AGRODEP Technical Note 0024 April 2022 MIRAGRODEP-AEZ 1.0: Documentation Antoine Bouët David Laborde Fousseini Traoré AGRODEP Technical Notes are designed to document state-of-the-art tools and methods. They are circulated in order to help AGRODEP members address technical issues in their use of models and data. The Technical Notes have been reviewed but have not been subject to a formal external peer review via IFPRI’s Publications Review Committee; any opinions expressed are those of the author(s) and do not necessarily reflect the opinions of AGRODEP or of IFPRI. 1 2 Table of Contents List of Tables ......................................................................................................................3 List of Figures .....................................................................................................................4 1. Introduction ................................................................................................................6 2. Model Structure ..........................................................................................................6 2.1 Dimensions and sets .................................................................................................. 6 2.2 Production ................................................................................................................. 7 2.3 Income and savings ................................................................................................. 13 2.3.1 Households ................................................................................................................... 13 2.3.2 Government.................................................................................................................. 13 2.4 Demand ................................................................................................................... 15 2.4.1 Private demand ............................................................................................................ 15 2.4.2 Public demand .............................................................................................................. 16 2.4.3 Demand for investment purposes ................................................................................ 17 2.4.4 Demand by geographic origin ...................................................................................... 17 2.4.5 Demand for transportation services ............................................................................ 20 2.5 Supply and market clearing ..................................................................................... 20 2.5.1 Transportation market ................................................................................................. 20 2.5.2 Commodity market ....................................................................................................... 21 2.5.3 Factors of production market ....................................................................................... 21 2.6 Macroeconomic constraints .................................................................................... 26 2.7 Economic Closures .................................................................................................. 27 3. Running MIRAGRODEP-AEZ...............................................................................28 4. Summary of Model Structure ..................................................................................30 References .........................................................................................................................42 3 List of Tables Table 1 : Equations of MIRAGRODEP-AEZ ................................................................. 30 Table 2 : Variables of MIRAGRODEP ............................................................................ 37 4 List of Figures Figure 1. Nested production function ................................................................................ 8 Figure 2 : Demand by geographic origin .......................................................................... 19 5 Abstract MIRAGRODEP-AEZ is a recursive dynamic multi-region, multi-sector Computable General Equilibrium (CGE) model based on MIRAGRODEP which in turn is based on MIRAGE (Modelling International Relations Under Applied General Equilibrium) with Agro-ecological zones (regions). It constitutes an extension of the MIRAGRODEP model that allows the user to perform analysis at the subnational level using spatial disaggregated data. The model is particularly suitable for agricultural policy analysis that require working at different levels of disaggregation to consider differences in agro-ecological conditions. Résumé MIRAGRODEP-AEZ est un modèle d'équilibre général calculable (EGC) dynamique multirégional et multisectoriel élaboré à partir de MIRAGRODEP qui à son tour est basé sur MIRAGE avec des zones agro-écologiques (régions). Il constitue une extension du modèle MIRAGRODEP qui permet à l'utilisateur d'effectuer une analyse au niveau infranational en utilisant des données spatiales désagrégées. Le modèle est particulièrement adapté pour l'analyse des politiques agricoles qui nécessite de travailler à différents niveaux de désagrégation pour tenir compte des différences de conditions agroécologiques. 6 1. Introduction MIRAGRODEP-AEZ is a Computable General Equilibrium (CGE) model based on MIRAGRODEP which in turn is based on MIRAGE (Modelling International Relations Under Applied General Equilibrium) with Agro-ecological zones (regions). It is an extension of MIRAGRODEP under the PARI project that allows the user to work at the subnational level using suitable spatial disaggregation levels. It is a multi-region, multi-sector model, dynamically recursive1 CGE model. MIRAGE was initially developed at CEPII and devoted to trade policy analysis. As opposed to a single country CGE model. A multi-country CGE model allows a detailed and consistent representation of the Rest of the World. This way, international economic linkages are captured through the international trade of goods and foreign direct investment (FDI). Social Accounting Matrix (SAM) and trade data in MIRAGRODEP is based on GTAP 9 (Narayanan and Walmsley, 2012). The GTAP 9 Data Base is a fully documented, publicly available global data base which contains complete bilateral trade information, transport and protection linkages among 140 regions for all 57 GTAP commodities for three reference years (2004, 2007 and 2011). For MIRAGRODEP-AEZ, the base year is 2011 and outlook period is from 2011 to 2025. For trade policy data, MAcMAP-HS6 is used. The objective of this Technical Note is two-folds. First, it aims to describe the mathematical structure2 of and the economic hypothesis behind the MIRAGRODEP-AEZ model, version 1.0. In this version of MIRAGRODEP-AEZ, the government is presented separately from the households and thus allows for a better understanding of the impact of shocks on the private and the public sectors distinctly. Furthermore, since MIRAGRODEP-AEZ builds upon MIRAGRODEP and MIRAGE and these models have been fully documented, parts of this document are extracts from Decreux and Valin (2007) and Laborde et al. (2013). The document is organized as follows. In Section 2, we present the main pillars of the model structure, with a summary of equations and variables mapped to their counterparts in GAMS code. 2. Model Structure 2.1 Dimensions and sets The MIRAGRODEP-AEZ model distinguishes multiple sectors (or activities, industries) each of them producing one single commodity (or good, product). Sectors and commodities are referred 1 Dynamically recursive models do not include expectation of value of variables in future periods in the model. Plus, value of variable X at the end of period t is the initial value of variable X at the beginning of period t+1. 2 For a comprehensive review of the functional forms commonly used in CGE models, please refer to Femenia (2012). 7 to using indices i or j, both representing the exact same elements. The subset Transport refers to the transportation commodities and sectors. MIRAGRODEP-AEZ is a global dynamic model. Each variable is thus indexed in time (index t) and by region using indices r (origin country), s (destination country), rr and ss, which all correspond to the same elements. A third region index z, represents the subnational division chosen by the user (AEZ). Set f refers to the five (5) factors of production: skilled labor (index SkLab), unskilled labor (UnSkLab), natural resources (NatlRes), capital (Capital) and land (Land). As will be discussed below, it is assumed that unskilled workers are not perfectly mobile across sectors of production. Hence, sectors are grouped according to the area, rural (L1) or urban (L2), both elements being included in set Ltype. 2.2 Production The production in each sector and in each region follows the nested structure depicted in Figure 1 below. At the top level, total output Yj,r,t is a Leontief of total value added, VAj,r,t, and of total intermediate consumption, CNTERj,r,t. In other words, there are no substitution possibilities between the two aggregated inputs, they are used in perfect complementarity, and thus their shares in total production are constant. Mathematically: 𝑌𝑌𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑉𝑉𝑉𝑉 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 (1) 𝑌𝑌𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 (2) with VA rja , Value added scale coefficient CNTER rja , Total intermediate consumption scale coefficient Hence, the producer price of output, PYj,r,t, is a weighted sum of the price of value added, PVAj,r,t, and of that of total intermediate consumption, PCNTERj,r,t. 𝑃𝑃𝑌𝑌𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑌𝑌𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 (3) 8 Figure 1. Nested production function3 At the second level, on the value added side, total value added is a combination of unskilled labor, Lj,r,t, land, TEj,r,t, natural resources, RNj,r,t, and capital-skilled labor bundle, Qj,r,t. Land demand is defined at the subnational (AEZ) level and total demand for land used in one sector is a CES aggregate of subregions demands (𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡)4. It is assumed that production technology is homogenous across regions and therefore the whole spatial disaggregation process takes place through the land market. For non PARI countries and sectors not producing focus crops, it is assumed that these inputs are imperfect substitutes for one another, which is represented through 3 The acronyms for the volume followed by its corresponding price appear in brackets. 