# Maximization of Bequests: The First Turnpike Theorem

# Maximization of Bequests: The First Turnpike Theorem

The conditions for the Golden Equilibrium have been established earlier in the book and this chapter turns to an examination of the economy for stability; it asks whether a Hicks–Malinvaud competitive equilibrium trajectory starting from the historically given initial point approaches nearer and nearer to the state of Golden Equilibrium when the order of the path gets larger. This problem, which amounts to asking whether an economy obeying the principle of competition can attain a Golden Age, is discussed repeatedly in this chapter and the following one. Convergence of this sort will be compared with another kind of convergence recently dealt with by many writers under the common heading of Turnpike Theorems, particular applications of which may occur in more or less planned economies but not in purely competitive economies. In this chapter, the simple case of ‘L‐shaped’ indifference curves is examined. The different sections of the chapter compare the Hicks–Malinvaud equilibrium trajectory (Hicks–Malinvaud equilibrium growth path) with the DOSSO‐efficient path, discuss the Final State Turnpike Theorem, offer a proof of the theorem by the *jyoseki* (a formula in the game of *go*), present a lemma by Gale, discuss the convergence to the Turnpike, discuss *yosses* (the final part of a game of *go*) of the proof and cyclic exceptions, and look at the tendency towards the Golden Equilibrium of a competitive economy with no planning authorities.

*Keywords:*
competitive economies, competitive equilibrium, convergence, DOSSO efficiency, economic growth, equilibrium growth, Final State Turnpike Theorem, First Turnpike Theorem, Golden Equilibrium, J. R. Hicks, Hicks–Malinvaud equilibrium growth path, L‐shaped indifference curves, E. Malvinaud, maximization of bequests, planned economies, stability, Turnpike Theorems

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