## 4 Materials and Methods
### The I-O Modeling Approach  
The model used is a multi-regional quantity and price input-output model. The quantity model delivers the economy-wide impacts of an exogenous change in the demand for products and in income levels of households. It can, therefore, be characterized as a demand-pull input-output model [45]. In this model, any change in product demand and income levels is assumed to be the starting point for a cascade of higher-order indirect impacts on industries and households through interindustry linkages and the circular flow of (labor) income and expenditure. Apart from the energy surcharge on industries, all other direct impacts described above are directly fed into the quantity model, in order to estimate total impacts on industries and households. Such direct impacts are exogenous inputs for the I-O modeling, and are estimated either through the use of an enterprise survey or other official statistics (see. Section 4.4). \[\mathbf{\Gamma}=\left(\mathbf{I}-\mathbf{D}\mathbf{B}\right)^{-1} \tag{1}\]  
Figure 2: Block diagram of the impact channels resulting from operation of RET within the modeling framework. In Equation (1) the Leontief inverse, \(\mathbf{\Gamma}\), consists of two components. The matrix product, \(\mathbf{DB}\), represents interregional interindustry relationships. The intermediate demand coefficients, \(\mathbf{B}\), are used to determine the change in intermediate input requirements of regional industries due to an exogenous change in the demand for their products, while industry market shares, \(\mathbf{D}\), translate these product-requirements into demand directed to industries. Here, \(b_{ji}^{rs}\in\mathbf{B}\) denotes intermediate demand for product \(j\) from region r per unit of output of industry \(i\) from region s and \(d_{ij}^{r}\in\mathbf{D}\) denotes the market share of industry \(i\) in the total supply of product \(j\) by region \(r\). \[\Delta\mathbf{va}=\omega\mathbf{\Gamma}\mathbf{D}[\Delta\mathbf{u};\Delta\mathbf{f}] \tag{2}\]  
\[\Delta\mathbf{va}=\omega\mathbf{\Gamma}\mathbf{D}\mathbf{C}[\Delta\mathbf{r};\Delta\mathbf{w};\Delta \mathbf{v}] \tag{3}\]  
Equation (2) gives the indirect impact on value added due to the direct impact on intermediate demand from the renewable and conventional energy sectors. \(\Delta\mathbf{u}\) is the exogenous direct impact on intermediate demand resulting both from the promoted operation of RET (positive effect), as well the crowded-out operation of conventional energy facilities (negative effect). Similarly, \(\Delta\mathbf{f}\) is direct impact on intermediate demand resulting both from the promoted production of RET and the crowded-out investments in new conventional power plant capacity. Since the extended Leontief inverse delivers total impacts on gross output of industries rather than on value added, \(\mathbf{va}\), it is pre-multiplied by exogenous value added per unit of output coefficients \(\mathbf{\omega}\). Equation (3) gives the induced impact on value added, resulting from an exogenous change in the income of households, here the Leontief inverse is post-multiplied by \(\mathbf{D}\mathbf{C}\), where \(\mathbf{C}\) delivers the corresponding private consumption expenditures, which are directed to industries. \(\Delta\mathbf{r}\) contains the additional income from the revenues of feed-in tariffs going to private households (direct impact), as well as the sub-vector \(\Delta\mathbf{r}_{\mathbf{sur}}\) which indicates the negative total impact resulting from higher living cost due to the energy surcharge. This includes both, the direct increase of the cost of living due to the increase of household's electricity prices, as well as the indirect losses due to increased electricity prices faced by companies passed on to households, which result from the price model (see below). Figure 3: Block diagram of the impact channels resulting from production of RET within the modeling framework.