4 A high value of the elasticity of substitution is used (20) to allow the high possibility to reallocate production across subregions. Capital (KTOT-PK) Skilled labor (H-PH) … CES-Leontief for PARI countries Leontief Production (Y-PY) Value added (VA-PVA) Natural resources (RN-PRN) Unskilled labor (L-PL) Capital-Skilled labor bundle (Q-PQ) Land (TE-PTE) CES-Leontief for PARI countries Intermediate consumption (CNTER-PCNTER) Commodity 1 (IC-PIC) Commodity I (IC-PIC) CES 9 the use of a constant elasticity of substitution (CES) function5. The representative firm minimizes its costs subject to the CES aggregator, which yield the following first order conditions: 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐿𝐿 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉−1 �𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉 (4) 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐶𝐶𝐶𝐶 ∙ 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉−1 ∙ �𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉 (5) 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑧𝑧_𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑙𝑙𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙𝑎𝑎𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝜎𝜎𝑗𝑗,𝑟𝑟 𝑧𝑧 −1 ∙ � 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶𝑃𝑃𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝜎𝜎𝑗𝑗,𝑟𝑟 𝑧𝑧 (6) 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐶𝐶𝐶𝐶 ∙ 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉−1 �𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉 (7) 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑄𝑄 ∙ 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉−1 ∙ �𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉 (8) with L rja , Unskilled labor coefficient TE rja , Land coefficient (country level) 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑧𝑧_𝐶𝐶𝐶𝐶 Land coefficient (AEZ level) RN rja , Natural resources coefficient Q rja , Capital-skilled labor aggregate coefficient VA jσ Value added elasticity 𝜎𝜎𝑗𝑗,𝑟𝑟 𝑧𝑧 elasticity of substitution for land demand trPGF , Total factor productivity 𝑙𝑙𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙𝑎𝑎𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 Land productivity parameter (shifter) For PARI countries and for focus crops sectors, it is assumed that the CES aggregates for inputs (CNTER) and factors (VA) are perfect complement (Leontief specification) yielding the following first order conditions for the firm cost minimization program: 5 It might be worth noting that some parameters are solely indexed in j. It is the case, for example, for the elasticity used in the value added functions ( VA jσ ). This specification implies that the same parameter is used for all regions, but that it differs from one sector to the other. 10 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐿𝐿 ∙ 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 (10) 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 (11) 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 (12) 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝑄𝑄 ∙ 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 (13) With: 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐿𝐿 Unskilled labor coefficient 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐶𝐶𝐶𝐶 Land coefficient 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐶𝐶𝐶𝐶 Natural resources coefficient 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝑄𝑄 Capital-skilled labor aggregate coefficient It follows that the price of value added is a weighted sum of the price of unskilled labor, PL j,r,t the price of land, PTE j,r,t the price of natural resources, PRNj,r,t , and the aggregated price of capital and skilled workers, PQj,r,t. 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 (9) The price paid by the producer for each factor differs from the one received by the households by the amount of taxes, which can be negative in the cases where factors are subsidized. The model also distinguishes ad valorem taxes from taxes that are applied on volume. Hence: 𝑃𝑃𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 = {[∑ 𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿 + ∑ 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓,𝑟𝑟,𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓 ] �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 �} + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 (14) 𝑃𝑃𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐿𝐿𝑈𝑈𝑈𝑈𝐿𝐿,𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 � + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐿𝐿𝑈𝑈𝑈𝑈𝐿𝐿,𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 (15) 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∙𝑧𝑧 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 (16) 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑊𝑊𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝑡𝑡𝑙𝑙𝐶𝐶𝐿𝐿𝑁𝑁,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 � + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝑡𝑡𝑙𝑙𝐶𝐶𝐿𝐿𝑁𝑁,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 (17) with trltypeWLt ,, Rate of return to unskilled labor (net of taxes) 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 Rate of return to land (net of taxes) 𝑃𝑃𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 Price of land (including taxes) in region z 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 Aggregate price of land (including taxes) 11 trjWRN ,, Rate of natural resources (net of taxes) trPIndC , Consumer price index VAL trjftaxf ,,, Rate of factor-based taxes (ad valorem) VOL trjftaxf ,,, Rate of factor-based taxes (on volume) In countries r_dual with dual-dual modelling, in the previous equations 𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 is replaced by WL_DDloc,form,r,t which corresponds to the rate of return to unskilled labor in urban and informal sectors, rural and informal sectors, urban and formal sectors, and rural and formal sectors. Consequently in these countries there are four equilibrium rates of return to unskilled labor (net of taxes). At the bottom level, on the value added side, capital, KTOTj,r,t and skilled labor, Hj,r,t, are combined through a CES function, once again to represent the imperfect substitutability between the two factors of production. Minimization of production costs subject to the CES aggregator gives the following demand functions: 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐻𝐻 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 �𝑃𝑃𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝐶𝐶𝑉𝑉𝐶𝐶 (18) 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐾𝐾 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝐶𝐶𝑉𝑉𝐶𝐶 (19) with H rja , Skilled labor coefficient K rja , Capital coefficient CAP jσ Capital-skilled labor elasticity The price of the capital-skilled labor bundle is thus a weighted sum of the rental rate of capital, PKj,r,t, and of the price of skilled labor, PHj,r,t. 𝑃𝑃𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 (20) Again, the prices paid for the factors of production differ from the ones received by households as there are taxes levied on each of them. 𝑃𝑃𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 = {[𝑊𝑊𝐻𝐻𝑟𝑟,𝑡𝑡 + ∑ 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑟𝑟,𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙 ]�1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 �} + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 (21) 12 𝑃𝑃𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑊𝑊𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝐿𝐿𝐶𝐶𝑡𝑡𝑈𝑈𝑙𝑙,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 � + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝐿𝐿𝐶𝐶𝑡𝑡𝑈𝑈𝑙𝑙,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 (22) with trWH , Rate of return to skilled labor (net of taxes) WH_DDloc,r,t Rate of return to skilled labor in countries with dual dual economy trjWK ,, Rate of return to capital (net of taxes) On the intermediate consumption side, for non PARI countries and non focus crops sectors, the commodities (index i) used in the production process are assumed to be imperfect substitutes. Once again, a CES function is used to represent this imperfect substitutability, and cost minimization yields the demand for each input, ICi,j,r,t : 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑗𝑗,𝑟𝑟 𝐼𝐼𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 �𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐼𝐼𝐶𝐶𝑖𝑖,𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝐼𝐼𝐶𝐶 (23) with 𝑎𝑎𝐶𝐶,𝑗𝑗,𝑟𝑟 𝐼𝐼𝐶𝐶 Intermediate consumption scale coefficient 𝜎𝜎𝐼𝐼𝐶𝐶 Intermediate consumption elasticity For PARI countries and for focus crops sectors, the intermediates commodities are assumed to be perfect complements (Leontief specification) yielding the following demand for each input: 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐼𝐼𝐶𝐶 ∙ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 (24) With 𝑎𝑎𝐶𝐶,𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐼𝐼𝐶𝐶 Intermediate consumption scale coefficient The price of total intermediate consumption is a weighted sum of the price paid for each commodity, PICi,j,r,t. 𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡𝐶𝐶 (25) The price of each input is subject to taxes, taxicci,j,r,t, and thus differ from the price received by producers PDEMTOTi,r,t. 𝑃𝑃𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡� (26) 13 2.3 Income and savings 2.3.1 Households Households are assumed to be homogenous and they own all factors of production. They, hence, receive all the payments made to factors of production. They also receive transfers from the government, which are indexed to take into account population growth and the evolution of the price index. 𝐶𝐶𝐶𝐶𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 = ∑ �𝑊𝑊𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + ∑ 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∙ 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡𝑧𝑧 𝑗𝑗,𝑟𝑟,𝑡𝑡 + (𝑊𝑊𝐻𝐻𝑟𝑟,𝑡𝑡 +𝑗𝑗 ∑ 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑟𝑟,𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙 ) 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 + (∑ 𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 + ∑ 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓,𝑟𝑟,𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓 ) 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 +𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿 ∑ 𝑊𝑊𝐾𝐾𝑗𝑗,𝑁𝑁,𝑡𝑡 𝐾𝐾𝑗𝑗,𝑟𝑟,𝑁𝑁,𝑡𝑡𝑁𝑁 �+ 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑙𝑙𝑡𝑡𝐿𝐿𝑙𝑙𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑎𝑎 𝐶𝐶𝐶𝐶𝐻𝐻𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 (27) with trREVH , Households’ income trTRH , Public transfers to households ag trtotpopPop ,, Population Households savings, SAVHr,t, are a fixed proportion epar of their income net of indirect taxes, RECDIRr,t , and the rest of their income is dedicated to consumption budget, BUDHr,t. 𝑆𝑆𝑉𝑉𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 = 𝑒𝑒𝑃𝑃𝑎𝑎𝑟𝑟 (𝐶𝐶𝐶𝐶𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝑃𝑃𝐶𝐶𝑟𝑟,𝑡𝑡) (28) 𝐵𝐵𝑈𝑈𝐷𝐷𝐻𝐻𝑟𝑟,𝑡𝑡 = 𝐶𝐶𝐶𝐶𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 − 𝑆𝑆𝑉𝑉𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝑃𝑃𝐶𝐶𝑟𝑟,𝑡𝑡 (29) 2.3.2 Government The income of the government, REVGr,t, consists of taxes collected on production, RECPRODi,r,t, on factors of production, RECFACi,r,t, on exports, RECEXPi,r,t, on imports, RECDDi,r,t,on consumption, RECCONSi,r,t, and households’ income, RECDIRr,t. 