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I remember Robbins asking me if I could turn the Hayek model into math — Equilibrium

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"I remember Robbins asking me if I could turn the Hayek model into mathematics... it began to dawn on me that... the model must be better specified. It was claimed that, if there were no monetary disturbance, the system would remain in equilibrium. What could such an equilibrium mean? This, as it turned out, was a very deep question; I could do no more, in 1932, than make a start at answering it. I began by looking at what had been said by... Pareto and Wicksell. Their equilibrium was a static equilibrium, in which neither prices nor outputs were changing... That, clearly, would not do for Hayek. His equilibrium must be progressive equilibrium, in which real wages, in particular, would be rising, so relative prices could not remain unchange … The next step in my thinking, was … equilibrium with perfect foresight. Investment of capital, to yield its fruit in the future, must be based on expectations, of opportunities in the future. When I put this to Hayek, he told me that this was indeed the direction in which he had been thinking. Hayek gave me a copy of a paper on intertemporal equilibrium, which he had written some years before his arrival in London; the conditions for a perfect foresight equilibrium were there set out in a very sophisticated manner."
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Equilibrium
Equilibrium
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"Maxwell... during the 1860s... showed that when the velocities reached the bell-shaped distribution, no further net change was likely. (...Ludwig Boltzmann further elaborated... and strengthened Maxwells results). Any specific molecule would speed up or slow down, but... other molecules would change in speed to compensate. When a gas reached that state... the gas was at equilibrium. ...[T]his notion of equilibrium is precisely analogous to the Nash equilibrium in game theory. ...[J]ust as the Nash equilibrium is typically a mixed set of strategies, a gas seeks an equilibrium state with a mixed distribution of molecular velocities."
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