## The Make Matrix: Diagonal and Non-diagonal (15 minute read)

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##### Learning Outcome:

At the end of this lesson, you will be able to identify the make matrix in the SAM, and explain the concepts of diagonal and non-diagonal make matrices.

Activities Sell Their Entire Output to Commodity Accounts

The activity rows of the SAM report the income received by each activity from the sale of its output. Each activity sells its output in its entirety to commodity column accounts.

Table 1 shows a section of the US333 SAM that describes the sale of output from the three activities, AGR, MFG and SER, to matching column accounts. For example, the gross output from the AGR activity, worth \$326 billion, is sold entirely to the AGR commodity account. The AGR commodity column account will then combine this domestic supply of AGR with imported AGR to create the composite commodity, AGR, that is sold to consumers (not shown in this snippet of the SAM). We studied the assembly of a composite commodity in depth in the lesson on Activities v. Commodities in the Data module.

Table 1. Make matrix - sales of activity output to commodity accounts

Large type version of table is available HERE.

##### The Make Matrix

The matrix formed by the intersecting cells in the activity rows/commodity columns (in the red box) is called the make matrix. It describes how commodity accounts use domestically-produced products to "make" commodities. Notice that the data in the US333 make matrix form a diagonal, with zeros (or no values) in the other cells. A diagonal make matrix is typical in standard CGE models, in which there is a one-to-one relationship between activities and commodities.  For example, the AGR activity only makes AGR products, sold entirely to the AGR commodity account.

##### Non-diagonal Make Matrix

SAMS and CGE models can have non-diagonal make matrices. This might happen when an activity makes more than one product. For example, the AGR activity could make two products - AGR and ENERGY. In this case, there can be more commodity than activity accounts (Table 2).

Table 2.  A non-diagonal make matrix with more commodities than activities

Large type version of table is available HERE.

Non-diagonal matrices also occur when more than one activity makes the same product.  For example, there could be two types of manufacturing - light and heavy - that both produce the same product, "MFG." In this case, there are more activity than commodity accounts (Table 3).

Table 3.  A non-diagonal make matrix with more activities than commodities

Large type version of table is available HERE.