Solar Module Price Determinants

Abstract

The decrease in solar module prices is one of the main factors behind the recent expansion of the global solar energy market. The mechanism underlying this price reduction has been the subject of numerous empirical research. However, the technological aspect of manufacturing has been the main focus of studies on the mechanism for solar module price reduction over the years. This chapter examines how economic and monetary factors, such as interest rates and exchange rates, affect solar module pricing in addition to other factors that have been examined in earlier studies, such as technology and wage rates. The economic factors that influence solar module prices are identified in this chapter. To determine the influence of each factor, the chapter develops a pricing model for solar modules in the top five solar module-producing countries, backed by a theoretical oligopolistic model. For every country, the determinants of solar module prices are different. While exchange rates, knowledge stocks, and oil prices often correlate negatively with solar module prices, interest rates generally have a positive correlation with them. Since the renewable industries are high-tech, capital costs significantly impact technology costs. The governments’ initiatives to offer low-interest financing to enterprises will hasten the commercialization of renewable energy. To expedite the growth of solar energy projects, there have been numerous attempts to lower interest rates for renewable energy technology; however, it is not enough, and specific green financing channels are required. Second, the governments must expand research and development (R&D) expenses relevant to renewable energy. Increasing targeted R&D expenditure through government policies will be an effective strategy for reducing costs and increasing the willingness of the private sector to invest in the solar energy projects.

Appendix

Solar Module Pricing Model

Using the following procedures, Taghizadeh-Hesary et al. (2019) developed a pricing model for solar modules. We assume that the Cobb-Douglas production function with five production inputs applies to the countries that produce solar modules, where (y_t) represents the total production of solar modules, (A_t) is the productivity parameter, (N_t) is labor input, (K_t) is capital stock, and (IM_t) is imports. The output elasticities of labor input, capital stock, and imports are (α), (β), and (γ):

$$ {y}_t={A}_t{N}_t^{\alpha }{K}_t^{\beta }{IM}_t^{\gamma }=f\left(A,N,K, IM\right) $$

(1)

In Eq. 2, the assumed inverse demand curve is depicted, along with the solar module price (p_{solar, t}) I, the intercept ($\overline{B}$), the coefficients (d₁) and (d₂), the price of oil in US dollars (p_{oil, t}), and the exchange rate (e_t). As an alternative for oil resources, renewable energy technology is considered in this situation together with the import price of oil. As a result, if the price of importing oil increases, so will the demand for solar modules and the prices of solar modules with increase accordingly.

$$ {p}_{\textrm{solar},t}=\overline{B}-{d}_1{y}_t+{d}_2{p}_{\textrm{oil},t}{e}_t $$

(2)

In Eq. 3, the solar module cost function is demonstrated. (C_t) is the cost of solar module production, (w_t) is the labor cost, (r_t) is the interest rate, and (e_t) is the exchange rate. In this equation, the cost is the sum of labor cost, capital cost, and import cost.

$$ {C}_t={w}_t{N}_t+{i}_t{K}_t+{e}_t{IM}_t $$

(3)

We assume that there is an oligopoly market in the solar energy industry. In order to maximize profit, the Lagrange multiplier minimizes the cost. With the production function acting as the constraint equation in Eq. 5, the profit equation for a producer of solar modules is shown in Eq. 4.

$$ \operatorname{Min}{C}_t={w}_t{N}_t+{r}_t{K}_t+{e}_t{IM}_t $$

(4)

$$ \textrm{subject}\ \textrm{to}\ y={A}_t{N}_t^{\alpha }{K}_t^{\beta }{IM}_t^{\gamma }=f\left(A,N,K, IM\right) $$

(5)

Eq. 6 provides the definition of the Lagrange function. The first order conditions for the cost minimization problem are Eqs. 7, 8, 9, and 10.

$$ {L}_t={w}_t{N}_t+{r}_t{K}_t+{e}_t{IM}_t+\lambda \left(y-f\left(A,N,K, IM\right)\right) $$

(6)

$$ \frac{\partial L}{\partial N}=w-\lambda \frac{\partial f}{\partial N}=0 $$

(7)

$$ \frac{\partial L}{\partial K}=r-\lambda \frac{\partial f}{\partial K}=0 $$

(8)

$$ \frac{\partial L}{\partial IM}=e-\lambda \frac{\partial f}{\partial IM}=0 $$

(9)

$$ \frac{\partial L}{\partial \lambda }=y-f\left(A,N,K, IM\right)=0 $$

(10)

Eqs. 11, 12, and 13 are obtained by utilizing Eq. 1 to differentiate f with respect to N, K, and IM.

$$ \frac{\partial f}{\partial N}=\alpha \frac{y}{N} $$

(11)

$$ \frac{\partial f}{\partial K}=\beta \frac{y}{K} $$

(12)

$$ \frac{\partial f}{\partial IM}=\gamma \frac{y}{IM} $$

(13)

Using Eqs. 7, 8, 9, 10, 11, 12, and 13, N, K, and IM can be expressed as below in equations Eqs. 14, 15, and 16.

