# Demand side (Outdated)

Demand nesting for good i

Final consumption is modelled in each region through a representative agent, whose utility function is intratemporal. A fixed share of the regional income is allocated to savings, the rest is used to purchase final consumption goods. The saving rate is calibrated at the reference year using GTAP database.

Government and final consumers are modelled with the same demand function and aggregated in a single regional representative agent. This agent therefore both pays and earns taxes, and no public budget constraint has to be taken into account explicitly: this constraint is implicit to meeting the representative agent's budget constraint. Unless otherwise indicated (modelling a distorsive replacement tax does not raise any technical problem), this implicitly assumes that any decrease in tax revenues (for example as a consequence of a trade liberalisation) is compensated by a non-distorsive replacement tax. However, the magnitude of the tax revenue losses is an interesting information, provided in standard result tables.

Total demand is made up of final consumption, intermediate consumption and capital goods. Sectoral demand of these three compounds follows the same pattern for quality and region of origin preference.

### Final consumption

Below this first-tier Cobb-Douglas function, preferences across sectors are represented by a LES-CES function (Linear Expenditure System - Constant Elasticity of Substitution). This allows to take into account differences among regions by assigning different level of minimum share to each aggregate good consumed. With this kind of utility function, the elasticity of substitution is constant only among the sectoral consumptions above a minimum level.

### Intermediate consumption and capital goods

Firms are considered having no minimum consumption requirements and their demand for intermediary consumption is modelled with a CES function (Constant Elasticity of Substitution). Investment is constituted of capital goods selected from sectors following a similar CES framework.

As far as consumption choices within each sector are concerned, a nesting of CES functions such as the one used in (G. W. Harrison, T. F. Rutherford, D. G. Tarr, 1997) allows the particular status of domestic goods, together with product differentiation according to geographical origin (the so-called Armington's assumption) and horizontal product differentiation between varieties to be taken into account.

### Differentiation of quality

Importance in trade of vertical differentiation and specialisation across quality ranges has been widely illustrated (see e.g. (Lionel Fontagné, Michaël Freudenberg, Nicolas Peridy, others, 1997), (David Greenaway, Johan Torstensson, 2000)). Even though it is not easy to model nor quantify, this is an important device as far as analysing the nature and intensity of competition is concerned.

This is why a further CES nesting level is added to the subutility function for some sectors of the aggregation, distinguishing between two quality ranges, defined on a geographical basis: goods produced in a developing economy are assumed to belong to a different quality range than those produced in a developed economy (the demand nesting is displayed in the figure below). The choice of substitution elasticities (the one between qualities is inferior to the Armington elasticity) implies that goods that do not belong to the same quality range are less substitutable than goods from the same quality range. This means for instance that, within a given sector, goods from a developing country compete more directly with goods from any other developing country, than with goods from any developed country.

### Armington assumption and import elasticities

This hypothesis allows to represent the substitution between domestic and foreign goods depending on their relative prices. A CES is assumed between demand for imported and domestic goods with sector specific elasticities. These elasticities are provided by GTAP. When different regions of quality are represented, this substitution is only effective in the zone of same quality as the production in the region considered. Imports are substitutable between regions with an elasticity of import which is also sector-specific. Armington elasticities $\sigma_{ARM}$ and import elasticities $\sigma_{IMP}$ are linked through the relation $\sigma_{ARM}-1 = \sqrt{2} \left(\sigma_{IMP}-1\right)$

### Varieties

In the Imperfect competition (Outdated) framework, goods can also be distinguished by varieties, even is these varieties are considered homogeneous. Varieties are supposed the most substitutable element in the subfunctions.

1. ^ G. W. Harrison, T. F. Rutherford, D. G. Tarr, 1997. Quantifying the Uruguay round. The Economic Journal, 107(444), pp.1405-1430.
2. ^ Lionel Fontagné, Michaël Freudenberg, Nicolas Peridy, others, 1997. Trade Patterns Inside the Single Market. CEPII Working Paper, 97-07.
3. ^ David Greenaway, Johan Torstensson, 2000. Economic geography, comparative advantage and trade within industries: evidence from the OECD. Journal of Economic Integration, JSTOR, pp.260–280.