## Technology Tree and Nested Production Functions (15 minute read)

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##### Learning Outcome:
After completing this lesson, you will know how "nested" production functions break the overall assembly of a final product into smaller production processes, and why nesting is useful in CGE models.

##### The Structure of a Technology Tree

The production technology in many CGE models is described as a “tree” (Fgure 1).  This means that the production process is broken down into smaller sub-processes.  Each sub-process is a “branch” of the tree. These smaller production processes are “nested” within the overall production process. Nests are combined in the final stage of producing a good, which is the tree trunk.

Figure 1.  Technology tree

It is perhaps more apt to think of the production process as an upside-down tree (Figure 2).  On the bottom left is the "value added" nest. Within this nest, the producer picks the optimal mix of labor, capital and any other factors of production, after taking into account the prices of each factor, the output price, and the planned quantity of output. For example, if wages are relatively high compared to the cost of equipment, the producer is likely to choose a less labor-intensive mix in her value added bundle.

At the bottom right of the tree is the intermediate input nest.  Within this nest, the producer decides on the optimal mix of intermediate inputs, given input and output prices, and the output level. At the top, the two bundles are combined into the final product.

Figure 2.  Upside-down Technology tree

##### Why Use Nested Production Functions?

Nesting allows a modeler to describe a production process with greater realism because it allows producers to have different substitution possibilities within each nest. Substitution possibilities are described by an elasticity of substitution (Figure 3).  For example, it might be very easy to replace workers with machine automation if wages rise relative to capital equipment rents. The modeler can represent this flexibility with a high value of the elasticity of factor substitution within the value-added nest.  In the UNI-CGE model, factor substitution is described by a CES production function, with a substitution elasticity named ESUBVA. That name stands for the Elasticity of factor SUBstitution in the Value-Added nest.

It is typically more difficult for the producer to substitute among intermediate inputs than to substitute among factors.  For example, it is difficult to create cars that have more than one, or less than one, steering wheel. The producer must have one steering wheel per car, and cannot substitute more tires for one less steering wheel. In this example, the intermediate input substitution has a value of zero.  In the UNI-CGE model, this intermediate input decision is described as a Leontief production function.  Leontief functions have an implied elasticity of substitution value of zero.

In some models, producers are described as having some flexibility to substitute between their bundle of factor inputs and their bundle of intermediate inputs at the top level of the nesting structure. But in many CGE models, including the UNI-CGE model, this final assembly is described by a Leontief production function, in which no substitution between the bundles is possible. The implicit substitution elasticity at the top level is zero. The producer must have some fixed quantity bundle of factors (allowing the ratio of factors within the bundle to vary) and a fixed quantity bundle of intermediates (input ratios within the intermediate bundle do not vary).

Figure 3.  Technology tree in UNI-CGE model

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Image " Winter Trees" by Melasina Parker

Last modified: Wednesday, 24 April 2024, 6:49 PM