𝐶𝐶𝐶𝐶𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 = ∑ �𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 +𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐾𝐾𝐶𝐶𝑆𝑆𝐶𝐶,𝑟𝑟,𝑡𝑡� + 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝑃𝑃𝐶𝐶𝑟𝑟,𝑡𝑡𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 ∗ 𝑙𝑙𝑙𝑙𝑙𝑙𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑟𝑟,𝑊𝑊 − 𝐿𝐿𝑙𝑙𝑙𝑙𝑃𝑃𝑆𝑆𝑙𝑙𝑙𝑙𝐶𝐶𝑎𝑎𝑡𝑡𝑟𝑟,𝑊𝑊 (30) With 𝑙𝑙𝑙𝑙𝑙𝑙𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑟𝑟,𝑡𝑡 Lumpsum tax 𝐿𝐿𝑙𝑙𝑙𝑙𝑃𝑃𝑆𝑆𝑙𝑙𝑙𝑙𝐶𝐶𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 slack variable for lump sum transfers from government to households 14 Taxes on production are collected on the value of output of each activity. It is important to note that tax rates should be considered as net rates, that is taxes net of subsidy. Hence, all tax rates can be either positive or negative. 𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 = (𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 − −𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶,𝑟𝑟,𝑡𝑡) 𝑃𝑃𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 (31) with tritaxP ,, Production tax rate 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝑡𝑡,𝑟𝑟,𝑊𝑊 Additional agricultural subsidies Receipt from taxes on factors of production is the sum of volume and value taxes on each factor. 𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 �𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐿𝐿𝑈𝑈𝑈𝑈𝐿𝐿,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝑡𝑡𝑙𝑙𝐶𝐶𝐿𝐿𝑁𝑁,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝐿𝐿𝐶𝐶𝑡𝑡𝑈𝑈𝑙𝑙,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡� + ∑ 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐿𝐿𝑈𝑈𝑈𝑈𝐿𝐿,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡𝑧𝑧 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝑡𝑡𝑙𝑙𝐶𝐶𝐿𝐿𝑁𝑁,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝑊𝑊𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 (𝑊𝑊𝐻𝐻𝑟𝑟,𝑡𝑡 + +∑ 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑟𝑟,𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙 )𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 (∑ 𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 + ∑ 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓,𝑟𝑟,𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓 )𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝐿𝐿𝐶𝐶𝑡𝑡𝑈𝑈𝑙𝑙,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝑊𝑊𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 (32) Exports may be subject to three taxes: taxes on production, taxPi,r,t, regular taxes on exports, taxEXPi,r,s,t, and export tax equivalent of multi-fiber arrangement quota premium, taxAMFi,r,s,t. 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶,𝑟𝑟,𝑡𝑡� ∑ �𝑊𝑊𝑎𝑎𝑡𝑡𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡 +𝑁𝑁 𝑊𝑊𝑎𝑎𝑡𝑡𝑉𝑉𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡�𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡 (33) with tsriTRADE ,,, Exports of commodity i from country r to country s Duties, DDi,s,r,t, are collected on imports evaluated at the CIF price, PCIFi,s,r,t. 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 = ∑ 𝐷𝐷𝐷𝐷𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡𝑁𝑁 (34) Taxes are levied on households’ consumption, CHi,r,t, government current expenditure on goods and services, CGi,r,t, on commodities sold for investment purposes, KGi,r,t, and on intermediate consumption, ICi,j,r,t. Each buyer faces a specific tax rate, respectively , taxcci,r,t, taxgci,r,t, taxkgci,r,t, and taxicci,j,r,t. 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐾𝐾𝐶𝐶𝑆𝑆𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 �(𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡) 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 + (𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡)𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 + (𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡) 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 + ∑ 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡𝑗𝑗 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡� (35) 15 With 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑊𝑊 additional consumption tax for specific public closures Finally, the government collects direct taxes on households’ income: 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝑃𝑃𝐶𝐶𝑟𝑟,𝑡𝑡 = [𝑊𝑊𝑎𝑎𝑡𝑡𝑙𝑙𝑡𝑡𝑟𝑟𝑟𝑟,𝑡𝑡 + 𝑎𝑎𝑙𝑙𝑊𝑊𝑙𝑙𝑟𝑟,𝑡𝑡] 𝐶𝐶𝐶𝐶𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 (36) With 𝑎𝑎𝑙𝑙𝑊𝑊𝑙𝑙𝑟𝑟,𝑊𝑊 additional income tax for specific public closures Government savings, SAVGr,t, are assumed to be a fixed proportion, PUBSOLDr, of GDP at market prices, GDPMPr,t. The budget allocated to public current expenditure on goods and services, BUDGr,t, is determined residually. 𝑆𝑆𝑉𝑉𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑈𝑈𝐵𝐵𝑆𝑆𝐾𝐾𝐿𝐿𝐷𝐷𝑟𝑟 𝑃𝑃𝐷𝐷𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 (37) 𝐵𝐵𝑈𝑈𝐷𝐷𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝐶𝐶𝐶𝐶𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 − 𝑆𝑆𝑉𝑉𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 − 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑙𝑙𝑡𝑡𝐿𝐿𝑙𝑙𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑎𝑎 𝐶𝐶𝐶𝐶𝐻𝐻𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 (38) Finally the compensation tax (either lumpsum or consumption tax or income tax) to maintain public budget constant in percentage of GDP and the value of subsidies to are given respectively by: 𝐵𝐵𝑈𝑈𝐷𝐷𝑃𝑃𝑟𝑟,𝑡𝑡 = ∏ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝛼𝛼_𝑎𝑎𝑖𝑖,𝑟𝑟𝐶𝐶𝑒𝑒𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑡𝑡𝑒𝑒𝑊𝑊_𝑃𝑃𝑡𝑡𝑟𝑟 ∗ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡𝐶𝐶 (39) 𝑉𝑉𝑎𝑎𝑙𝑙𝑙𝑙𝑒𝑒𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶,𝑟𝑟,𝑡𝑡 = −[𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡] (40) 2.4 Demand Domestic absorption of each commodity, 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡, is the sum of consumer demand, 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 demand from public administrations, 𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 intermediate demand, 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 and demand for investment purposes, 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡. 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 + ∑ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡𝑗𝑗 + 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 (41) 2.4.1 Private demand Households’ demand is characterized by a LES-CES (Linear Expenditure System - Constant Elasticity of Substitution) specification. This specific utility function allows the evolution of the demand structure of each region to be accounted for as its income level changes. Additionally, the elasticity of substitution is constant only among the sectoral consumptions over and above a minimum level. The minimal level of consumption can vary across region (e.g. developing versus developed country). 16 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑙𝑙𝑡𝑡𝐿𝐿𝑙𝑙𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑎𝑎 �𝑡𝑡𝑙𝑙𝑡𝑡𝑃𝑃𝐶𝐶,𝑟𝑟 + 𝑎𝑎𝐶𝐶,𝑟𝑟𝐶𝐶 𝑉𝑉𝑈𝑈𝑅𝑅𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝑖𝑖,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑟𝑟𝐶𝐶 � (42) with ricmin , Minimal consumption of commodity i (per capita) C ria , Household consumption coefficient trAUX , Utility trP , Shadow price of utility triPC ,, Price of final private consumption C rσ Households’ consumption elasticity of substitution Households maximize their utility subject to their consumption budget, BUDHr,t, from which one can derive the shadow price of utility, Pr,t. 𝐵𝐵𝑈𝑈𝐷𝐷𝐻𝐻𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡𝐶𝐶 (43) 𝑃𝑃𝑟𝑟,𝑡𝑡 𝑉𝑉𝑈𝑈𝑅𝑅𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝐶𝐶𝐻𝐻𝑖𝑖,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑙𝑙𝐿𝐿𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑟𝑟,𝑡𝑡 𝑎𝑎𝑎𝑎 − 𝑡𝑡𝑙𝑙𝑡𝑡𝑃𝑃𝐶𝐶,𝑟𝑟�𝐶𝐶 (44) The price paid by household for each commodity, PCi,r,t, differs from the one received by the suppliers, PDEMTOTi,r,t, by the amount of taxes collected, taxcci,r,t. 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑟𝑟,𝑡𝑡� + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡 (45) Finally, the consumer price index, PIndCr,t, is a Fisher index. 𝑃𝑃𝑡𝑡𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 = �� ∑ 𝑃𝑃𝐶𝐶𝑖𝑖,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐻𝐻𝑖𝑖,𝑟𝑟 𝑂𝑂 𝑖𝑖 ∑ 𝑃𝑃𝐶𝐶𝑖𝑖,𝑟𝑟 𝑂𝑂 𝐶𝐶𝐻𝐻𝑖𝑖,𝑟𝑟 𝑂𝑂 𝑖𝑖 � �∑ 𝑃𝑃𝐶𝐶𝑖𝑖,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐻𝐻𝑖𝑖,𝑟𝑟,𝑡𝑡𝑖𝑖 ∑ 𝑃𝑃𝐶𝐶𝑖𝑖,𝑟𝑟 𝑂𝑂 𝐶𝐶𝐻𝐻𝑖𝑖,𝑟𝑟,𝑡𝑡𝑖𝑖 � (46) with O riCH , Benchmark value of households’ consumption O riPC , Benchmark value of final private consumption 2.4.2 Public demand Government spending on each commodity is a fixed share, G ri,α , of total public expenditure in goods and services, BUDGr,t, and government purchases are subject to taxes, taxgci,r,t. 17 𝑃𝑃𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝛼𝛼𝐶𝐶,𝑟𝑟𝐺𝐺 𝐵𝐵𝑈𝑈𝐷𝐷𝑃𝑃𝑟𝑟,𝑡𝑡 (47) 𝑃𝑃𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑟𝑟,𝑡𝑡� + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡 (48) with triPCG ,, Price of final public consumption 2.4.3 Demand for investment purposes Finally, demand for investment purposes, KGi,r,t, is characterized by a CES function. Cost minimization subject to the CES aggregator yields the following demand function: 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑟𝑟𝐾𝐾𝐺𝐺 𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 �𝑃𝑃𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑉𝑉𝐶𝐶𝑟𝑟,𝑡𝑡 𝑃𝑃𝐾𝐾𝐺𝐺𝑖𝑖,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝐾𝐾𝐾𝐾 (49) with KG ria , Capital good scale coefficient trINVTOT , Total investment trPINVTOT , Price of investment triPKG ,, Price of capital good consumption KGσ Capital good elasticity The aggregated price of capital, PINVTOTr,t, is thus a weighted sum of the price paid for each commodity, PKGi,r,t. 𝑃𝑃𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡𝐶𝐶 (50) Again, the price paid by the purchaser differs from the one received by the seller, as taxes apply. 𝑃𝑃𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑟𝑟,𝑡𝑡� + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡 (51) 2.4.4 Demand by geographic origin MIRAGRODEP is a bilateral trade model consistent with the Armington assumption: commodities are assumed to be heterogeneous according to their origin, and thus, imperfect substitutes for one another (Armington 1969). Nested CES functions are used to reflect preferences among varieties originating from different countries. Therefore, countries can export and import the same product at the same time due to consumer preferences for different varieties. The price transmission between domestic and international market is imperfect and highly dependent on the choice of the CES trade elasticities and the initial share of trade. 18 At the top level, total demand, DEMTOTi,r,t, combines aggregated imports, Mi,r,t, and local production, Di,r,t, through a CES function. From cost minimization subject to the CES aggregator, the following demand functions can be derived: 𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑟𝑟𝐷𝐷 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝑖𝑖,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐷𝐷𝑖𝑖,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑖𝑖 𝑉𝑉𝐴𝐴𝐴𝐴 (52) 𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑟𝑟𝑃𝑃 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝑖𝑖,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑖𝑖,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑖𝑖 𝑉𝑉𝐴𝐴𝐴𝐴 (53) with D ria , Local demand scale coefficient M ria , Total import demand scale coefficient ARM iσ Armington elasticity triPD ,, Price of demand for domestic commodity triPM ,, Aggregated price of imports Consequently, the price of the aggregated commodity, PDEMTOTi,r,t, is a weighted sum of aggregated imports, PMi,r,t, and of the price of the domestically produced commodity, PDi,r,t, which differs from the amount received by the producer, PYi,r,t, since taxes, taxPi,r,t, apply. 