# Incorporating New Technologies in EEIO Models
## 2 Methodology
### Augment/Modify Make and Use Tables
#### 2.1.1 Use Table  
To modify the Use table, one row and \(k\) columns are added. The future uses, in physical units, of the new commodity and the similar commodity follow Equations (1) and (2) for intermediate inputs and Equations (3) and (4) for final demand elements. Here, a percentage of current uses of the similar commodity is substituted by the new commodity for all existing industries on a physical unit basis. Theoretically, this percentage corresponds to the commodity being replaced. For example, if the new commodity is bio-gasoline, the similar commodity being replaced is gasoline. However, since the commodity being represented by the Petroleum Refineries industry in the input-output framework is an aggregated commodity that includes gasoline and more, to substitute a % of the similar commodity may not simply substitute gasoline. This can be addressed by estimating, for example, the share of gasoline in petroleum refineries, %g and use %used = %used = %g instead of %. See an example of this on the case study in Section 3. \[I_{m+1,j}^{1} =I_{s_{1},j}^{0}\cdot\%\,\forall j\in\{1,\ldots,n\}\] (1) \[I_{s_{1},j}^{1} =I_{s_{1},j}^{0}-I_{m+1,  
Once future uses for the new commodity are calculated, the total production, in physical units, for the new commodity \(NP\) can be calculated as shown in Equation (7).  
\[NP=\sum_{j=1}^{n}I_{m+1,j}^{1}+\sum_{k=1}^{\Gamma}f_{m+1,k}^{c,1} \tag{7}\]  
The methodology considers that there are potentially several different technologies that produce, as a primary and only product, the new commodity. Therefore, the production of \(NP\) must be divided between all producing industries. This is done with parameters \(\%_{i1}\), \(\%_{i2}\), \(\ldots\), \(\%_{iR}\), which are the percentages of \(NP\) being produced by each of the technologies, respectively. The amount produced by each technology follows Equation (8). \[P_{n+i,m+1}^{1}=NP\cdot\%_{ti}\,\forall i=1...k \tag{8}\]  
Here, \(P_{n+i,m+1}^{1}\) is the future amount produced, in physical units, of the new commodity \(m+1\) by each of the new technologies \(i\). Intermediate inputs for the new industries \(U_{i,j}^{1}\)\(i\in\{1,\ldots,m+1\},j\in\{n+1,\)\(n+2,\ldots,n+k\}\) are filled using external information (Process-based LCA, techno-economic analysis or direct information from the developers of the new technologies are good sources of external information). Specifically, \(\Upsilon_{i,j}\) that correspond to the expenditures of each of the commodities \(i\) to produce one physical unit of the new-commodity in each of the new industries \(j\) are required. Then, future use, in monetary terms, follows Equation (9). It is assumed that the new industries do not use the new commodity as input. \[U_{i,j}^{1}= \begin{cases}(P_{j,m+1}^{1}\cdot\Upsilon_{i,j}),&\text{if }i\in\{1, \ldots,m\}.\\ 0,&\text{if }i=m+1.\end{cases}  \tag{9}\]  
Figure 1: Structure and dimensions of the Input–Output tables based on the Make and Use tables from BEA 2012. (**a**) The current tables and (**b**) modified tables. \(V^{0}\) and \(U^{0}\) are the current Make and Use transactions, respectively. \(V^{1}\) and \(U^{1}\) are the future Make and Use transactions, respectively. In blue are new uses of the existing commodities and value added of the new industries. In green are changes in existing industry uses of commodities due to substitution in use/demand of the similar commodity. In yellow are changes in the quantity of the similar commodity produced by the similar industry as well as the quantity of the new commodity produced by new industries, and in grey are assumptions about the production of the new commodity and the new industries. Similarly, the three value-added components \(v^{1}_{i,j}\), \(i\in\{1,\ldots,3\}\), \(j\in\{n+1,\)\(n+2,...,n+k\}\) come from \(\varphi_{i,j}\) that correspond to the value-added component \(i\), per unit of new commodity being produced by the new industry \(j\), calculated using external data.