*3.1. Input-Output Analysis*

This study analyzes domestic mineral production in Japan utilizing the Japanese Input-Output (I-O) Tables from 2011, the latest version available at the time of writing, in which copper is differentiated from other minerals [24]. The I-O table is a statistical table showing inter-industry transactions of goods and services conducted in the domestic economy for a certain period (usually one year) in matrix form. This table has been prepared for the purpose of understanding the economic structure of a single region (country, prefecture or city level, although international I-O tables also exist). It is also possible to analyze economic ripple (multiplier) effects by using this table. Economic ripple effect can be defined as new economic production which is triggered to meet new demand. Currently, there are no industries dedicated specifically to deep ocean mining, secondary copper smelting/refining and end-of-life product collection in Japan. Deep ocean resource exploration requires mining and concentration processes which do not currently exist in Japan. Within the I-O table, the recycling sector is reflected, however this is not specific to copper recycling. Should domestic mineral production become mainstream, such sectors would likely emerge in the I-O table. However, it is impossible to investigate these sectors when employing the I-O table in its current form, and for this reason the Japanese 2011 I-O table has been extended in order to add these emerging sectors.

Although I-O analysis is widely used, we will present a brief description of the methods here. Figure 3 shows a conceptualized I-O table. Each row of the I-O table indicates the output of inter-industry transactions, while the columns of the I-O table show the inputs to each industry on a monetary basis. Intermediate demand sectors, which are sectors producing each good or service, perform production activities through the purchase of raw materials, services or energy and applying capital and labor. The final demand sector, which covers consumption, exports and imports, is mainly a buyer of consumer and capital goods as finished products. The intermediate input sector is a supplier of goods and services as intermediate goods. Each supply industry supplies goods and services to demand industries. The gross value added sector consists of a factor cost for production (such as capital and labor). Essentially, the subtotal of final demand and the subtotal of gross added value are balanced. The I-O table is balanced by Equations (1) and (2).

$$\left[\mathbf{x} + \mathbf{F} + \mathbf{E}\mathbf{x} - \mathbf{I}\mathbf{m} = \mathbf{Y}\right] \tag{1}$$

$$\left[\mathbf{x} + \mathbf{V} = \mathbf{Y}\right] \tag{2}$$

*x*: Intermediate input, *F*: Domestic final demand, *Ex*: Export, *Im*: Import, *Y*: Domestic production, *V*: Value added.


**Figure 3.** General conceptualized input-output table.

The input coe fficient matrix, which is explained by Equation (3) and also known as the technology coe fficient matrix, represents the raw material inputs required to produce 1 unit of the desired product. By utilizing the inverse matrix of the input coe fficient matrix, the economic ripple e ffect can be estimated using Equation (4). The inverse matrix in Equation (4), (*I* − *<sup>A</sup>*)−1, is known as the Leontief inverse matrix.

$$a\_{i\bar{j}} = \mathbf{x}\_{i\bar{j}} / \mathbf{Y}\_{\bar{j}} \tag{3}$$

$$\text{Economic ripple effect} = \left(I - A\right)^{-1} \Delta \tag{4}$$

*ai*,*j*: input coe fficient, *xi*,*j*: intermediate input in sector *ij*, *Yj*: Domestic production in sector *j*, *A*: Input coe fficient matrix, *I*: Identity matrix.

As noted above, since the Japanese I-O table combines various mineral ore industries into one sector, copper ore should be separated from this sector to consider domestic mineral production. Also, the recycling sector does not clearly delineate copper flows. Thus, this study modifies the conventional I-O table to suit to domestic mineral production by using the procedures detailed below.