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 (54) 𝑃𝑃𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 (1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶,𝑟𝑟,𝑡𝑡) (55) At the second level, total imports, Mi,r,t, are a CES combination of imports from the different trading partners, DEMAi,s,r,t. Cost minimization under the CES aggregation constraint leads to the following demand function: 𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑁𝑁,𝑟𝑟 𝐼𝐼𝑃𝑃𝑃𝑃 𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝑃𝑃𝑖𝑖,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝑖𝑖,𝑠𝑠,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑖𝑖 𝐼𝐼𝐴𝐴𝐶𝐶 (56) with IMP rsia ,, Import demand scale coefficient IMP iσ Import elasticity trsiPDEMA ,,, Price of bilateral trade 19 This specification implies that the price of aggregated imports is a weighted sum of the price paid to the different partners. The price paid by the purchaser differs from the CIF price as import duties, A trsiDD ,,, , apply. 𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡𝑁𝑁 (57) 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 �1 + 𝐷𝐷𝐷𝐷𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑉𝑉 � (58) And the CIF price is determined by the production costs, on which taxes apply, plus the transportation costs. 𝑃𝑃𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑌𝑌𝐶𝐶,𝑁𝑁,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑉𝑉𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡� �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶,𝑁𝑁,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶,𝑟𝑟,𝑡𝑡� + 𝑃𝑃𝑈𝑈𝐾𝐾𝐶𝐶,𝑁𝑁,𝑟𝑟 𝑃𝑃𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 (59) with trsiPtr ,,, Price of transportation per commodity exported rsiMUO ,, Transport coefficient Following the consistent aggregator methodology as defined in(Laborde, Martin, and van der Mensbrugghe, 2011), aggregation of volumes differ whether they are estimated at world prices or at domestic prices. Hence, the shadow price of bilateral trade, PDEMi,s,r,t, is evaluated as follow: 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡�1 + 𝐷𝐷𝐷𝐷𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡� (60) which leads to the definition of the aggregator TRADEi,s,r,t: 𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 (61) Figure 2 : Demand by geographic origin6 6 The acronyms for the volume followed by its corresponding price appear in brackets. 20 2.4.5 Demand for transportation services The volume of transportation Tri,s,r,t required to move commodity i imported by region r from region s is a fixed proportion MUOi,s,r of total imports TRADEi,s,r,t. 𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑈𝑈𝐾𝐾𝐶𝐶,𝑁𝑁,𝑟𝑟 𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 (62) Transportation demand per mode, TrModeTransport,i,s,r,t, is then determined as being a fixed share Tr rsiTransporta ,,, of total transportation demand. Implicitly, thus, total demand for transportation is a Cobb-Douglas type of function. Hence, the exact price formulation for the aggregated price of transportation, PTri,s,r,t, is the dual form of a Cobb-Douglas. 𝑃𝑃𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝐶𝐶𝑟𝑟 𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 (63) 𝑃𝑃𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = ∏ 𝑃𝑃𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 𝑈𝑈𝑇𝑇𝑟𝑟𝑎𝑎𝑇𝑇𝑠𝑠𝑡𝑡𝑡𝑡𝑟𝑟𝑡𝑡,𝑖𝑖,𝑠𝑠,𝑟𝑟 𝑇𝑇𝑟𝑟 𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡 (64) with tTransportPTrMode , Price of transport per mode tsriPTr ,,, Price of transportation by commodity and partners 2.5 Supply and market clearing 2.5.1 Transportation market The world supply of transportation services per mode, WorldTrTransport,t, follows a Cobb-Douglas specification. It follows that the supply from each region, TrSupplyTransport,r,t, is a constant share of the world value of transportation. Domestic absorption (DEMTOT-PDEMTOT) Local demand (D-PD) Total imports (M-PM) CES Partner 1 (DEMA-PDEMA) Partner S (DEMA-PDEMA) … CES 21 𝑊𝑊𝑃𝑃𝑟𝑟𝑙𝑙𝑙𝑙𝐶𝐶𝑟𝑟𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 = 𝑡𝑡𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡𝐶𝐶 ∏ 𝐶𝐶𝑟𝑟𝑆𝑆𝑙𝑙𝑃𝑃𝑃𝑃𝑙𝑙𝑇𝑇𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑇𝑇𝑟𝑟𝑎𝑎𝑇𝑇𝑠𝑠𝑡𝑡𝑡𝑡𝑟𝑟𝑡𝑡,𝑟𝑟 𝑇𝑇𝑟𝑟𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡𝑇𝑇𝑇𝑇 𝑟𝑟 (65) 𝑃𝑃𝑌𝑌𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡� 𝐶𝐶𝑟𝑟𝑆𝑆𝑙𝑙𝑃𝑃𝑃𝑃𝑙𝑙𝑇𝑇𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟 𝐶𝐶𝑟𝑟𝑈𝑈𝑇𝑇𝐿𝐿𝐿𝐿𝑙𝑙𝐿𝐿 𝑃𝑃𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 𝑊𝑊𝑃𝑃𝑟𝑟𝑙𝑙𝑙𝑙𝐶𝐶𝑟𝑟𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 (66) with T Transportc Scale coefficient TrSupply rTransporta , Share of each region in the world transport production Market for transportation clears, since demand of transportation is equal to supply. Equilibrium on the transportation market determines the world prices of transportation per mode, PTrModeTransport,t. 𝑊𝑊𝑃𝑃𝑟𝑟𝑙𝑙𝑙𝑙𝐶𝐶𝑟𝑟𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 = ∑ 𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡𝐶𝐶,𝑟𝑟,𝑁𝑁 (67) 2.5.2 Commodity market In each region, supply of each commodity is equal to demand. Market clearing determines the price of each commodity, PYi,r,t. 𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 + ∑ 𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡𝑁𝑁 + 𝐶𝐶𝑟𝑟𝑆𝑆𝑙𝑙𝑃𝑃𝑃𝑃𝑙𝑙𝑇𝑇𝐶𝐶,𝑟𝑟,𝑡𝑡 (68) 2.5.3 Factors of production market 2.5.3.1 Labor market Total supply of skilled workers, 𝐻𝐻�𝑟𝑟,𝑡𝑡, is fixed and grows exogenously. Skilled workers are assumed to be perfectly mobile across formal sectors, and there is no unemployment. Hence, the equilibrium between supply and demand determines the wage rate. 𝐻𝐻�𝑟𝑟,𝑡𝑡 = ∑ 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 (𝑗𝑗,𝑟𝑟)∈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙(𝑗𝑗,𝑟𝑟) (69) In countries with dual-dual modeling, skilled workers are employed only in formal sectors, but amid formal sectors they may decide to migrate to urban or rural sectors. Skilled workers get better salaries in urban areas. There may be different explanations for this prevailing gap. One is that everything else being equal, there is a preference for living in rural areas. Another one is the existence of a monopolistic union that determines urban wages of skilled workers in formal urban sectors by maximization of its utility, which depends on the number of the union’s members and the level of salary given to its members: this results in a salary higher than the one that would prevail without a monopolistic union. 22 Consequently, three group of equations determine the levels of wages and employment for skilled labor in countries with dual-dual modeling. If r is a country with dual-dual modeling we have 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑟𝑟,𝑡𝑡 = 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑟𝑟𝑇𝑇𝑟𝑟𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡(1 + 𝑡𝑡𝑎𝑎𝑃𝑃ℎ𝑟𝑟) (70) ∑ 𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑟𝑟,𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙 = 𝐻𝐻�𝑟𝑟,𝑡𝑡 (71) 𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑟𝑟,𝑡𝑡 = ∑ 𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡𝐶𝐶 (72) With 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑟𝑟,𝑡𝑡 The rate of return of Skilled labor in urban areas in countries regions with dual dual economy; 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑟𝑟𝑇𝑇𝑟𝑟𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 The rate of return of Skilled labor in rural areas in countries regions with dual dual economy; 𝑡𝑡𝑎𝑎𝑃𝑃ℎ𝑟𝑟 a positive parameter; 𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑃𝑃𝑡𝑡,𝑟𝑟,𝑊𝑊 Skilled labor in sectors in countries regions with dual dual economy 𝐻𝐻�𝑟𝑟,𝑡𝑡 The total supply of skilled labor in country r at time t. Regarding unskilled workers (𝐿𝐿�𝑟𝑟,𝑡𝑡), total supply is exogenous and grows at an exogenous rate. In countries without dual-dual modeling, it is assumed that unskilled workers cannot move freely between rural and urban areas. A constant elasticity of transformation (CET) is used to characterize the regional supply of unskilled workers. Unskilled workers maximize their income subject to the CET aggregator, which leads to the following supply function: 𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 = 𝑙𝑙𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟 𝐿𝐿𝑡𝑡 𝐿𝐿�𝑟𝑟,𝑡𝑡 �𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝑡𝑡𝑇𝑇𝑡𝑡𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑊𝑊𝐿𝐿�����𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝐿𝐿 (73) with trLtypeLt ,, Labor supply on the Ltype market Lt rLtypeb , Labor scale coefficient trWL , Aggregated wage for unskilled workers Lσ Labor elasticity It follows that the aggregated wage for unskilled workers 𝑊𝑊𝐿𝐿�����𝑟𝑟,𝑡𝑡 is a weighted sum of the wages received on each market: 𝑊𝑊𝐿𝐿�����𝑟𝑟,𝑡𝑡 𝐿𝐿�𝑟𝑟,𝑡𝑡 = ∑ 𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿 (74) 23 which is determined by the equilibrium between supply and demand. 𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 = ∑ 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡𝑗𝑗 (75) In countries with dual-dual modeling, for unskilled workers, wages are lower in informal sectors than in formal sectors. There are potentially different explanations of this gap: minimum wages, transaction costs, higher productivity in formal sectors due to a capital-intensive process of production. According to which these are urban or rural sectors, this gap may differ. The mobility of unskilled labor between rural and urban areas is ruled by an equation of migration: migration stops when the salary in formal rural sectors, 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑟𝑟𝑇𝑇𝑟𝑟𝑈𝑈𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡, is equal to the expected salary that can be obtained in urban areas where either an unskilled worker works in urban formal sector (probability Prob_mig𝑟𝑟,𝑡𝑡) and gets a salary of 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 or he works in a urban informal sector (probability1 − Prob_mig𝑟𝑟,𝑡𝑡) and gets a salary of 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝐶𝐶𝑈𝑈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 . This probability is a function of the share of the urban formal employment of unskilled labor 𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 in total employment of unskilled labor in urban sectors. Consequently there are 5 groups of equations describing this double segmentation of the employment of unskilled labor in countries with dual-dual modeling: 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑟𝑟𝑇𝑇𝑟𝑟𝑈𝑈𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑟𝑟𝑃𝑃𝑙𝑙_𝑙𝑙𝑡𝑡𝑡𝑡𝑟𝑟,𝑡𝑡𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 + [1 − 𝑃𝑃𝑟𝑟𝑃𝑃𝑙𝑙_𝑙𝑙𝑡𝑡𝑡𝑡𝑟𝑟,𝑡𝑡]𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝐶𝐶𝑈𝑈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 (76) 𝑃𝑃𝑟𝑟𝑃𝑃𝑙𝑙_𝑙𝑙𝑡𝑡𝑡𝑡𝑟𝑟,𝑡𝑡 = 𝑡𝑡𝑃𝑃𝑟𝑟 𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑢𝑢𝑎𝑎𝑇𝑇,𝑓𝑓𝑡𝑡𝑟𝑟𝑓𝑓𝑎𝑎𝑇𝑇,𝑟𝑟,𝑡𝑡 𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑢𝑢𝑎𝑎𝑇𝑇,𝑓𝑓𝑡𝑡𝑟𝑟𝑓𝑓𝑎𝑎𝑇𝑇,𝑟𝑟,𝑡𝑡+𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑢𝑢𝑎𝑎𝑇𝑇,𝑖𝑖𝑇𝑇𝑓𝑓𝑡𝑡𝑟𝑟𝑓𝑓𝑎𝑎𝑇𝑇,𝑟𝑟,𝑡𝑡 (77) ∑ 𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙𝐶𝐶𝑡𝑡𝐿𝐿,𝑟𝑟,𝑡𝑡𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙𝐶𝐶𝑡𝑡𝐿𝐿 = 𝐿𝐿�𝑟𝑟,𝑡𝑡 (78) 𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙𝐶𝐶𝑡𝑡𝐿𝐿,𝑟𝑟,𝑡𝑡 = ∑ 𝐿𝐿𝐶𝐶.