$$ \frac{\partial L}{\partial N}=w-\alpha \lambda \frac{y}{N}=0 $$

$$ \leftrightarrow \textrm{N}=\upalpha \lambda \frac{y}{w} $$

(14)

$$ \frac{\partial L}{\partial K}=r-\beta \lambda \frac{y}{K}=0 $$

$$ \leftrightarrow \textrm{K}=\upbeta \lambda \frac{y}{r} $$

(15)

$$ \frac{\partial L}{\partial IM}=e-\lambda \frac{y}{IM}=0 $$

$$ \leftrightarrow \textrm{IM}=\upgamma \lambda \frac{y}{e} $$

(16)

Using Eqs. 14, 15, and 16, cost function (Eq. 3) and marginal cost can be written as below.

$$ \textrm{C}=w\left(\upalpha \lambda \frac{y}{w}\right)+r\left(\upbeta \lambda \frac{y}{r}\right)+e\left(\upgamma \lambda \frac{y}{e}\right)=\textrm{C}\ \left(w,r,e,y\right) $$

(17)

$$ \textrm{Marginal}\ \textrm{Cost}:\frac{\partial C}{\partial y}=\lambda\ \left(w,r,e,y\right) $$

(18)

Equation 19 may be used to represent the profit of a company that produces solar modules. It is possible to identify the ideal output at which profit is maximized by computing a partial derivative of profit with respect to solar module production (y_t). According to Eq. 20, profit is maximized in an oligopolistic market when marginal revenue and marginal cost are equal. The ideal production of solar modules (y_t) is therefore given by Eq. 21, using Eqs. 16 and 18.

$$ \pi ={p}_{\textrm{solar}}y-C\left(w,r,e,y\right) $$

$$ =\left(\overline{B}-{d}_1y+{d}_2{p}_{\textrm{oil}}e\right)\ast y-C\left(w,r,e,y\right) $$

(19)

$$ \frac{\partial \pi }{\partial y}=\left(\textrm{Marginal}\ \textrm{Revenue}\right)-\left(\textrm{Marginal}\ \textrm{Cost}\right)=0 $$

(20)

$$ \overline{B}-2{d}_1y+{d}_2{p}_{\textrm{oil}}e-\lambda =0 $$

$$ \leftrightarrow \textrm{y}=\frac{1}{2{d}_1}\left(\overline{B}+{d}_2{p}_{\textrm{oil}}e-\lambda \right) $$

(21)

Using Eqs. 2 and 21 can be rewritten as below.

$$ {p}_{\textrm{solar}}=\overline{B}-\frac{1}{2}\left(\overline{B}+{d}_2{p}_{\textrm{oil}}e-\lambda \right)=\frac{1}{2}\ \left(\overline{B}-{d}_2{p}_{\textrm{oil}}e+\lambda \right) $$

(22)

As presented in Eq. 18, λ is a function of wage (w_t), interest rate (r_t), exchange rate (e_t), and production of solar modules (y_t). Hence, using Eq. 22, we can comprehend that price of solar modules (p_{solar, t}) is a function of wage (w_t), interest rate (r_t), exchange rate (e_t), and price of oil (p_{oil, t}).

$$ {p}_{\textrm{solar}}=\frac{1}{2}\ \left(\overline{B}-{d}_2{p}_{\textrm{oil}}e+\lambda \left(w,r,e,y\right)\right)=g\ \left(w,r,e,y,{p}_{\textrm{oil}}\right) $$

Derived from the results, the pricing model for solar modules can be written as below:

$$ \log \left({p}_{\textrm{solar},t}\right)={p}_0+{p}_1\left({r}_t\right)+{p}_2\log \left({p}_{\textrm{oil},t}\right)+{p}_3\log \left({e}_t\right)+{p}_4\log \left({A}_t\right)+{\varepsilon}_t $$

(23)

This pricing model will be used to conduct an econometric analysis. The coefficients will be computed and factors will be analyzed to determine which have a significant influence on the price of solar photovoltaic modules.

Knowledge Stock

In this research, the productivity parameter A_t is defined as the total expenditure of research and development. Below is the definition of A_t:

$$ {A}_t=\left(1-\delta \right){A}_{t-1}+{RD}_t $$

This is based on a study conducted by Youah (2013) that suggested it is more acceptable to analyze solar module pricing by utilizing accumulated expenditures of R&D. Here, RD_t is a country’s R&D expenditure on photovoltaic technology and δ is the R&D expenditure’s depreciation rate. In this study, it is presumpted that, given the stated depreciation rate δ, the impact of R&D expenditures will diminish with time. We simplify by assuming that knowledge stock depreciation is constant across all countries and terms. There has been little research on the knowledge stock depreciation rate in the solar industries, according to Nemet and Arnulf’s (2012) evaluation of various knowledge depreciation rates in energy technologies. The research conducted by Watanabe, Nagamatsu, and Griffy-Brown is one that should be highlighted (Watanabe et al., 2003). According to their findings, the Japanese solar industry’s mean knowledge stock yearly depreciation rate is around 30%. As a result, the analysis’s basic depreciation rate is set at 30%.