Model outlines

The spatial price determination model

The spatial price determination model (SpPDM) is developed for spatial pricing of multi-market heterogeneously distributed resources. The theoretical spatial pricing mechanism is similar to non-spatial pricing, where the interaction of demand and supply determines the market price. However, in spatial pricing both the demand and supply need be spatial in their character and the markets need to be product as well as geographically delineated.

The theoretical spatial pricing mechanism is similar to non-spatial pricing, where the interaction of demand and supply determines the market price. However, in spatial pricing both the demand and supply need be spatial in their character and the markets need to be product as well as geographically delineated.The spatial price determination model (SpPDM) is developed for spatial pricing of multi-market heterogeneously distributed resources. The theoretical spatial pricing mechanism is similar to non-spatial pricing, where the interaction of demand and supply determines the market price. However, in spatial pricing both the demand and supply need be spatial in their character and the markets need to be product as well as geographically delineated. The product delineation is based on resource categorisations, while the geographical delineation is based on a system of two-dimensional quadratic shaped gridcells. That is, each gridcell represents a separate market, where transactions between the resource suppliers and users can occur, thus generating spatial price equilibrium for each categorised resource.

Spatial structure of supply

The on-site supply, i.e., the supply in each gridcell, is derived based on a bottom-up approach using gridcell-specific resource availability and extraction costs for each type of resource. Each gridcell has a single observed availability per type of resource and a unique extraction cost associated with that availability. The gridcell-specific availability and extraction cost is the fundamental building block for the quantity-cost relationship of the spatial supply.

The spatial structure of the supply is captured by aggregating the on-site availability with that of adjacent gridcells, creating a supply area for each gridcell. The number of adjacent gridcells to include is based on assumptions on transportation distance. Aggregated, regional supply curves are constructed for each gridcell and resource, using a merit-order framework.

Spatial structure of demand

The main rationale for using a merit-order approach for constructing the supply curves is twofold. First, the need to make strict theoretical assumption on the quantity-cost relationship is eliminated. Second, it allows the use of empirical data that often are availability for heterogeneously distributed resources, such as forestry and agricultural resources.

The spatial demand structure is represented by two demand concepts: Site demand and demand pressure. They are aggregated in each gridcell and for each resource to create an aggregate demand per resource in each gridcell. The site demand is representing the demanded quantity of a resource by all the users in a specific gridcell. The demand pressure is measuring the spatial interaction across gridcell with a site demand. The estimation of the demand pressure is based on a distance-decay framework. The demand pressure is monotonically decreasing with distance until it eventually disappears. The only reason a gridcell might not have an aggregated demand is if it is located too far away from a site demand so that the demand pressure drops to zero.

Market equilibrium

The market price determination is given by the intersection of the aggregate demand and the regional supply curve. Equilibrium is established for each market, but no general equilibrium is solved. Instead, the equilibrium should be interpreted as partial since no price equalising condition is imposed between markets. The spatial price equilibrium is stable if no user can decrease its cost by changing procurement markets, i.e., buying the resource from another gridcell. In this framework, resource owners can make excess profits due to locational cost advantages.

The method can be used for a wide range of applications assessing spatial heterogeneously distributed resources, e.g., forest and agricultural resources. Based on the application, the method can also be used to assess direct policy options and their implications on market conditions. It allows the modelling of a wide range of pricing behaviours, especially when considering the interaction of competitive policies. By also including conjectural variation into the demand structure, it is possible to identify interdependencies between spatial markets.

BeWhere

BeWhere is a family of techno-economic, geographically explicit, bottom-up optimisation models that are used to analyse localisations and properties of different energy conversion plants, in order to, for example, investigate different policy instruments and to provide decision support for the development of strategies and policies. The model has been applied at local, national and supranational levels. Initially the scope of application was limited to bioenergy plants, but has been expanded to also include e.g. solar, wind, hydropower, public transport, and algae-based plants.

BeWhere Sweden is focused particularly on forest biomass, biofuel production and design of forest-based value chains, with a high degree of detail regarding the biomass supply and industrially integrated biofuel production, where potential plant hosts are largely modelled individually. The model is primarily used to analyse how future bio-based value chains can be implemented cost-effectively from a system perspective, what role the existing energy infrastructure (industry and energy facilities) can play, and how different parameters affect, for example, the choice of conversion technologies, localisation, and integration, in a system where the same limited resource (biomass) is also in demand from other sectors. The parameters considered include e.g. policy instruments, future scenarios for energy market conditions, technological development and industrial investment opportunities.