𝑟𝑟,𝑡𝑡𝐶𝐶 (79) 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 = 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝐶𝐶𝑈𝑈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡(1 + 𝑡𝑡𝑎𝑎𝑃𝑃𝑙𝑙𝑟𝑟) (80) with 𝑡𝑡𝑃𝑃𝑟𝑟 : a positive constant; 𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡: urban formal employment of unskilled labor; 𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝐶𝐶𝑈𝑈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 : urban informal employment of unskilled labor; 𝐿𝐿�𝑟𝑟,𝑡𝑡: total employment of unskilled labor; 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡: the remuneration of unskilled labor in formal sectors in country r at time t; 24 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝐶𝐶𝑈𝑈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 : the remuneration of unskilled labor in informal sectors in country r at time t; 𝑡𝑡𝑎𝑎𝑃𝑃𝑙𝑙𝑟𝑟: a positive constant; 2.5.3.2 Land market The spatial disaggregation of the model is implemented through the land market at the regional (AEZ) level, assuming homogenous production technology across regions. We use a two tier-tier land allocation system (CET) to avoid excessive land substitution and make a distinction between high and low elasticity of substitution value crops. Land mobility across sectors is assumed to be imperfect. Land supply, 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑧𝑧,𝑡𝑡 behaves as an isoelastic function of the real return to land (Lee and Mensbrugghe, 2001)). This implies that the greater the real overall return to land, the greater will be the overall supply of land. 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑧𝑧 𝑉𝑉 �𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑃𝑃𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑟𝑟𝑇𝑇𝑇𝑇 (81) with 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑧𝑧 𝑉𝑉 Benchmark value of total land supply in region z 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑧𝑧,𝑡𝑡 Aggregated price for land in region z TE rσ Total land supply elasticity To represent the imperfect mobility of land, supply to each activity, TEj,r,z,t, is determined following a CET aggregation. Land owners maximize their income subject to the CET aggregator, which leads to the following first order condition: 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑙𝑙𝑗𝑗,𝑟𝑟 𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑧𝑧,𝑡𝑡 �𝑊𝑊𝐶𝐶𝐶𝐶𝑃𝑃𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝜎𝜎𝑇𝑇𝑇𝑇 𝑗𝑗 ∈ crops (82) with TE rjb , Land scale coefficient TEσ Land elasticity It follows that the aggregated price of land is a weighted sum of the price received in each activity. 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑧𝑧,𝑡𝑡 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑧𝑧,𝑡𝑡 = ∑ 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡𝑗𝑗 (83) The two tier demand system for land yield the following first order conditions and average price of land for high (sigma) value crops: 25 𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑙𝑙𝑟𝑟,𝑧𝑧 𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂 ∙ 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝑊𝑊𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂𝑃𝑃𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝜎𝜎𝑇𝑇𝑇𝑇 (84) 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑙𝑙𝑗𝑗,𝑟𝑟,𝑧𝑧 𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂𝐶𝐶 𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝑊𝑊𝐶𝐶𝐶𝐶𝑃𝑃𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑊𝑊𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂𝑃𝑃𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝜎𝜎𝑇𝑇𝑇𝑇_𝑂𝑂𝑂𝑂 𝑗𝑗 ∈ crops subgroup mapCET1(j) (85) 𝑊𝑊𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 = ∑ 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡𝑗𝑗 𝑗𝑗 ∈ crops subgroup mapCET1(j) (86) With 𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 Aggregate land supply (subgroup of crops CES aggregate) 𝑙𝑙𝑟𝑟,𝑧𝑧 𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂 Land scale coefficient 𝑊𝑊𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 Aggregate price of land (subgroup of crops CES aggregate) 𝜎𝜎𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂 subgroup of crops land supply elasticity In the default specification the subgroup of crops is associated with higher level of substitutability (𝜎𝜎𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂 > 𝜎𝜎𝐶𝐶𝐶𝐶) 2.5.3.3 Capital market At each period, the capital stock invested by region s in activity j in region r, Kj,s,r,t, is given by the depreciated stock of capital inherited from the preceding period plus new investment INVj,s,r,t 𝐾𝐾𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝐾𝐾𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡−1(1 − 𝛿𝛿𝑟𝑟) + 𝑃𝑃𝐶𝐶𝑉𝑉𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡 (87) with rδ Depreciation rate Where the investment per activity and region of destination depends on the rate of return to capital, the aggregated price of new capital and capital stock7. 𝑃𝑃𝐶𝐶𝑉𝑉𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝐵𝐵𝑁𝑁,𝑡𝑡 𝑎𝑎𝑗𝑗,𝑁𝑁,𝑟𝑟 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑒𝑒 𝛼𝛼 � 𝑊𝑊𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐼𝐼𝑃𝑃𝑉𝑉𝑇𝑇𝑂𝑂𝑇𝑇𝑟𝑟,𝑡𝑡 � (88) with tsB , Scale coefficient for investment rsja ,, Investment scale coefficient α Elasticity of investment to return on capital Total investment made in region r, INVTOTr,t, is simply the sum of investment made in each sector of each region: 7 For a complete discussion on the investment behaviour, see Decreux and Valin (2007). 26 𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝐶𝐶𝑉𝑉𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡𝑗𝑗,𝑁𝑁 (89) In each sector, total supply of capital equals demand, which determines the rate of return to capital specific to this sector (WKi,r,t). 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 = ∑ 𝐾𝐾𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡𝑁𝑁 (90) 2.6 Macroeconomic constraints In each region, total investment must be equal to total savings: 𝑆𝑆𝑉𝑉𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 + 𝑆𝑆𝑉𝑉𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 − 𝐶𝐶𝑉𝑉𝐵𝐵𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑁𝑁,𝑡𝑡 𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡𝐶𝐶,𝑁𝑁 (91) Where CABr,t represents the current account balance, which is a constant share SOLDr,t of world GDP, PIBMVALt. 𝐶𝐶𝑉𝑉𝐵𝐵𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑃𝑃𝐵𝐵𝑃𝑃𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡 𝑆𝑆𝐾𝐾𝐿𝐿𝐷𝐷𝑟𝑟𝑈𝑈𝑙𝑙𝑡𝑡∈𝑁𝑁𝑇𝑇𝑟𝑟𝐿𝐿𝑙𝑙𝑇𝑇𝑁𝑁(𝑟𝑟),𝑡𝑡 ∗ 𝑆𝑆𝐶𝐶𝑉𝑉𝐵𝐵𝑡𝑡 + 𝑃𝑃𝑃𝑃𝐵𝐵𝑃𝑃𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡 𝑆𝑆𝐾𝐾𝐿𝐿𝐷𝐷𝑟𝑟∈𝑁𝑁𝑇𝑇𝑟𝑟𝐿𝐿𝑙𝑙𝑇𝑇𝑁𝑁(𝑟𝑟),𝑡𝑡 (92) With 𝑆𝑆𝐶𝐶𝑉𝑉𝐵𝐵𝑡𝑡 A scaling factor for countries not in surplus 𝑙𝑙𝑙𝑙𝑟𝑟𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙(𝑟𝑟) Countries in surplus World GDP is the simply the sum of regional GDPs, GDPMRr,t: 𝑃𝑃𝑃𝑃𝐵𝐵𝑃𝑃𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡 = ∑ 𝑃𝑃𝐷𝐷𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡𝑟𝑟 (93) The sum of current account balances should be zero at the world level ∑ 𝐶𝐶𝑉𝑉𝐵𝐵𝑟𝑟,𝑊𝑊 = 0𝑟𝑟 (94) Remittances are given by: 𝐶𝐶𝐶𝐶𝑃𝑃𝑟𝑟,𝑙𝑙,𝑊𝑊 ∗ �∑ �∑ WLtOLtype,rLtype + ∑ WLDDOloc,formality,rloc,formality �𝑗𝑗 � ∗ 𝐿𝐿𝐾𝐾𝑗𝑗,𝑟𝑟 = 𝐶𝐶𝐶𝐶𝑃𝑃𝐾𝐾𝑟𝑟,𝑙𝑙 ∗ �∑ �∑ WLtLtype,r,tLtype + ∑ WLDDloc,formality,r,tloc,formality �𝑗𝑗 � ∗ 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑊𝑊 (95) With 𝐶𝐶𝐶𝐶𝑃𝑃𝑟𝑟,𝑙𝑙,𝑊𝑊 Remittances from country/region r to s 𝐶𝐶𝐶𝐶𝑃𝑃𝐾𝐾𝑟𝑟,𝑙𝑙 Base year Remittances from country/region r to s Consistent with the system of national accounting, each region’s GDP at market prices is given by the sum of payments to factors of production and of indirect taxes. 𝑃𝑃𝐷𝐷𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = ∑ 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡𝑗𝑗 + ∑ �𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 +𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐾𝐾𝐶𝐶𝑆𝑆𝐶𝐶,𝑟𝑟,𝑡𝑡� (96) 27 Real GDP, GDPVOLr,t, is computed by dividing GDP at market prices by a consumer price index: 𝑃𝑃𝐷𝐷𝑃𝑃𝑉𝑉𝐾𝐾𝐿𝐿𝑟𝑟,𝑡𝑡 = 𝐺𝐺𝐷𝐷𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 ∏ 𝑃𝑃𝐶𝐶𝑖𝑖,𝑟𝑟,𝑡𝑡 𝐿𝐿𝑙𝑙𝑈𝑈𝐿𝐿𝐶𝐶𝑖𝑖,𝑟𝑟𝑖𝑖 (97) Total factor productivity is computed at the sectoral level via: 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡,𝑟𝑟,𝑊𝑊 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑊𝑊 (98) With 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡,𝑟𝑟,𝑊𝑊 Sectoral (i) total factor productivity 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑊𝑊 Economy-wide total factor productivity Finally an equation is introduced to allow the endogenous calibration of land productivity to target yields index: 𝑌𝑌𝑡𝑡𝑒𝑒𝑙𝑙𝑙𝑙_𝐶𝐶𝑎𝑎𝑟𝑟𝑡𝑡𝑒𝑒𝑊𝑊𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∗ 𝐶𝐶𝐶𝐶𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑌𝑌𝑇𝑇𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 (99) With 𝑌𝑌𝑡𝑡𝑒𝑒𝑙𝑙𝑙𝑙_𝐶𝐶𝑎𝑎𝑟𝑟𝑡𝑡𝑒𝑒𝑊𝑊𝐶𝐶,𝑟𝑟,𝑡𝑡 Target yield index 𝑌𝑌Z𝐶𝐶,𝑟𝑟,z,𝑡𝑡 Production by (subnational) region And the production for subnational regions is given by: 𝑌𝑌𝑇𝑇𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶𝑃𝑃𝑖𝑖,𝑟𝑟,𝑧𝑧,𝑡𝑡∗𝐶𝐶𝐶𝐶𝑃𝑃𝑖𝑖,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∑ 𝑃𝑃𝐶𝐶𝐶𝐶𝑃𝑃𝑖𝑖,𝑟𝑟,𝑧𝑧,𝑡𝑡∗𝐶𝐶𝐶𝐶𝑃𝑃𝑖𝑖,𝑟𝑟,𝑧𝑧,𝑡𝑡𝑧𝑧 (100) 2.7 Economic Closures In MIRAGRODEP, every economic agent balances income and expenditures: income of households equals to spending of households (consumption, savings and transfers), firms’ spending (including payment to capital) equals firms’ revenue. At a global level, savings must be equal to investment. At the country level, a gap between the two variables can occur due to international capital movements. Nevertheless, constraints on current account surplus or deficits are also considered, leading to real exchange rate adjustments (determining relative international prices among economies). Furthermore, supply equals demand for all commodities and factors in the economy. More specifically, the following assumptions are made regarding the savings-investment balance, the public closure and the current account balance. For this research, the so-called Neo-Classical closure is adopted: the marginal propensity to save is constant such that variations in income lead to variations in savings, which lead to variations in investment. Thus, investment is “savings driven.” 28 Regarding the public closure, the when implementing a scenario the user has the choice between 4 options: • Public expenses per head vary and adjust to variation in public revenues such that the ratio public deficit / GDP is constant • no variation in real public expenses per head and a lumpsum tax is levied such that the ratio public deficit / GDP is constant • no variation in real public expenses per head and a consumption tax is levied such that the ratio public deficit / GDP is constant • no variation in real public expenses per head and an income tax is levied such that the ratio public deficit / GDP is constant The choice of either option is not neutral and particularly important when it comes to welfare analysis. In order not to bias the welfare results a closure with no variation in real public expenses per head and a lumpsum tax (not distorsive) levied to maintain the ratio public deficit / GDP constant should be preferred. Finally, we assume in MIRAGRODEP-AEZ that the current account balance is fixed (in the model, this is expressed as a percent of global GDP). The fixed level of the current account balance is maintained through an adjustment of the real exchange rate. With this specification, there is no “free lunch;” if a country needs to increase its imports, it will have to increase its exports as well through a depreciation of its real exchange rate. In doing so we avoid biased welfare analysis, where the country’s consumption, and welfare, is “subsidized” through transfers from the rest of the world (capital inflows). 