NOTICE
- DO NOT TRUST THE FOLLOWING
MOTIVATION
- Existence of Walrasian equilibrium manifold depends on continuous contraction mapping in n-space of goods with non-negativity of price and quantity
- Think in n+1-"spacetime" and see evolution along time or convergence to above manifold at a point of Ramsey's "bliss"
CONTINUITY OF TIME
- I mean dt/dx in n+1-spacetime, or in adequately blown-ups of such spacetime
- In other words, regularity of stochastic process
- In other words, completeness of expectation
- (added) dynamic constraints like transversality and no Ponzi game must be related to continuity of time
PROBLEM OF JUMP VARIABLES AND DIVERGENT PATH
- "Walrasian equilibrium" in spacetime needs continuity of time
- If no continuity of time is assured, generally divergent paths exist
- ex-ante vs ex-post (realized state of economy is always continuous evolution of the past in ex-post)
- how we treat ex-ante irregular changes as extra dimension added to continuous economic spacetime?
STRATEGIC FOUNDATION OF ECONOMIC DYNAMICS
- existence of pay-off in infinitely repeated games follows from axiom of determinacy (Mycielski-Steinhaus(1962))
- such axiomatics support is really needed? one serious problem is AD contradicts AC so it hurts Walrasian equilibrium thru Uzawa equivalence
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