 + I c q   i f   q ≤ T C f q − 1 + I C θ   o t h e r w i s e . (19)

The subscript “1” of u 1 q , s in Equation 19 is used to distinguish the revenue when q ≤ d s . The regret of the production decision q under scenario s when q ≤ d s can be calculated in Equation 20 as R 1 q , s = u s * − g q . (20)

According to Lemma 7, u s * is non-decreasing with d s , the worst-case scenario exists when the demand equals its upper bound. We use scenario s ¯ to denote that scenario, i.e., d s ¯ = d ¯ . The corresponding maximum regret can be calculated in Equation 21 as R max ⁡ , 1 q = u s ¯ * − g q . (21)

In order to minimize the maximum regret R max ⁡ , 1 q , we should find the appropriate decision on production quantity q to maximize g q . According to Lemma 4, if T C > q 0 or T C ≤ q 0 and q > 1 + I C θ p − 1 + I c , R max ⁡ , 1 q decreases with q ; Otherwise T C ≤ q 0 and q ≤ 1 + I C θ p − 1 + I c , R max ⁡ , 1 q is minimized when q = T C . The lemma is proved.

Lemma 9

When q > d s , the maximum regret can be calculated in Equation 22 as R max ⁡ , 2 q = u s _ * − p d _ + 1 + I c q   i f   q ≤ T C 1 + I c q − T θ q + C θ   o t h e r w i s e , (22) which increases with q .

Proof. According to Equation 17, when q > d s , u 2 q , s = p d s − 1 + I c q   i f   q ≤ T C p d s − 1 + I c q − T θ q + C θ   o t h e r w i s e . (23)

The subscript “2” of u 2 q , s in Equation 23 is used to distinguish the revenue when q > d s .

The regret of the production decision q under scenario s when q > d s can be calculated in Equation 24 as R 2 q , s = u s * − u q , s . (24)

Because u s * − p d s = − 1 + I c d s   i f   d s ≤ T C p − 1 + I c T C − p d s   i f   T C < d s ≤ 1 + I C θ p − 1 + I c − 1 + I c d s + 1 + I T θ d s − 1 + I C θ   o t h e r w i s e , (25) which is decreasing with d s , the worst-case scenario exists when the demand equals its lower bound. We use scenario s _ to denote that scenario, i.e., d s _ = d _ . According to Equation 25, the maximum regret is R max ⁡ , 2 q = u s _ * − p d _ + 1 + I c q   i f   q ≤ T C 1 + I c q − T θ q + C θ   o t h e r w i s e , (26) which increases with q . According to Equation 26, lemma 9 is proved.

In conclusion, once a production decision is determined under uncertain environment, if the production quantity is less than the actual demand, i.e., q ≤ d s , R max q = R max ⁡ , 1 q . Otherwise, if the production quantity is more than the actual demand, i.e., q > d s , R max q = R max ⁡ , 2 q . Because min-max regret criterion focuses on hedging against the worst-case performance, R max q = max R max ⁡ , 1 q , R max ⁡ , 2 q . Based on the above analysis, we can determine the robust production and green investment decisions of GCF with minimal maximum regret under uncertain environment as follows:

Theorem 2

The robust production and green investment decisions of GCF with minimal maximum regret under uncertain environment can be calculated in Equations 27, 28 as q r = T C   i f   T C ≤ q 0   a n d   T C < d ¯ + 1 p u s ¯ * − u s ¯ * ≤ 1 + I C θ p − 1 + I c d ¯ + 1 p u s ¯ * − u s ¯ *   o t h e r w i s e , (27) K r = 0   i f   q r ≤ T C C θ − T θ q r   o t h e r w i s e , (28)

Proof. According to Lemma 8, 9, when T C > q 0 , R max ⁡ , 1 q , K and R max ⁡ , 2 q , K are decreasing and increasing function of q respectively as shown in Figure 4. Hence, R max q , K is minimized when R max ⁡ , 1 q , K = R max ⁡ , 2 q , K , i.e., q = d _ + 1 p u s ¯ * − u s _ * .

Similarly, when T C ≤ q 0 and q > 1 + I C θ p − 1 + I c , R max ⁡ , 1 q , K and R max ⁡ , 2 q , K are also decreasing and increasing function of q respectively as shown in Figure 5. Hence, R max q , K is minimized when q = d _ + 1 p u s ¯ * − u s _ * .

Otherwise, when T C ≤ q 0 and q ≤ 1 + I C θ p − 1 + I c , we derive the minimal maximum regret through a further discussion on the relationship between T C and d _ + 1 p u s ¯ * − u s _ * .

As shown in Figure 6A, if d _ + 1 p u s ¯ * − u s _ * > T C , which implies R max ⁡ , 1 T C > R max ⁡ , 2 T C , and thus R max T C = R max ⁡ , 1 T C . Because R max ⁡ , 1 q takes its minimum value at q = T C , R max q ≥ R max ⁡ , 1 q ≥ R max ⁡ , 1 T C holds for any feasible production quantity q . Hence, R max q is minimized when q = T C .

Otherwise d _ + 1 p u s ¯ * − u s _ * ≤ T C . As shown in Figure 6B, because R max ⁡ , 1 q decreases with q when q ≤ d _ + 1 p u s ¯ * − u s _ * , R max q ≥ R max ⁡ , 1 q > R max ⁡ , 1 d _ + 1 p u s ¯ * − u s _ * holds for any q ≤ d _ + 1 p u s ¯ * − u s _ * . Similarly, because R max ⁡ , 2 q increases with q when q > d _ + 1 p u s ¯ * − u s _ * , R max q ≥ R max ⁡ , 2 q > R max ⁡ , 1 d _ + 1 p u s ¯ * − u s _ * holds for any q > d _ + 1 p u s ¯ * − u s _ * . Hence, R max q is minimized when q = d _ + 1 p u s ¯ * − u s _ * . The theorem is proved.