3. Running MIRAGRODEP-AEZ Using MIRAGRODEP-AEZ for policy analysis requires a number of steps the user need to follow strictly so that the model can run properly. It is important to follow the indicated sequence, otherwise a bug will occur. Also not all the files have to be modified by the user. First of all the aggregation levels for products and regions have to be defined in the Aggregation.xlsx file. Once this is done, the AggregationGTAP.gms file must be run to execute the selected aggregation. After the aggregation done, the user needs to define in options.gms file the first and last year of the simulation, the selection of the Dual Dual specification or not and the choice for the public closure. Once all the options are selected, running a simulation involves the execution of four (4) files in the following order8: 8 All the other files must remain unchanged. 29 MSD.gms: the core model file, solves for the first year and includes the calibration file (Calib.gms) Ref.gms: the file for the reference (baseline) scenario Simul.gms: the simulation file Results.gms: the results file The execution sequence is managed by GAMS save and restarts functions that reduce considerably the amount of work when working with large models. So the MSD.gms9 file is first run and saved, then the Ref.gms file is run starting with the results of the MSD.gms file. and is saved in turn. The Simul.gms file is then run starting from the Ref.gms results and is saved to be the starting point of the Results.gms file. Using this configuration, if one needs to just change the reporting of some results, there is no need to run the whole model. The only thing to do is to modify the results file and run it, saving potentially a huge amount of time10. Alternatively, one can run all the four files using master_file.gms with the following commands11: EXECUTE 'gams MSD.gms s=restart/msd gdx=gdx/msd' EXECUTE 'gams Ref.gms r=restart/msd s=restart/ref gdx=/gdx/ref' EXECUTE 'gams Simul.gms r=restart/ref s=restart/simul gdx=/gdx/simul' EXECUTE 'gams Results.gms r=restart/simul gdx=/gdx/results' It is of course necessary before running the master file, that the aggregation is done as well as the selection of the options of the model. 9 One may also run the Calib.gms file alone to check some features of the model and the aggregation/calibration process. 10 Depending on the degree of disaggregation, the type of simulation and the period (number of years), each scenario may take more than 30 mns. 11 The results at each stage are stored in a gdx file. 30 4. Summary of Model Structure Table 1 : Equations of MIRAGRODEP-AEZ Production First level: Leontief GAMS 1. 𝑌𝑌𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑉𝑉𝑉𝑉 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 EQ_VA 2. 𝑌𝑌𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 EQ_CNTER 3. 𝑃𝑃𝑌𝑌𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑌𝑌𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 EQ_Y Second level – Value added: CES GAMS 4. 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐿𝐿 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉−1 � 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉 EQ_CES_L 5. 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐶𝐶𝐶𝐶 ∙ 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉−1 ∙ � 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗 ,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉 EQ_CES_TE 6. 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑧𝑧_𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑙𝑙𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙𝑎𝑎𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝜎𝜎𝑗𝑗,𝑟𝑟 𝑧𝑧 −1 ∙ � 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝜎𝜎𝑗𝑗,𝑟𝑟 𝑧𝑧 EQ_CES_TEZ 7. 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐶𝐶𝐶𝐶 ∙ 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉−1 � 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉 EQ_CES_RN 8. 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑄𝑄 ∙ 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉−1 ∙ � 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑄𝑄𝑗𝑗 ,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝑉𝑉𝑉𝑉 EQ_CES_Q 9. 𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝑄𝑄𝑗𝑗 ,𝑟𝑟,𝑡𝑡 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 EQ_CES_PVA Second level-Value added: Leontieff GAMS 10. 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐿𝐿 ∙ 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 EQ_LEO_L 11. 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝐶𝐶𝑗𝑗 ,𝑟𝑟,𝑡𝑡 EQ_LEO_TE 12. 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐶𝐶𝐶𝐶 ∙ 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 EQ_LEO_RN 13. 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝑙𝑙_𝑄𝑄 ∙ 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 EQ_LEO_Q 14. 𝑃𝑃𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 = {[∑ WLtLtype,r,tLtype + ∑ WL_DDloc,form,r,tloc,form ] �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 �} + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 EQ_PL 15. 𝑃𝑃𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐿𝐿𝑈𝑈𝑈𝑈𝐿𝐿,𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 � + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐿𝐿𝑈𝑈𝑈𝑈𝐿𝐿,𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 EQ_PTEZ 16. 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 ∙ 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∙ 𝑧𝑧 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 EQ_PTE 31 17. 𝑃𝑃𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑊𝑊𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝑡𝑡𝑙𝑙𝐶𝐶𝐿𝐿𝑁𝑁,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 � + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝑡𝑡𝑙𝑙𝐶𝐶𝐿𝐿𝑁𝑁,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 EQ_PRN Third level – Capital-Skilled labor bundle: CES GAMS 18. 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐻𝐻 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐻𝐻𝑗𝑗 ,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝐶𝐶𝑉𝑉𝐶𝐶 With 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 in formal sectors in countries with dual-dual modelling and 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 = 0 in informal sectors in countries with dual- dual modelling. EQ_H 19. 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝑗𝑗,𝑟𝑟 𝐾𝐾 𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐾𝐾𝑗𝑗 ,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑗𝑗 𝐶𝐶𝑉𝑉𝐶𝐶 EQ_KTOT 20. 𝑃𝑃𝑄𝑄𝑗𝑗 ,𝑟𝑟,𝑡𝑡 𝑄𝑄𝑗𝑗 ,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗 ,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 With:𝑃𝑃𝑄𝑄𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐻𝐻𝑗𝑗 ,𝑟𝑟,𝑡𝑡 in countries with dual-dual modelling EQ_PQ 21. 𝑃𝑃𝐻𝐻𝑗𝑗 ,𝑟𝑟,𝑡𝑡 = {[𝑊𝑊𝐻𝐻𝑟𝑟,𝑡𝑡 + �WH_DDloc,r,t loc ]�1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 �} + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 EQ_PH 22. 𝑃𝑃𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑊𝑊𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝐿𝐿𝐶𝐶𝑡𝑡𝑈𝑈𝑙𝑙,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 � + 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝐿𝐿𝐶𝐶𝑡𝑡𝑈𝑈𝑙𝑙,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 EQ_PK Second level – Intermediate consumption: CES GAMS 23. 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑗𝑗,𝑟𝑟 𝐼𝐼𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝐼𝐼𝐶𝐶 EQ_IC Second level-Intermediate consumption: Leontief GAMS 24. 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑗𝑗,𝑟𝑟 𝑙𝑙_𝐼𝐼𝐶𝐶 ∙ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 EQLEO_IC 25. 𝑃𝑃𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶 EQ_PCNTER 26. 𝑃𝑃𝑃𝑃𝐶𝐶𝐶𝐶 ,𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶 ,𝑗𝑗,𝑟𝑟,𝑡𝑡� EQ_PIC Income and Savings Households GAMS 27. 𝐶𝐶𝐶𝐶𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 = ��𝑊𝑊𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + �𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∙ 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑧𝑧 𝑗𝑗,𝑟𝑟,𝑡𝑡𝑗𝑗 + (𝑊𝑊𝐻𝐻𝑟𝑟,𝑡𝑡 + �WH_DDloc,r,t loc ) 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 + � (𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿 + � WL_DDloc,form,r,t loc,form ) 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 + �𝑊𝑊𝐾𝐾𝑗𝑗,𝑁𝑁,𝑡𝑡 𝐾𝐾𝑗𝑗,𝑟𝑟,𝑁𝑁,𝑡𝑡 𝑁𝑁 � + 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑙𝑙𝑡𝑡𝐿𝐿𝑙𝑙𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑎𝑎 𝐶𝐶𝐶𝐶𝐻𝐻𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 EQ_REVH 32 28. 𝑆𝑆𝑉𝑉𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 = 𝑒𝑒𝑃𝑃𝑎𝑎𝑟𝑟 (𝐶𝐶𝐶𝐶𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝑃𝑃𝐶𝐶𝑟𝑟,𝑡𝑡) EQ_SAVH 29. 𝐵𝐵𝑈𝑈𝐷𝐷𝐻𝐻𝑟𝑟,𝑡𝑡 = 𝐶𝐶𝐶𝐶𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 − 𝑆𝑆𝑉𝑉𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝑃𝑃𝐶𝐶𝑟𝑟,𝑡𝑡 EQ_BUDH Government GAMS 30. 𝐶𝐶𝐶𝐶𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 = ��𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝐷𝐷𝐶𝐶 ,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐾𝐾𝐶𝐶𝑆𝑆𝐶𝐶,𝑟𝑟,𝑡𝑡� + 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝑃𝑃𝐶𝐶𝑟𝑟,𝑡𝑡𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 ∗ 𝑙𝑙𝑙𝑙𝑙𝑙𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑟𝑟,𝑡𝑡 − 𝐿𝐿𝑙𝑙𝑙𝑙𝑃𝑃𝑆𝑆𝑙𝑙𝑙𝑙𝐶𝐶𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 EQ_REVG 31. 𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 = (𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶 ,𝑟𝑟,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶,𝑟𝑟,𝑡𝑡)𝑃𝑃𝑌𝑌𝐶𝐶 ,𝑟𝑟,𝑡𝑡 𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 EQ_RECPROD 32. 𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 �𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐿𝐿𝑈𝑈𝑈𝑈𝐿𝐿,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝑡𝑡𝑙𝑙𝐶𝐶𝐿𝐿𝑁𝑁,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝐿𝐿𝐶𝐶𝑡𝑡𝑈𝑈𝑙𝑙,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡� + �𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐿𝐿𝑈𝑈𝑈𝑈𝐿𝐿,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑧𝑧 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝑡𝑡𝑙𝑙𝐶𝐶𝐿𝐿𝑁𝑁,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝑊𝑊𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 (𝑊𝑊𝐻𝐻𝑟𝑟,𝑡𝑡 + +�WH_DDloc,r,t loc )𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝐿𝐿𝑈𝑈𝑈𝑈,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 ( � 𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿 + � WL_DDloc,form,r,t loc,form ) 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝐶𝐶𝑈𝑈𝐿𝐿𝐶𝐶𝑡𝑡𝑈𝑈𝑙𝑙,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝐿𝐿 𝑊𝑊𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗 ,𝑟𝑟,𝑡𝑡 EQ_RECFAC 33. 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶 ,𝑟𝑟,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶 ,𝑟𝑟,𝑡𝑡� ��𝑊𝑊𝑎𝑎𝑡𝑡𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡 𝑁𝑁 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑉𝑉𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡�𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶 ,𝑟𝑟,𝑁𝑁,𝑡𝑡 EQ_RECEXP 34. 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝐷𝐷𝐶𝐶 ,𝑟𝑟,𝑡𝑡 = �𝐷𝐷𝐷𝐷𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶 ,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑁𝑁 EQ_RECDD 35. 