M4: World Economy

The world economy model (M4) represents the question “which GDP is produced from a given amount of investment, technology, energy and workforce?”. It works in two steps: it first compute what the GDP could be given enough energy and without dagames, using a classical exponential growth model (as is the case of most earth models) based on productive assets creating value over a unit of time through the use of energy, that may be characterized as inspired by the Robert Solow model (Grandjean, 2024). The exponential growth comes from the fact that a part of the output at time N is invested into adding to the productive assets for the next years, as illustrated by Figure 6. Investments are separated into energy transition investments, which are necessary to perform the transition steps (see M3), and growth investments. The second step takes the energy and global warming consequences into account: the “max theoretical GDP is reduced if not enough energy is available, or if some resources are incapacitated by the catastrophic consequences of global warming (output from model 5). This figure also illustrates some aspects of energy demand shown in M2, namely the influence of population, technology and economic activity. The input loop of “energy demand” represents the positive influence of population growth and technology improvement on economic growth.  

The key variable here is the worldwide GPD, decomposed into each zone’s GDP, measured in constant (2010) dollars. To make the results easier to understand, CCEM also produces current dollars estimates (at an inflation rate of 2% - cf. Section 4.2). Still, monetary values (GDP, as well as energy prices) are to be considered with caution; however, their main role in CCEM is to act as a regulation agent between sub-models, and this works irrespectively of what the value represents (i.e., whatever 500 $/MWh may mean in 2060, what matters is that the economy cannot consume more oil that is available at this time).

 Because GDP as a measure of economic health is often criticized, we have added two material outputs that are reasonably easy to forecast and may act as “proxies” of the material economy, namely steel output and wheat output.Taking steel production into account is a way to capture “raw materials” as a limiting factor for energy transition (Vidal, 2021). As shown in Figure 7, the steel output is derived from iron density (observed through the past decade and defined as a new CCEM “known unknown” parameter). The steel price evolution considers the “energy density” of steel production and the energy price computed by M2.

M4 uses the following state variables to describe the economy system:

•   Mz(y): theoretical “max output” for zone z, that is the “GDP that would have occurred if all necessary energy was here, without global warming impact”.

•               Gz(y): GDP for zone z on year y  (with G(y) = Sz Gz(y))

•   Iz(y): amounts of investments (energy + growth)

•   IGz(y): amounts of growth investments

•   SCz(y): steel consummation for zone z at year y

The logic of M4 can be described with the following numbered equations.     
  

(1)    We first compute the “maximum output” expected from the previous investments. It is the sum of two factors. The first is the value produced by previous assets, adjusted for population growth and reduced by natural decay. As with WORLD3(LtG), we assume a natural decay of productive assets, but we use a much lower value of 2%/year. The second favor reflects the growth of productive assets thanks to (growth) investments, multiplied by a RoI factor that is specific to each zone and varies in time (one of the “input belief”).

(2)    We compute GWDz(y), the loss of productive capacity from global warming impact. Because this value is read from a “belief table” that gives the impact as a fraction of GDP, we multiply by 0.7 to factor in the propagation towards investment (proportional to results, cf equation (6)).

(3)    The population growth is the growth factor (value for year y divided by the value for year y-1) of the population expected at year y in the input table “population” modulo a productivity factor that is derived from the pain lever (cf. M5). This feedback loop may capture multiple effects of disruption onto productive hours of work: disengagement, absence because of catastrophic heat waves or other disaster, social unrest from strikes to larger conflicts. The coefficient that defines this feedback loop is a key parameter for the CCEM model.

(4)    The actual GDP of zone z on year y, Gz(y), is derived from the unconstrained output times the cancelation factor (1 – impactFactor(z) and the tradeFactor (see model M2).

(5) The function impactCancel(z,y) returns the part of the GDP that is not produced when energy is lacking. It is a combination (with weight = alpha(z,y) – the fraction of energy that is redistributed through subsidies) between “a redistribution model” (all activity is equally affected) and a “market model” (where activities that consume more energy per creation of value unit are more impacted by energy price hikes, using the impact(e,p) parametric input defined in M2).

(6)    The new amount of total investment is computed using the previously introduced linear regression and is split between previously computed “energy investments” (to which CO2 taxes are subtracted – see model M3), and “growth investments”.

(7)    Last, we compute the amount of iron that was necessary to produce this GDP, based on expected iron density at year y, as well as the cost of iron (per ton), using the price of energy as a driver, which is itself multiplied by the forecasted energy intensity of steel production at year y (either from digging ore from mines or from recycling).

These equations used additional parametric functions that represents the “known unknown” associated to M4:

•   roi(z,y) : expected return on investment (R/I) = additional GDP expected R for investment I
          in future year y for zone z

•   disasterLoss(z,T) : loss of GDP (%) when temperature raises to T

•   ironDensity(z,y): density of iron in z economy (GDP / Gt of steel)

•   alpha(z,t) : fraction of energy that is “redistributed” with subsidy (versus free market)

•   IRatio(z) : part of GDP that zone z attributes to investments

•   iRevenue(z): share of revenue that is invested

•   energy4steel(y) : energy needed to produce one ton of steel in year y

Let us emphasize the simplicity of the investment model that does not take any “time shifting” into account, such as debt or capitalization for future use. If there is no energy and the activity reduced, the associated investment will be governed by the iRevenue(z) ratio