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Micro–Macro Integration — A Unified Economic Theory

How the CDR macro growth model integrates with the micro-economic Cobb-Douglas production function

Learning Objectives

  • Explain the fallacy of composition that prevents a simple aggregation of micro production functions into a macroeconomic aggregate
  • Describe the conformal mapping from macro CDR space to micro Cobb-Douglas units
  • State the global monetary value of production formula integrating CDR with micro production across m countries

Why No Aggregate Production Function Exists

A production function Q=f(K,L) relates physical inputs to physical outputs from a single machine. There can be no macroeconomic production function when inputs are different types of items or outputs are made by different constructs (Cohen & Harcourt, 2003). The CDR model sidesteps this: G=f(C,D,R) is defined at the aggregate without requiring aggregation from micro units. It then maps conformally into micro domains where Cobb-Douglas is valid for each single production unit.

The Integration Formula

For m countries, each with ni micro production units, total global output is:

Global Monetary Value of Production
Σi=1m Σj=1ni Aij {fij[f(Ci,Di,Ri)(Gmax−Gmin)+Gmin]}αij · Wij(1−αij)
Aij is total factor productivity for micro unit j in country i; αij and (1−αij) are the output elasticities of capital and labor respectively. The inner bracket recovers the country's actual GDPppp from its standardized g = f(C,D,R) via the inverse transform used throughout this app. This homeomorphic mapping preserves economic relationships across scales, letting each individual firm's Cobb-Douglas production sit inside the aggregate CDR-determined wealth ceiling for its country.

Brain & Brawn Framework (Figure 2, P4)

The wealth creation diagram distinguishes: BRAIN (conceptual wealth: new human capital ideas + market capitalization C = new + capital stock) from BRAWN (physical production: distribution via fij·Li → micro production process f(kij,Wij) → realized wealth aggregate). CDR G potential (macroeconomic) is the bridge connecting intellectual source to physical output.

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Figure 2 (P4) · Brain / Brawn Wealth Creation Diagram
Two-track flow: BRAIN (entrepreneurship + capital stock → C) feeding into macro CDR G-potential; BRAWN (labor W, wage rate, physical production units) realizing that potential at the firm level via Cobb-Douglas f(k,W). Diagram not yet rendered — see P4 Fig. 2.
Sources
P2 · Appendix F: Integrating CDR macro with micro production function, pp. 20 P4 · §2 Supply-side wealth (Brain/Brawn Fig.2), §3 Structures of CDR (endogenous/exogenous), pp. 3–6 P3 · §Discussion (production function fallacy, plus-sum capitalism), p. 15