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐾𝐾𝐶𝐶𝑆𝑆𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 �(𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶 ,𝑟𝑟,𝑡𝑡 + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡) 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 + (𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶 ,𝑟𝑟,𝑡𝑡 + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡)𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 + (𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡) 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 + � 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑗𝑗 𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡� EQ_RECCONS 36. 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝑃𝑃𝐶𝐶𝑟𝑟,𝑡𝑡 = [𝑊𝑊𝑎𝑎𝑡𝑡𝑙𝑙𝑡𝑡𝑟𝑟𝑟𝑟,𝑡𝑡 + 𝑎𝑎𝑙𝑙𝑊𝑊𝑙𝑙𝑟𝑟,𝑡𝑡] 𝐶𝐶𝐶𝐶𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 EQ_RECDIR 37. 𝑆𝑆𝑉𝑉𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑈𝑈𝐵𝐵𝑆𝑆𝐾𝐾𝐿𝐿𝐷𝐷𝑟𝑟 𝑃𝑃𝐷𝐷𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 EQ_SAVG 38. 𝐵𝐵𝑈𝑈𝐷𝐷𝑃𝑃𝑟𝑟,𝑡𝑡 = 𝐶𝐶𝐶𝐶𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 − 𝑆𝑆𝑉𝑉𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 − 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑙𝑙𝑡𝑡𝐿𝐿𝑙𝑙𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑎𝑎 𝐶𝐶𝐶𝐶𝐻𝐻𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 EQ_comptax 33 39. 𝐵𝐵𝑈𝑈𝐷𝐷𝑃𝑃𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝛼𝛼_𝑎𝑎𝑖𝑖,𝑟𝑟𝐶𝐶𝑒𝑒𝑎𝑎𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑡𝑡𝑒𝑒𝑊𝑊_𝑃𝑃𝑡𝑡𝑟𝑟 ∗ 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝐶𝐶 EQ_BUDG 40. 𝑉𝑉𝑎𝑎𝑙𝑙𝑙𝑙𝑒𝑒𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶 ,𝑟𝑟,𝑡𝑡 = −[𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡] EQ_SubV Demand 41. 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶 ,𝑟𝑟,𝑡𝑡 = 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 + �𝑃𝑃𝐶𝐶𝐶𝐶,𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑗𝑗 + 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 EQ_DEMTOT Private demand GAMS 42. 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑙𝑙𝑡𝑡𝐿𝐿𝑙𝑙𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑎𝑎 �𝑡𝑡𝑙𝑙𝑡𝑡𝑃𝑃𝐶𝐶,𝑟𝑟 + 𝑎𝑎𝐶𝐶,𝑟𝑟𝐶𝐶 𝑉𝑉𝑈𝑈𝑅𝑅𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑟𝑟𝐶𝐶 � EQ_CH 43. 𝐵𝐵𝑈𝑈𝐷𝐷𝐻𝐻𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶 EQ_AUX 44. 𝑃𝑃𝑟𝑟,𝑡𝑡 𝑉𝑉𝑈𝑈𝑅𝑅𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑙𝑙𝑡𝑡𝐿𝐿𝑙𝑙𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑎𝑎 − 𝑡𝑡𝑙𝑙𝑡𝑡𝑃𝑃𝐶𝐶,𝑟𝑟� 𝐶𝐶 EQ_P 45. 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 (1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶 ,𝑟𝑟,𝑡𝑡)+ 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡 EQ_PC 46. 𝑃𝑃𝑡𝑡𝑃𝑃𝑙𝑙𝐶𝐶𝑟𝑟,𝑡𝑡 = �� ∑ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟𝑉𝑉𝐶𝐶 ∑ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟𝑉𝑉 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟𝑉𝑉𝐶𝐶 � � ∑ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡𝐶𝐶 ∑ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟𝑉𝑉 𝐶𝐶𝐻𝐻𝐶𝐶,𝑟𝑟,𝑡𝑡𝐶𝐶 � EQ_PI Public demand GAMS 47. 𝑃𝑃𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝛼𝛼𝐶𝐶,𝑟𝑟𝐺𝐺 𝐵𝐵𝑈𝑈𝐷𝐷𝑃𝑃𝑟𝑟,𝑡𝑡 EQ_CG 48. 𝑃𝑃𝐶𝐶𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶,𝑟𝑟,𝑡𝑡�+𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡 EQ_PCG Demand for investment purposes GAMS 49. 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑟𝑟𝐾𝐾𝐺𝐺 𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 𝑃𝑃𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝐾𝐾𝐾𝐾 EQ_KG 50. 𝑃𝑃𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶 EQ_PINVTOT 51. 𝑃𝑃𝐾𝐾𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶 ,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐶𝐶 ,𝑟𝑟,𝑡𝑡� + 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡 EQ_PKG Demand by geographic origin GAMS 52. 𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑟𝑟𝐷𝐷 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑖𝑖 𝑉𝑉𝐴𝐴𝐴𝐴 EQ_D 53. 𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑟𝑟𝑃𝑃 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑖𝑖 𝑉𝑉𝐴𝐴𝐴𝐴 EQ_M 54. 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶 ,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶 ,𝑟𝑟,𝑡𝑡 𝐷𝐷𝐶𝐶 ,𝑟𝑟,𝑡𝑡 + 𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 EQ_PDEMTOT 55. 𝑃𝑃𝐷𝐷𝐶𝐶 ,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑌𝑌𝐶𝐶 ,𝑟𝑟,𝑡𝑡 [�1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶 ,𝑟𝑟,𝑡𝑡�] EQ_PD 34 56. 𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶,𝑁𝑁,𝑟𝑟 𝐼𝐼𝑃𝑃𝑃𝑃 𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 � 𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑖𝑖 𝐼𝐼𝐴𝐴𝐶𝐶 EQ_DEMA 57. 𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑁𝑁 EQ_PM 58. 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶 ,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 �1 + 𝐷𝐷𝐷𝐷𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑉𝑉 � EQ_PDEMA 59. 𝑃𝑃𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑌𝑌𝐶𝐶,𝑁𝑁,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑉𝑉𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡� �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶 ,𝑁𝑁,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶 ,𝑟𝑟,𝑡𝑡� + 𝑃𝑃𝑈𝑈𝐾𝐾𝐶𝐶,𝑁𝑁,𝑟𝑟 𝑃𝑃𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 EQ_PCIF 60. 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶 ,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐶𝐶𝑃𝑃𝑃𝑃𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡�1 + 𝐷𝐷𝐷𝐷𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡� EQ_PDEM 61. 𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝑉𝑉𝐶𝐶 ,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝐶𝐶𝑃𝑃𝐶𝐶 ,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 EQ_TRADE Demand for transportation services GAMS 62. 𝐶𝐶𝑟𝑟𝐶𝐶 ,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑈𝑈𝐾𝐾𝐶𝐶,𝑁𝑁,𝑟𝑟 𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 EQ_Tr 63. 𝑃𝑃𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝐶𝐶𝑟𝑟 𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 EQ_TrMode 64. 𝑃𝑃𝐶𝐶𝑟𝑟𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 = � 𝑃𝑃𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 𝑈𝑈𝑇𝑇𝑟𝑟𝑎𝑎𝑇𝑇𝑠𝑠𝑡𝑡𝑡𝑡𝑟𝑟𝑡𝑡,𝑖𝑖,𝑠𝑠,𝑟𝑟 𝑇𝑇𝑟𝑟 𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡 EQ_PTr Supply and market clearing Transportation market GAMS 65. 𝑊𝑊𝑃𝑃𝑟𝑟𝑙𝑙𝑙𝑙𝐶𝐶𝑟𝑟𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 = 𝑡𝑡𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡𝐶𝐶 �𝐶𝐶𝑟𝑟𝑆𝑆𝑙𝑙𝑃𝑃𝑃𝑃𝑙𝑙𝑇𝑇𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡 𝑈𝑈𝑇𝑇𝑟𝑟𝑎𝑎𝑇𝑇𝑠𝑠𝑡𝑡𝑡𝑡𝑟𝑟𝑡𝑡,𝑟𝑟 𝑇𝑇𝑟𝑟𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡𝑇𝑇𝑇𝑇 𝑟𝑟 EQ_WorldTr 66. 𝑃𝑃𝑌𝑌𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡 �1 + 𝑊𝑊𝑎𝑎𝑡𝑡𝑃𝑃𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡 − 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝑡𝑡𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡� 𝐶𝐶𝑟𝑟𝑆𝑆𝑙𝑙𝑃𝑃𝑃𝑃𝑙𝑙𝑇𝑇𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟,𝑡𝑡 = 𝑎𝑎𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑟𝑟 𝐶𝐶𝑟𝑟𝑈𝑈𝑇𝑇𝐿𝐿𝐿𝐿𝑙𝑙𝐿𝐿 𝑃𝑃𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 𝑊𝑊𝑃𝑃𝑟𝑟𝑙𝑙𝑙𝑙𝐶𝐶𝑟𝑟𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 EQ_TrSupply 67. 𝑊𝑊𝑃𝑃𝑟𝑟𝑙𝑙𝑙𝑙𝐶𝐶𝑟𝑟𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝑡𝑡 = �𝐶𝐶𝑟𝑟𝑃𝑃𝑃𝑃𝑙𝑙𝑒𝑒𝐶𝐶𝑟𝑟𝑈𝑈𝑈𝑈𝑁𝑁𝐿𝐿𝑙𝑙𝑟𝑟𝑡𝑡,𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡 𝐶𝐶 ,𝑟𝑟,𝑁𝑁 EQ_PTrMode Commodity market GAMS 68. 𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝐷𝐷𝐶𝐶,𝑟𝑟,𝑡𝑡 + � 𝐶𝐶𝐶𝐶𝑉𝑉𝐷𝐷𝐶𝐶𝐶𝐶 ,𝑟𝑟,𝑁𝑁,𝑡𝑡 𝑁𝑁 + 𝐶𝐶𝑟𝑟𝑆𝑆𝑙𝑙𝑃𝑃𝑃𝑃𝑙𝑙𝑇𝑇𝐶𝐶 ,𝑟𝑟,𝑡𝑡 EQ_PY Factors of production market Labor market GAMS 69. 𝐻𝐻�𝑟𝑟,𝑡𝑡 = �𝐻𝐻𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑗𝑗 EQ_WH 70. 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑟𝑟,𝑡𝑡 = 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑟𝑟𝑇𝑇𝑟𝑟𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡(1 + 𝑡𝑡𝑎𝑎𝑃𝑃ℎ𝑟𝑟) EQ_Hurban 71. �𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑃𝑃𝑡𝑡,𝑟𝑟,𝑊𝑊 𝑙𝑙𝑃𝑃𝑡𝑡 = 𝐻𝐻�𝑟𝑟,𝑊𝑊 EQ_Hrural 35 72. 𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑃𝑃𝑡𝑡,𝑟𝑟,𝑊𝑊 = �𝐻𝐻𝑡𝑡,𝑟𝑟,𝑊𝑊 𝑡𝑡 EQ_WHloc 73. 𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 = 𝑙𝑙𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟 𝐿𝐿𝑡𝑡 𝐿𝐿�𝑟𝑟,𝑡𝑡 � 𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 𝑊𝑊𝐿𝐿�����𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝐿𝐿 EQ_CET_Lt 74. 𝑊𝑊𝐿𝐿�����𝑟𝑟,𝑡𝑡 𝐿𝐿�𝑟𝑟,𝑡𝑡 = � 𝑊𝑊𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿 EQ_CET_WLbar 75. 𝐿𝐿𝑊𝑊𝐿𝐿𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿,𝑟𝑟,𝑡𝑡 = �𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑗𝑗 EQ_WLt 76. 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑟𝑟𝑇𝑇𝑟𝑟𝑈𝑈𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑟𝑟𝑃𝑃𝑙𝑙_𝑙𝑙𝑡𝑡𝑡𝑡𝑟𝑟,𝑡𝑡𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 + [1 − 𝑃𝑃𝑟𝑟𝑃𝑃𝑙𝑙_𝑙𝑙𝑡𝑡𝑡𝑡𝑟𝑟,𝑡𝑡]𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝐶𝐶𝑈𝑈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 EQ_Lurban 77. 𝑃𝑃𝑟𝑟𝑃𝑃𝑙𝑙_𝑙𝑙𝑡𝑡𝑡𝑡𝑟𝑟,𝑡𝑡 = 𝑡𝑡𝑃𝑃𝑟𝑟 𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 + 𝐿𝐿_𝐷𝐷𝐷𝐷𝑇𝑇𝑟𝑟𝑈𝑈𝑈𝑈𝑈𝑈,𝐶𝐶𝑈𝑈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 EQ_Prob 78. � 𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑃𝑃𝑡𝑡,𝑡𝑡𝑃𝑃𝑟𝑟𝑙𝑙𝑎𝑎𝑙𝑙𝑡𝑡𝑊𝑊𝑇𝑇,𝑟𝑟,𝑊𝑊 𝑙𝑙𝑃𝑃𝑡𝑡,𝑡𝑡𝑃𝑃𝑟𝑟𝑙𝑙𝑎𝑎𝑙𝑙𝑡𝑡𝑊𝑊𝑇𝑇 = 𝐿𝐿�𝑟𝑟,𝑊𝑊 EQ_Lrural 79. 𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙 ,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙𝐶𝐶𝑡𝑡𝐿𝐿,𝑟𝑟,𝑡𝑡 = �𝐿𝐿𝐶𝐶.𝑟𝑟,𝑡𝑡 𝐶𝐶 EQ_WL 80. 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙 ,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡 = 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝐶𝐶𝑈𝑈𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙,𝑟𝑟,𝑡𝑡(1 + 𝑡𝑡𝑎𝑎𝑃𝑃𝑙𝑙𝑟𝑟) EQ_Lfor Land market GAMS 81. 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑡𝑡 = 𝐶𝐶𝐶𝐶����𝑟𝑟𝑉𝑉 � 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑡𝑡 𝑃𝑃𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑟𝑟𝑇𝑇𝑇𝑇 ���� EQ_TEbar 82. 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 = 𝑙𝑙𝑗𝑗,𝑟𝑟 𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑡𝑡 � 𝑊𝑊𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑡𝑡 � 𝜎𝜎𝑇𝑇𝑇𝑇 EQ_CET_WTE 83. 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑡𝑡 = �𝑊𝑊𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝐶𝐶𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑗𝑗 EQ_CET_WTEbar 84. 𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑙𝑙𝑟𝑟,𝑧𝑧 𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂 ∙ 𝐶𝐶𝐶𝐶����𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝑊𝑊𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝜎𝜎𝑇𝑇𝑇𝑇 EQ_CET_TE_OF 85. 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑙𝑙𝑗𝑗,𝑟𝑟,𝑧𝑧 𝐶𝐶𝐶𝐶_𝑉𝑉𝑂𝑂𝐶𝐶 𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑊𝑊𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 � 𝜎𝜎𝑇𝑇𝑇𝑇_𝑂𝑂𝑂𝑂 EQ_CET_TE_OFi 86. 𝑊𝑊𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡𝐶𝐶𝐶𝐶_𝐾𝐾𝑃𝑃𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 = �𝑊𝑊𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝐶𝐶𝐶𝐶𝑇𝑇𝑗𝑗,𝑟𝑟,𝑧𝑧,𝑡𝑡 𝑗𝑗 EQ_CET_WTE_OF Capital market GAMS 87. 𝐾𝐾𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝐾𝐾𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡−1(1 − 𝛿𝛿𝑟𝑟) + 𝑃𝑃𝐶𝐶𝑉𝑉𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡 EQ_K 88. 𝑃𝑃𝐶𝐶𝑉𝑉𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡 = 𝐵𝐵𝑁𝑁,𝑡𝑡 𝑎𝑎𝑗𝑗,𝑁𝑁,𝑟𝑟 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑒𝑒 𝛼𝛼 � 𝑊𝑊𝐾𝐾𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑉𝑉𝐶𝐶𝑟𝑟,𝑡𝑡 � EQ_INV 89. 𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝐶𝐶𝑉𝑉𝑗𝑗,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑗𝑗 ,𝑁𝑁 EQ_INVTOT 90. 𝐾𝐾𝐶𝐶𝐾𝐾𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 = �𝐾𝐾𝐶𝐶,𝑁𝑁,𝑟𝑟,𝑡𝑡 𝑁𝑁 EQ_WK 36 Macroeconomic constraints 91. 𝑆𝑆𝑉𝑉𝑉𝑉𝐻𝐻𝑟𝑟,𝑡𝑡 + 𝑆𝑆𝑉𝑉𝑉𝑉𝑃𝑃𝑟𝑟,𝑡𝑡 − 𝐶𝐶𝑉𝑉𝐵𝐵𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶𝐾𝐾𝐶𝐶𝑁𝑁,𝑡𝑡 𝑃𝑃𝐶𝐶𝑉𝑉𝐶𝐶,𝑟𝑟,𝑁𝑁,𝑡𝑡 𝐶𝐶,𝑁𝑁 EQ_B 92. 