The model minimises the cost of the entire studied system to simultaneously meet a certain defined biofuel production demand, as well as the demand for biomass from other sectors. The system cost includes costs and revenues for production and transportation of biomass, production facilities, transportation and delivery of biofuels, by-products sales, and economic policy instruments. The cost is minimised under a number of constraints that describe and limit, for example, supply and demand for biomass, possible import and export of biomass, plant operation and demand for end products. The model will thus choose the least costly combinations of feedstocks, production facilities and biofuel distribution. The resulting model output includes a set of new biofuel production facilities in order to meet the defined production target, the resulting supply chain configurations, the origin of used biomass, and costs related to the different parts of the supply chain.

Forest biomass supply and demand

Focus is on woody biomass resources: virgin forest biomass from forestry operations (sawlogs, pulp wood, harvesting residues, stumps), by-products from forest industry (chips, bark, sawdust), farmed wood from abandoned arable land, waste wood, and refined wood pellets. In addition to demand as feedstock for biofuel production, competing demand from the forest industry (pulp mills, sawmills and pellets industries) as well as the stationary energy sector (heat and electricity) are also considered explicitly.

For biofuel production, the main focus is on forest-based biofuels produced via thermochemical (gasification, HTL, pyrolysis) or biochemical (fermentation, anaerobic digestion) conversion. Also commercial biofuel production technologies that are currently in operation in Sweden are included in the model (biogas from anaerobic digestion, grain-based ethanol, RME, and tall oil based HVO).

Spatial structure

BeWhere Sweden is geographically explicit regarding woody biomass cost-supply, competing biomass demand, existing and potential new biofuel production, transportation infrastructure, and biofuel demand. The figure below gives an overview of the main biomass flows and geographic scope of the BeWhere Sweden model. Two different geographic representations are used: a base model grid with 0.5 degree spatial resolution (“G” in the figure), and explicit locations (“E” in the figure).

The Global Biosphere Management Model

The Global Biosphere Management Model (GLOBIOM) is a global recursive dynamic partial equilibrium model of the forest and agricultural sectors, where economic optimisation is based on the spatial equilibrium modelling approach.

The model is based on a bottom-up approach where the supply side of the model is built-up from the bottom (land cover, land use, management systems) to the top (production/markets). The agricultural and forest productivity is modelled at the level of gridcells of 5 x 5 to 30 x 30 minutes of arc, using biophysical models, while the demand and international trade occur at regional level (30 to 53 regions covering the world, depending on the model version and research question). Besides primary products, the model has several final products and by-products, for which the processing activities are defined.

The model computes market equilibrium for agricultural and forest products by allocating land use among production activities to maximise the sum of producer and consumer surplus, subject to resource, technological and policy constraints. The level of production in a given area is determined by the agricultural or forestry productivity in that area (dependent on suitability and management), by market prices (reflecting the level of demand), and by the conditions and cost associated to conversion of the land, to expansion of the production and, when relevant, to international market access. Trade is modelled following the spatial equilibrium approach, which means that the trade flows are balanced out between different specific geographical regions. Trade is furthermore based purely on cost competitiveness as goods are assumed to be homogenous. This allows tracing of bilateral trade flows between individual regions.

Woody biomass demand and forest industry technologies

The forest sector is modelled to have seven final products (chemical pulp, mechanical pulp, sawn wood, plywood, fibreboard, other industrial roundwood, and household fuelwood). Demand for the various final products is modelled using regional level constant elasticity demand functions. Forest industrial products (chemical pulp, mechanical pulp, sawn wood, plywood and fibreboard) are produced by Leontief production technologies, with input-output coefficients based on the engineering literature. By-products of these technologies (bark, black liquor, sawdust, and woodchips) can be used for energy production or as raw material for pulp and fibreboard. Production capacities for the base year 2000 of forest industry final products are based on production quantities from FAOSTAT. After the base year the capacities evolve according to investment dynamics, which depend on depreciation rate and investment costs. This implies that further investments can be done to increase production capacities or allow industries to reduce their production capacities or be closed.

Nicklas Forsell
International Institute for Applied Systems Analysis (IIASA)
Ecosystems Services and Management
Schlossplatz 1
A-2361 Laxenburg, Austria
Email: forsell@iiasa.ac.at