M2: Energy Consumption

The model M2 captures the answer to the question “How is each part of our GDP dependent on energy?”. Some economic activities are very sensitive to energy since energy is one of their major costs associated with value creation. For some others, energy plays a much smaller role. Let’s break the economy into slices of homogeneous ratio (value produced / cost of required energy). The illustration shown on the intoduction slide illustrates this idea with 10 “slices”. Although this curve is the central belief of M2 and one of the core parameters of CCEM since it dictates how the economy will react if not enough energy is available in the future, it is actually difficult to sample.

To simplify CCEM simulation, we represent the histogram of Figure 4 with three curves (that could be derived from this histogram if we knew it for each geographical zone):

·         For each region z, cancel(z,p) is a function that associate to each price (of energy) the fraction of activity that is no longer profitable (hence is “cancelled”), expressed as an energy consumption share. We use the equivalent oil price to normalize these functions with the simplifying assumption of using the same function for each energy source.

·         For each region r, impact(z,p) is another function that tells, for a given percentage p of activity that is “cancelled”, which share of the associated GDP is lost. If market laws are in action, we expect the less profitable activities to stop first (on the right on Figure 4). If energy redistribution is involved, it may be different: a management of energy shortages through restrictions and policies may produce a bigger impact (loss of the same share of GDP and activity). The impact(z,p) factor is applied twice in M4’s equations : to reduce the GDP and to reduce the investments that are generated. As the of energy goes up, it eats a faction of the profit made by the activity (using the same factor for GDP output and for investment is a crude simplification, in the spirit of a “coarse” model).

·         Last, the histogram of Figure 4 is not constant and evolves with time (represented with the small red arrows).  The KPI that is used to represent this evolution is dematerialize(e,y) : expected decline in energy density (GDP/ energy consumption) for zone z. This is also called energy intensity of the economy for zone z. As the share of “immaterial” economy (such as services) increases over “material” economy (such as manufacturing), the dematerialize(e,y) ratio decreases.

However, there is another force at play, namely that of technological progress, that increases the energy efficiency, thus reducing the amount of energy needed to produce the same value. Somehow a key prospective question for the next century is to evaluate the race between resource depletion due to overconsumption and technology innovation. This is captured with another belief associated to M2:

·         For each region z, savings(z,y) is a “roadmap”, a function that associate to each year y the percentage of energy consumption that could be saved while keeping the same output. This is a “technology potential”, which requires each region to invest (the “energy investment”) at a cost (G$ / installed MW) that declines over time (a coefficient that is part of the same “belief”). Note that “dematerialization” talks about the evolution of the economy, where “savings” talks about efficiency for the existing activity.

·         energyIntensity(z,e,y) is the combination of (1 - dematerialize(z,e,y)) and (1 – savings(z,y)).

M2 uses the following state variables to describe the energy system year after year:

•       Rz(e,y):   raw needs for energy e in PWh at year y (before efficiency or transition is applied)

•       Nz(e,y):   needs for energy e in zone z during year y once energy transition transfers are applied

•       Tr(e1,e2,y): fraction of energy e1 demand that has been transferred to energy source e2 at year y

•       Uz(e,y) : usage (constrained consumption) for zone z of energy e

•       Pe(y):  Price for energy e ($/toe) at year y

•       Sz(y): percentage of savings reached at year y

•       GWz(y): percentage of capacity lost because of global warming, cumulative to year y

M2 is computed at the region level. Its input are the economic activity of the previous year, the demographic evolution, and the history of consumption for each energy source. Its output is a set of vectors, for each energy source, that represents the expected required energy for each possible market price (same discretization for demand and for supply). The computation of the energy demand goes through three steps:

·         The initial “raw” demand (Rz(e,y):   raw needs) is assessed from previous consumption and the product of a few evolution factors (2).

·         The “constrained” demand (Nz(e,y)) is adjusted modulo the “energy transition”. The substitutions produced by M3 (see next section) are applied to transfer part of the remaining needs from one source of energy to another. Since substitutions are ordered, it requires to iterate Energy in the proper order.

·         The demand vector is produced by factoring, for each possible price, the level of cancellation that is triggered by this price.

M2 may be described with the following state equations:

(1)    Rz(e,y) computes the raw need for zone z of energy e using the initial demand (year 1) multiplied by the product of the unconstrained GDP growth (economyRatio) by the dematerialization ratio, then multiplied by population growth and reduced by the global warming damage factor (1 - GWz(y)).   

(2)    populationRatio(z,y) represents the expected energy consumption for zone z associated with its projected population level (population(z)) modulo the reduction of productivity caused by the pain level (see M5).

(3)    economyRatio(z,y): heuristics that combines the expected growth of the zone GDP (from the amount of past investments) and the mutual influence of zones through global trade. The GDP is decomposed into local economy and trade (both import and export). The global ratio that is applied is Mz(y – 1)/Mz(1), growth of unconstrained economy output (see M4). It is applied directly to innerTrade(z) = the faction of GDP associated to domestic activity, and with additional trade coefficients for the fraction of GDP that is respectively associated to imports and exports. Note that for imports, we multiply by M1(1)/Mz1(1) because the share of activity associated to z1 export (trade(z1,z)) is expressed as faction of z1’s GDP.

(4)    The energy need Nz(e,y) is deduced the raw demand through substitutions using Tr(e1,e2,z) which is the percentage of the consumption of energy of type e1 for zone that has been moved to energy e2. This function is computed in M3.

(5)    Last, the actual “net” demand Demand(e,z,y,p) is a parametric function of the sell price p. The energy need is reduced by the cancellation factor associated for each zone to a price p. The sell price is augmented by the current level of CO2 tax in zone z at time y.

(6)    By construction, demand and supply are two respectively decreasing and increasing monotonic functions, so the sell price may be set as the unique value for which supply matches demand.

(7)    Once the price is setup, we can compute both the production capacity for year y (notice that M1 uses the capacity at year y-1 for the supply function) and the actual production Oe(y)

These equations used additional parametric functions that represents the “known unknowns” associated to M2. Once again, the first four functions names are in bold to indicate that they represent the “belief” associated to “energy consumption”.

•       cancel(z,p): share (percentage) of economy for zone z if the oil price equivalent reaches p

•       impact(z,p): associated impact on GDP (output of the remaining activities) when price is p

•      margin(z,p): impact on profits for remaining activities of zone z (i.e., those that are not cancelled) when oil-equivalent price is p

•       dematerialize(z,e,y): expected decline in energy density (GDP/consumption) for zone z. This is the sum of two component: an input parameter (belief) that describes the expected decline in energy density based from past observation, and savings(z,y), a share (percent) of energy that can be saved (efficiency) with iso-output for zone z at year y (a political decision for each zone, triggering the associated investments).

•   population(z,y): expected population of zone z at year y

•       pop2energy(z): ratio between energy consumption growth and population growth

•       CarbonTax(z,y): carbon tax set up in zone z in the year y