# **Annex A: Summary description of the Envisage model and the model dimensions**

The description of the Envisage Model follows the circular flow of an economy paradigm. Firms purchase input factors (for example labor and capital) to produce goods and services. Households receive factor income and in turn demand goods and services produced by firms. And, equality of supply and demand determine equilibrium prices for factors, goods and services. The model is solved as a sequence of comparative static equilibria where the factors of production are exogenous for each time period and linked between time periods with accumulation expressions.

Production is implemented as a series of nested constant-elasticity-of-substitution (CES) functions the aim of which is to capture the substitutability across all inputs. Three production archetypes are implemented. The first is for crops that reflects intensification of inputs versus land extensification. The second is for livestock that reflects range-fed versus ranch-fed production. The final, also referred to as the default, revolves largely around capital/labor substitutability. Some production activities highlight specific inputs (for example agricultural chemicals in crops and feed in livestock) and all activities include energy and its components as part of the cost minimization paradigm. Production is also identified by vintage—divided into _Old_ and _New_ — with typically lower substitution possibilities associated with _Old_ capital.

Each production activity is allowed to produce more than one commodity—for example the ethanol sector can produce ethanol and distiller’s dried grains with solubles (DDGS). And commodities can be formed by the output of one or more activities (for example electricity). ENVISAGE therefore uses a different classification of activities and commodities.<sup>18</sup> One of the features of the model is that it integrates the new GTAP power data base that disaggregates GTAP’s electricity sector (‘ely’) into 11 different power sources plus electricity transmission and distribution. Though the database has both the supply and demand side for all 11 power sources, the aggregation facility permits the aggregation of electricity demand into a single commodity and the ‘make’ matrix specification combines the output from the different power activities into a single electricity commodity.

Income accrues from payments to factors of production and is allocated to households (after taxes). The government sector accrues all net tax payments and purchases goods and services. The model incorporates multiple utility functions for determining household demand. There is a set of three household demand functions linked to the ubiquitous linear expenditure system (LES): the standard LES, the extended LES (ELES) that incorporates household saving into the utility function, and ‘an implicitly directly additive demand system’ (AIDADS), that allows for nonlinear Engel curves in the LES framework.<sup>19</sup> The fourth option uses the constant differences in elasticity (CDE) utility function that is used in the core GTAP model (Hertel 1997 and Corong et al. 2017). The ELES incorporates the decision to save in a top-level utility function. The other demand systems assume savings is an exogenous proportion of disposable income in the default closure. The consumer utility function determines consumer demand bundles that are subsequently

> 18 Production activities are indexed with _a_ and commodities are indexed with _i_ . 19  Users can also specify implementing a Cobb-Douglas (CD) utility function, which can be considered part of the LES framework.

- 59 -