𝐶𝐶𝑉𝑉𝐵𝐵𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑃𝑃𝐵𝐵𝑃𝑃𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡 𝑆𝑆𝐾𝐾𝐿𝐿𝐷𝐷𝑟𝑟𝑈𝑈𝑙𝑙𝑡𝑡∈𝑁𝑁𝑇𝑇𝑟𝑟𝐿𝐿𝑙𝑙𝑇𝑇𝑁𝑁(𝑟𝑟),𝑡𝑡 ∗ 𝑆𝑆𝐶𝐶𝑉𝑉𝐵𝐵𝑡𝑡 + 𝑃𝑃𝑃𝑃𝐵𝐵𝑃𝑃𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡 𝑆𝑆𝐾𝐾𝐿𝐿𝐷𝐷𝑟𝑟∈𝑁𝑁𝑇𝑇𝑟𝑟𝐿𝐿𝑙𝑙𝑇𝑇𝑁𝑁(𝑟𝑟),𝑡𝑡 EQ_CAB 93. 𝑃𝑃𝑃𝑃𝐵𝐵𝑃𝑃𝑉𝑉𝑉𝑉𝐿𝐿𝑡𝑡 = �𝑃𝑃𝐷𝐷𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 𝑟𝑟 EQ_PIBMVAL 94. �𝐶𝐶𝑉𝑉𝐵𝐵𝑟𝑟,𝑡𝑡 = 0 𝑟𝑟 Eq_CABbal 95. 𝐶𝐶𝐶𝐶𝑃𝑃𝑟𝑟,𝑁𝑁,𝑡𝑡 ∗ ���� WLtOLtype,r Ltype𝑗𝑗 + � WLDDOloc,formality,r loc,formality �� ∗ 𝐿𝐿𝐾𝐾𝑗𝑗,𝑟𝑟 = 𝐶𝐶𝐶𝐶𝑃𝑃𝐾𝐾𝑟𝑟,𝑁𝑁 ∗ ���� WLtLtype,r,t Ltype𝑗𝑗 + � WLDDloc,formality,r,t loc,formality �� ∗ 𝐿𝐿𝑗𝑗,𝑟𝑟,𝑡𝑡 EQ_REM 96. 𝑃𝑃𝐷𝐷𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 = �𝑃𝑃𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑉𝑉𝑉𝑉𝑗𝑗,𝑟𝑟,𝑡𝑡 𝑗𝑗 + ��𝐶𝐶𝐶𝐶𝐶𝐶𝑃𝑃𝐶𝐶𝐾𝐾𝐷𝐷𝐶𝐶 ,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 𝐶𝐶 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐷𝐷𝐷𝐷𝐶𝐶 ,𝑟𝑟,𝑡𝑡 + 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐾𝐾𝐶𝐶𝑆𝑆𝐶𝐶,𝑟𝑟,𝑡𝑡� EQ_GDP 97. 𝑃𝑃𝐷𝐷𝑃𝑃𝑉𝑉𝐾𝐾𝐿𝐿𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝐷𝐷𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 ∏ 𝑃𝑃𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝑃𝑃𝑃𝑃𝑙𝑙𝐶𝐶𝐶𝐶 ,𝑟𝑟𝐶𝐶 EQ_PGF 98. 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 EQ_PGFI 99. 𝑌𝑌𝑡𝑡𝑒𝑒𝑙𝑙𝑙𝑙_𝐶𝐶𝑎𝑎𝑟𝑟𝑡𝑡𝑒𝑒𝑊𝑊𝐶𝐶,𝑟𝑟,𝑡𝑡 ∗ 𝐶𝐶𝐶𝐶𝐶𝐶,𝑟𝑟,𝑡𝑡 = 𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 EQ_YieldZ 100. 𝑌𝑌𝑇𝑇𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 = 𝑌𝑌𝐶𝐶,𝑟𝑟,𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶𝑇𝑇𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∗ 𝐶𝐶𝐶𝐶𝑇𝑇𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∑ 𝑃𝑃𝐶𝐶𝐶𝐶𝑇𝑇𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 ∗ 𝐶𝐶𝐶𝐶𝑇𝑇𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡𝑧𝑧 EQ_ProdZ 37 Table 2 : Variables of MIRAGRODEP Variable Definition GAMS AUXr,t Utility AUX(r,Temps,simul) Br,t Investment scale coefficient B(r,Temps,simul) BUDGr,t Budget allocated to public consumption BUDG(r,Temps,simul) BUDHr,t Budget allocated to private consumption BUDH(r,Temps,simul) CABr,t Current account balance CAB(r,temps,simul) CGi,r,t Public consumption of commodity i CG(i,r,Temps,simul) CHi,r,t Consumption of commodity i by households CH(i,r,Temps,simul) CNTERj,r,t Aggregate intermediate consumption by sector j CNTER(j,r,Temps,simul) Di,r,t Demand for domestic commodity i D(i,r,Temps,simul) DEMAi,r,s,t Bilateral trade from r to s (volume) DEMA(i,r,s,Temps,simul) DEMTOTi,r,t Total demand for composite commodity i DEMTOT(i,r,Temps,simul) GDPMPr,t Gross domestic product at market prices (nominal) GDPMP(r,Temps,simul) GDPVOLr,t Gross domestic product at market prices (real) GDPVOL(r,Temps,simul) Hj,r,t Demand for skilled labor by sector H(j,r,Temps,simul) 𝐻𝐻�𝑟𝑟,𝑡𝑡 Total skilled labor supply Hbar(r,Temps,simul) ICi,j,r,t Intermediate consumption of good i by sector j IC(i,j,r,Temps,simul) INVj,s,r,t Investment made by s in sector j of region r INV(j,s,r,Temps,simul) INVTOTr,t Total investment in region r INVTOT(r,Temps,simul) Kj,s,r,t Capital stock invested by s in r K(j,s,r,Temps,simul) KGi,r,t Demand of good i for investment purposes KG(i,r,Temps,simul) KTOTj,r,t Capital stock available in sector j KTOT(j,r,Temps,simul) Lj,r,t Demand for unskilled labor by sector j L(j,r,Temps,simul) 𝐿𝐿�𝑟𝑟,𝑡𝑡 Total supply of unskilled labor Lbar(r,Temps,simul) LtLtype,r,t Supply of unskilled labor per type Lt(Ltype,r,Temps,simul) 38 Mi,r,t Aggregate imports by region r M(i,r,Temps,simul) Pr,t Price of utility P(r,Temps,simul) PCi,r,t Price of final private consumption PC(i,r,Temps,simul) PCGi,r,t Price of final public consumption PCG(i,r,Temps,simul) PCIFi,r,s,t CIF price PCIF(i,r,s,Temps,simul) PCNTERj,r,t Price of aggregate intermediate consumption by sector j PCNTER(j,r,Temps,simul) PDi,r,t Price of for domestic good i (including taxes) PD(i,r,Temps,simul) PDEMi,r,s,t Price of bilateral trade from r to s PDEM(i,r,s,Temps,simul) PDEMAi,r,s,t Price of bilateral trade from r to s PDEMA(i,r,s,Temps,simul) PDEMTOTi,r,t Price of composite commodity i PDEMTOT(i,r,Temps,simul) PGFr,t Total factor productivity PGF(r,Temps,simul) PHj,r,t Price of skilled labor (including taxes) PH(j,r,Temps,simul) PIBMVALt World gross domestic product (value) PIBMVAL(Temps,simul) PICi,j,r,t Price of intermediate consumption good i for sector j (including taxes) PIC(i,j,r,Temps,simul) PIndCr,t Consumer price index PIndC(r,Temps,simul) PINVTOTr,t Aggregate price of investment in region r PINVTOT(r,Temps,simul) PKj,r,t Price of capital (including taxes) PK(j,r,Temps,simul) PKGi,r,t Price of capital good consumption of good i (including taxes) PKG(i,r,Temps,simul) PLj,r,t Price of unskilled labor (including taxes) PL(j,r,Temps,simul) PMi,r,t Price of aggregate imports PM(i,r,Temps,simul) PQj,r,t Price of capital - skilled labor aggregate PQ(j,r,Temps,simul) PRNj,r,t Price of natural resources (including taxes) PRN(j,r,Temps,simul) PTEj,r,t Average Price of land (including taxes) PTE(j,r,Temps,simul) PTEZj,r,z,t Price of land (including taxes) PTEZ(j,r,z,Temps,simul) PTri,r,s,t Price of aggregate transport by export PTr(i,r,s,Temps,simul) 39 PTrModej,t World price of transport per mode PTrMode(j,Temps,simul) PVAj,r,t Price of value added PVA(j,r,Temps,simul) PYj,r,t Output price PY(j,r,Temps,simul) Qj,r,t Capital - skilled labor aggregate Q(j,r,Temps,simul) RECCONSi,r,t Consumption tax receipts RECCONS(i,r,Temps,simul) RECDDi,r,t Tariff revenues RECDD(i,r,Temps,simul) RECDIRr,t Tax receipts from direct taxation RECDIR(r,Temps,simul) RECEXPi,r,t Export tax receipts RECEXP(i,r,Temps,simul) RECFACj,r,t Receipts from taxes on factors of production RECFAC(j,r,Temps,simul) RECPRODi,r,t Production tax receipts RECPROD(i,r,Temps,simul) REVGr,t Government total income REVG(r,Temps,simul) REVHr,t Households income REVH(r,Temps,simul) RNj,r,t Demand for natural resources by sector RN(j,r,Temps,simul) SAVGr,t Government savings SAVG(r,Temps,simul) SAVHr,t Households savings SAVH(r,Temps,simul) SOLDr,t Initial share of current account balance in world GDP SOLD(r,Temps,simul) TEZj,r,t Land used in sector j TEZ(j,r,z,Temps,simul) TE_OFZj,r,z,,t Land used in sector j (other crops) TE_OFZ(j,r,z,Temps,simul) 𝐶𝐶𝐶𝐶𝑇𝑇������𝑟𝑟,𝑧𝑧,𝑡𝑡 Total land supply TEbarZ(r,z,Temps,simul) Tri,r,s,t Transport demand by export Tr(i,r,s,Temps,simul) TRADEi,r,s,t Bilateral trade from r to s (volume) TRADE(i,r,s,Temps,simul) TRHr,t Public transfers to households TRH(r,Temps,simul) TrModej,i,r,s,t Transport demand by export, per mode TrMode(j,i,r,s,Temps,simul) TrSupplyj,r,t Supply of international transportation by region r TrSupply(j,r,Temps,simul) VAj,r,t Value added VA(j,r,Temps,simul) WHr,t Rate of return to skilled labor WH(r,Temps,simul) WKi,r,t Rate of return to capital WK(i,r,Temps,simul) 𝑊𝑊𝐿𝐿�����𝑟𝑟,𝑡𝑡 Price of aggregate unskilled labor WLbar(r,Temps,simul) 40 WLtLtype,r,t Rate of return to unskilled labor WLt(Ltype,r,Temps,simul) WorldTrj,t World supply of international transportation WorldTr(j,Temps,simul) WRNj,r,t Rate of return to natural resources WRN(j,r,Temps,simul) WTEZj,r,z,t Rate of return to land WTEZ(j,r,z,Temps,simul) WTE_OFZj,r,z,t Rate of return to land (other crops) WTEZ(j,r,z,Temps,simul) 𝑊𝑊𝐶𝐶𝐶𝐶�������𝑇𝑇𝑟𝑟,𝑧𝑧,𝑡𝑡 Aggregate price of land WTEbarZ(r,z,Temps,simul) Yj,r,t Total output of sector j Y(j,r,Temps,simul) 𝑃𝑃𝑟𝑟𝑃𝑃𝑙𝑙_𝑙𝑙𝑡𝑡𝑡𝑡𝑟𝑟,𝑡𝑡 Probability of being hired in a formal sector when an unskilled worker has migrated to an urban area in country r (a country with dual-dual modelling) Prob_mig(r,Temps,simul) 𝑊𝑊𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙 ,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙𝐶𝐶𝑡𝑡𝐿𝐿,𝑟𝑟,𝑡𝑡 Rate of return of Unskilled labor in sectors in countries regions with dual dual economy WL_DD(location,formality,r,Temps,simul) 𝐿𝐿_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙 ,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙𝐶𝐶𝑡𝑡𝐿𝐿,𝑟𝑟,𝑡𝑡 Unskilled labor in sectors in countries regions with dual dual economy L_DD(location,formality,r,Temps,simul) 𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙 ,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙𝐶𝐶𝑡𝑡𝐿𝐿,𝑟𝑟,𝑡𝑡 Skilled labor in sectors in countries regions with dual dual economy H_DD(location,r,Temps,simul) 𝑊𝑊𝐻𝐻_𝐷𝐷𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙,𝑓𝑓𝑙𝑙𝑟𝑟𝑓𝑓𝑈𝑈𝑙𝑙𝐶𝐶𝑡𝑡𝐿𝐿,𝑟𝑟,𝑡𝑡 Rate of return of Skilled labor in sectors in countries regions with dual dual economy WH_DD(location,r,Temps,simul) 𝑉𝑉𝑎𝑎𝑙𝑙𝑙𝑙𝑒𝑒𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶 ,𝑟𝑟,𝑡𝑡 Value of agricultural subsidies ValueSUBV(i,s,Temps,Simul) 𝑎𝑎𝑙𝑙𝑙𝑙𝑆𝑆𝑈𝑈𝐵𝐵𝑉𝑉𝐶𝐶 ,𝑟𝑟,𝑡𝑡 Additional agricultural subsidies addSUBV(i,s,Temps,Simul) 𝑙𝑙𝑙𝑙𝑙𝑙𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑟𝑟,𝑡𝑡 Lumpsum tax lumpsum(r,Temps,simul) 𝐿𝐿𝑙𝑙𝑙𝑙𝑃𝑃𝑆𝑆𝑙𝑙𝑙𝑙𝐶𝐶𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡 slack variable for lump sum transfers from government to households LumpSumTax(r,temps,Simul) 𝑎𝑎𝑙𝑙𝑊𝑊𝑙𝑙𝑟𝑟,𝑡𝑡 Additional Income tax addtaxdir(r,Temps,simul) 41 𝑎𝑎𝑙𝑙𝑊𝑊𝑡𝑡𝑟𝑟,𝑡𝑡 Additional consumption tax addtaxcc(r,Temps,simul) 𝑌𝑌𝑇𝑇𝐶𝐶,𝑟𝑟,𝑧𝑧,𝑡𝑡 Sub-national production for region z yz(i,r,z,t,simul) 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝐶𝐶,𝑟𝑟,𝑡𝑡 Sectoral TFP PGFI(i,r,t,simul) 𝑃𝑃𝑃𝑃𝑃𝑃𝑟𝑟,𝑡𝑡 Aggregate TFP PGF(i,r,t,simul) 𝑆𝑆𝐶𝐶𝑉𝑉𝐵𝐵𝑡𝑡 Scaling factor SCAB(t,simul) 𝐶𝐶𝐶𝐶𝑃𝑃𝑟𝑟,𝑁𝑁,𝑡𝑡 Remittances REM(r,s,t,simul) 42 References Decreux, Y., & Valin, H. (2007). MIRAGE: Updated Version of the Model for Trade Policy Analysis Focus on Agriculture and Dynamics. CEPII. FAO (2013). FAOSTAT. Available Online at < http://faostat.fao.org/> Femenia, F. (2012). Functional Forms Commonly Used in CGE Models. AGRODEP Technical Note 02. Washington, DC: International Food Policy Research Institute. Available Online at Foure, J., A. Benassy-Quere and L. Fontagne (2012). The Great Shift: Macroeconomic Projections for the World Economy at the 2050 Horizon, CEPII Working paper 2012-03. - Available Online at < http://www.cepii.fr/anglaisgraph/bdd/baseline.htm#sthash.LTHY86Pg.dpuf> Laborde, D., V. Robichaud and S. Tokgoz (2013). MIRAGRODEP 1.0: Documentation. AGRODEP Technical Note 20. Washington, DC: International Food Policy Research Institute. Available Online at Laborde, D., Martin, W., & van der Mensbrugghe, D. (2011). Measuring the Impacts of Global Trade Reform with Optimal Aggregators of Distortions. Washington, D.C. Lee, H., & Mensbrugghe, D. Van Der. (2001). Interactions between Direct Investment and Trade in the Asia-Pacific Region. ILO (2013). International Labor Organization. Statistics and Databases. Available Online IMF (2013). International Monetary Fund. World Economic Outlook Database. Available Online at Narayanan, B. G. and T. L. Walmsley, (2012). Global Trade, Assistance, and Production: The GTAP 9 Data Base, Center for Global Trade Analysis, Purdue University. http://faostat.fao.org/ http://www.agrodep.org/resource/functional-forms-commonly-used-cge-models http://www.ilo.org/global/statistics-and-databases/lang--en/index.htm https://www.imf.org/external/pubs/ft/weo/2013/01/weodata/index.aspx List of Tables List of Figures 1. Introduction 2. Model Structure 2.1 Dimensions and sets 2.2 Production 2.3 Income and savings 2.3.1 Households 2.3.2 Government 2.4 Demand 2.4.1 Private demand 2.4.2 Public demand 2.4.3 Demand for investment purposes 2.4.4 Demand by geographic origin 2.4.5 Demand for transportation services 2.5 Supply and market clearing 2.5.1 Transportation market 2.5.2 Commodity market 2.5.3 Factors of production market 2.5.3.1 Labor market 2.5.3.2 Land market 2.5.3.3 Capital market 2.6 Macroeconomic constraints 2.7 Economic Closures 3. Running MIRAGRODEP-AEZ 4. Summary of Model Structure References