Emergent properties and Energy in Economics

Stymied by stylized facts Four unsolved anomalies for mainstream economics Rise in inequality Financial crisis Preceded by “Great Moderation” Slow growth after it Easily solved by system dynamics/complex systems approach Describe fundamental structure of the system Postulate simplest possible relationships between entities in system See what happens… Define Employment Rate, Wages Share, Debt Ratio, Productivity, Profit, Profit Share

Explained by simplest possible dynamic monetary model Differentiate system states with respect to time: “Employment will rise if economic growth exceeds the sum of population & labor productivity growth” “Wages share of output will rise if wage rise exceeds growth in labor productivity” “Debt ratio will rise if debt grows faster than GDP” Add simplest possible relationships between system states

Explained by simplest possible dynamic monetary model Results in simple 3-dimensional model Moderation then crisis Simulated as ODEs in Minsky: And a second outcome with stylized characteristics just like those mainstream “anomalies” Inequality Crrisis

Explained by simplest possible dynamic monetary model Same model in system dynamics form:

Where did economics go astray?: History Energy absent—or effectively non-essential—in all current models of production Marxists: Labor theory of value Surplus derived from & proportional to labour input Neoclassicals: Output by substitutable “factors of production” No Energy input No Energy input No Energy input Post-Keynesians: Output by fixed proportions Kummel-Ayres LINEX: Substitutable “factors of production” including energy Energy input, but… Could hypothetically set Energy input to zero & still get output Independent Labour & Capital inputs imply they can function without energy…

Where must economics start?: Energy & Thermodynamics Concept of labour and capital without energy is absurd Labour without energy is a corpse Capital without energy is a sculpture Think of them instead as means to harness “free” energy And think of GDP as “useful work”. Then we start with All measured in energy terms: megajoules Actual work by capital & labour depends on Number of units of L (unskilled workers) and “K” (machines) Flow of energy/time (E) harnessed by L and K Ratio (x<1) of energy available for useful work(Exergy, Ex) to energy (E) Efficiency (e<1) of use of exergy

Where must economics start?: Energy & Thermodynamics In multiplicative constant returns to scale form: Rearranging: Components: Units of capital & labour as in standard CDPF Energy parameters for Labour: EL say 4000 calories/day xL say 0.5 eL say 0.5 Effectively a constant  1000 Raised to a power Energy parameters for Capital: EK (Energy consumption per machine per day) has risen exponentially over time xK & eK time-varying but maxima below 1 Raised to a power

Where must economics start?: Energy & Thermodynamics Final formula is Compared to Cobb-Douglas Production Function “Solow Residual” is energy converted to useful work by machinery Compared to Kummel-Ayres in CDE form Can be put in output per worker form, unlike Kummel-Ayres function: Can also relate output per head to “useful work by machines” per head a a scaling factor, rather than statement of “marginal productivity” Can remove “K” & use measured energy consumption by industry Total energy consumed by industry is an empirically known quantity Substitute to yield

Where must economics start?: Energy & Thermodynamics Energy-substituted equation is Putting this in per capita real income form yields: Energy per head; trend Employ-ment rate; cyclical GDP per head; cyclical trend Data exists for GDP per head, employment rate (l) & energy per head But not (time-varying) exergy-energy ratio or efficiency…

Introducing energy into a dynamic model Cobb-Douglas form still implies unrealistic substitutability of Labour & Capital Can instead modify Post Keynesian relations… From To

Introducing energy into a dynamic model Machinery as way of harnessing free energy to do work Labour hired proportional to energy Could also model investment as accessing proportion (<100%) of current capability to exploit energy