Climate effects on the diversification strategy of export firms: Evidence from China

Consumer side Assuming a representative consumer in a country with a utility function characterized by a constant elasticity of substitution (σ>1), the function is expressed as: U ¼ Z o2O ½qðoÞ� s 1 s doÞ ( ) s s 1 ð1Þ Here, ω represent a specific product category, O is the set of all product categories exported, and q(ω) denotes the quantity of product ω exported. The demand function is derived by maximizing consumer utility, as shown in the subse- quent equation. qðoÞ ¼ p s o Ps 1Y ð2Þ Where, pω is the export price of product ω, P is the price index, P ¼ ð Z o2O p1 s o doÞ 1 1 s , and Y is the national income. Production side Assuming a Cobb-Douglas production function, firms produce product ω using both labor (l) and capital (k). The production function is expressed as follows: qoðTÞ ¼ φoðTÞlakb ð3Þ Where, φω is productivity, T is temperature, a and b are the proportions of labor and capital inputs, satisfying a+b = 1. Productivity is modelled following Chatterjee et al. (2013) [16] as: φoðTÞ ¼ φðTÞZ ðn 1Þ φ ; Zφ > 1 ð4Þ Where, ηφ>1 represents product gradient. The parameter n indicates the ranking of the dis- tance of product ω from the firm’s core competitive product (i.e. the number of product cate- gories). if n = 1, representing the core product, φω decreases as n increases, indicating a greater distance from the firm’s core product. For the firm’s productivity, existing research shows an inverted U-shaped relationship with temperature, revealing an optimal temperature T* at

which productivity peaks [24,27]. Specifically, for T<T*. φ0(T)>0, and for T>T*, φ0(T)<0. Optimal export decision Assuming a fixed export cost fe for product ω, the profit function for the exported product is expressed as: Po ¼ ðpo MCÞ � qo fe ð5Þ Where MC is the marginal cost of producing product ω. The marginal cost is derived from cost minimization: MC ¼ apk b � �b þ b apk � �b � pk " # � 1 φo ð6Þ Where labor wages are normalized to 1, pk denotes the price of capital. Applying the profit maximization condition and combining Formulas (2) and (5), we derive the following PLOS ONE Climate effects on the diversification strategy of export firms PLOS ONE | https://doi.org/10.1371/journal.pone.0308391 August 16, 2024 4 / 28