Carbon policies, fossil fuel price, and the impact on employment

Abstract

Carbon policies can be expected to increase the price of fossil fuel, either directly through a cap-and-trade system or carbon tax, or indirectly by regulations that place an implicit tax on fossil fuel. We construct a theoretical model to decompose the effect on employment in a specific industry caused by an increase in the price of fossil fuel. We find that the total effect is determined by the market’s responsiveness to the changes of the prices of fossil fuel and final product. We verify the theoretical model by an empirical analysis of China’s thermal power industry. Because China is the largest carbon emitter in the world and thermal power industry is the biggest carbon emitter industry in China, the empirical model has strong reference value for other countries and industries. Policy makers should be prepared to mitigate any adverse effects on employment that a carbon policy might cause.

Graphic abstract

Appendix

Derivative of Eq. (3)

We get MP_Zand MP_L by partially differentiating Eq. (1), and substitute them into Eq. (2): $\frac{{A\alpha Z^{\alpha - 1} L^{\beta } K^{\gamma } }}{p} = \frac{{A\beta Z^{\alpha } L^{\beta - 1} K^{\gamma } }}{w}$. After simplifying, we get Eq. (3).

Derivative of Eq. (4)

Totally differentiating Eq. (3), we get $\frac{\partial L}{\partial p} = \frac{\beta Z}{\alpha w} + \frac{\beta p}{\alpha w} \cdot \frac{\partial Z}{\partial p} = \frac{\beta Z}{\alpha w}\left( {1 + \frac{p}{Z} \cdot \frac{\partial Z}{\partial p}} \right)$. Using $\varepsilon_{{\mathrm{Zp}}}$ to represent $\frac{p}{Z} \cdot \frac{\partial Z}{\partial p}$, we get Eq. (4).

Derivative of Eq. (8)

We get MP_Zand MP_K by partially differentiating Eq. (1), and substitute them into Eq. (2): $\frac{{A\alpha Z^{\alpha - 1} L^{\beta } K^{\gamma } }}{p} = \frac{{A\gamma Z^{\alpha } L^{\beta } K^{\gamma - 1} }}{g}$. After simplifying, we get Eq. (8).

Derivative of Eq. (10)

Differentiating (9) with respect to p, we get

$$\frac{\partial C}{\partial p} = \left( {\frac{\beta Z}{\alpha } + \frac{\beta p}{\alpha } \cdot \frac{\partial Z}{\partial p}} \right) + \left( {Z + p \cdot \frac{\partial Z}{\partial p}} \right) + \left( {\frac{\gamma Z}{\alpha } + \frac{\gamma p}{\alpha } \cdot \frac{\partial Z}{\partial p}} \right) = \left( {\frac{\beta Z}{\alpha } + Z + \frac{\gamma Z}{\alpha }} \right) + \left( {\frac{\beta p}{\alpha } \cdot \frac{\partial Z}{\partial p} + p\frac{\partial Z}{\partial p} + \frac{\gamma p}{\alpha } \cdot \frac{\partial Z}{\partial p}} \right) = \frac{\beta + \alpha + \gamma }{\alpha }Z + \frac{\beta + \alpha + \gamma }{\alpha }p\frac{\partial Z}{\partial p} = \frac{\beta + \alpha + \gamma }{\alpha }Z\left( {1 + \frac{p}{Z} \cdot \frac{\partial Z}{\partial p}} \right) = \frac{\alpha + \beta + \gamma }{\alpha }Z(1 + \varepsilon_{{\mathrm{Zp}}} ).$$

Derivative of Eq. (12)

Substituting Eqs. (10) and (11) into (7), we get

$$\frac{\partial L}{\partial p} = \frac{\beta Z}{\alpha w}(1 + \varepsilon_{{\mathrm{Zp}}} ) + \frac{\alpha + \beta + \gamma }{\alpha }Z(1 + \varepsilon_{{\mathrm{Zp}}} )\varepsilon_{{\mathrm{d}}} \frac{\beta }{{w\left( {\alpha + \beta + \gamma } \right)}} = \frac{\beta Z}{\alpha w}(1 + \varepsilon_{{\mathrm{Zp}}} ) + \frac{\beta Z}{\alpha w}(1 + \varepsilon_{{\mathrm{Zp}}} )\varepsilon_{{\mathrm{d}}} = \frac{\beta Z}{\alpha w}(1 + \varepsilon_{{\mathrm{Zp}}} )(1 + \varepsilon_{{\mathrm{d}}} ).$$