According to Theorem 2, when q r ≤ T C , the manufacturer is relieved of the concern of potential default when opting for GCF, even in the absence of any green investment. Hence, we define T C as the safe yield. Besides, given that f T C = f 1 + I C θ p − 1 + I c , we define 1 + I C θ p − 1 + I c as the dual safe yield. Consistent with the formal definition of the safe yield, when q r ≤ T C , it can be inferred that GCF is essentially a distinct subset of conventional credit instruments, characterized by their notably reduced interest rates. In this case, GCF is not sufficient to incentivize manufacturers to engage in green investments. In other words, GCF can promote the green transformation of the manufacturing industry only when q r > T C .

In order for GCF to play a positive role in the green transformation of the manufacturing industry, we discuss the robust production and green investment decisions of GCF from the following six cases.

Case 1

The safe yield does not exceed the dual safe yield., i.e. T C ≤ 1 + I C θ p − 1 + I c .

Case 1.1

d _ ≤ d ¯ ≤ T C .

Because q r ≤ d ¯ ≤ T C , GCF cannot promote manufacturers to engage in green investments.

Case 1.2

d _ ≤ T C < d ¯ ≤ 1 + I C θ p − 1 + I c .

According to Lemma 5, u s ¯ * = p − 1 + I c T C , (29) u s _ * = p − 1 + I c d , _ (30)

According to Equations 29, 30, d _ + 1 p u s ¯ * − u s _ * = p − 1 + I c p T C + 1 + I c p d _ = T C + 1 + I c p d _ − T C ≤ T C .

According to Theorem 2, q r = d _ + 1 p u s ¯ * − u s _ * ≤ T C . Consequently, GCF cannot promote manufacturers to engage in green investments.

Case 1.3

d _ ≤ T C < 1 + I C θ p − 1 + I c < d ¯ .

According to Lemma 5, u s ¯ * = f d ¯ − 1 + I C θ , (31) u s _ * = p − 1 + I c d _ , (32)

According to Equations 31, 32, d _ + 1 p u s ¯ * − u s _ * = d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C .

According to Theorem 2, only when d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C >   1 + I C θ p − 1 + I c , GCF can effectively incentivize manufacturers to engage in green investments, and the robust production and green investment decisions are q r = d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C and K r = C θ − T θ q r respectively.

Case 1.4

T C < d _ < d ¯ .

Because q r ≥ d _ > T C , GCF can effectively incentivize manufacturers to engage in green investments.

Case 2

The safe yield is larger than the dual safe yield., i.e. T C > 1 + I C θ p − 1 + I c .

Case 2.1

d _ ≤ d ¯ ≤ T C .

Because q r ≤ d ¯ ≤ T C , GCF cannot promote manufacturers to engage in green investments.

Case 2.2

d _ ≤ T C < d ¯ .

According to Lemma 6, u s ¯ * = f d ¯ − 1 + I C θ (33) u s _ * = p − 1 + I c d _ (34)

Hence, d _ + 1 p u s ¯ * − u s _ * = d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C .

According to Theorem 2, only when d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C > T C , GCF can effectively incentivize manufacturers to engage in green investments, and the robust production and green investment decisions are q r = d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C and K r = C θ − T θ q r respectively.

Case 2.3

d ¯ ≥ d _ > T C

Because q r ≥ d _ > T C , GCF can effectively incentivize manufacturers to engage in green investments.

Table 1 summarizes the results of the above six cases. According to Table 1, when d _ > T C , the GCF can effectively incentivize manufacturers to engage in green investments. When d ¯ ≤ T C , GCF cannot promote manufacturers to engage in green investments. When d _ ≤ T C < d ¯ , in order for GCF to play a positive role in the green transformation of the manufacturing industry, it is essential that the demand must simultaneously satisfy the conditions where min d ¯ , d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C > ⁡ max T C , 1 + I C θ p − 1 + I c (35)

Observing the expressions on the right-hand side of the greater-than symbol in Equation 35, T C is naturally greater than 1 + I C θ p − 1 + I c when parameters T , p , θ exhibit a substantial numerical magnitude relative to parameters I , C , c . This case implies lenient carbon emissions constraints in GCF, advanced emissions reduction technologies, high-priced products, low-interest rate of GCF, low initial carbon emissions, and cost-efficient production processes. Hence, we define the case when T C > 1 + I C θ p − 1 + I c as the favorable environment. On the contrary, the case when T C ≤ 1 + I C θ p − 1 + I c is defined as the unfavorable environment. We call the parameters T , p , θ and I , C , c as the promotion and inhibition parameters respectively. The greater the promotion (resp. inhibition) parameters are, the more favorable (resp. unfavorable) the environment is.

A detailed analysis of the promotion of green production and green technology investment in manufacturing companies by GCF under favorable and unfavorable environmental conditions is conducted as follows.

When considering the carbon emission cap T in accordance with Equation 35, it is worth noting that GCF plays a crucial role in promoting green transformation when min d ¯ , d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C > 1 + I C θ p − 1 + I c in an unfavorable environment. Because min d ¯ , d ¯ + 1 + I c p d _ − d ¯ + 1 + I p θ T d ¯ − C increases with T, it can be concluded that a relatively lenient carbon emission cap is more likely to make Equation 35 holds. Therefore, a lenient carbon emission cap of GCF is more conducive to encouraging manufacturing enterprises to invest in green technologies in the unfavorable environment.