Does it imply that the solution to the optimal growth

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Consider the expanding input variety model of Section 13.1. Show that it is possible for the equilibrium allocation to satisfy the transversality condition, while the optimal growth path may violate it. Interpret this result. Does it imply that the solution to the optimal growth problem is less compelling? Show that when the condition in Proposition 13.3 is satisfied, the optimal growth path satisfies the transversality condition and yields a finite level of utility for the representative household.

Proposition 13.3

In the above-described expanding input variety model, the decentralized equilibrium is always Pareto suboptimal. Moreover, provided that (1- θ)η(1- β)-1/ββL , starting with any N(0) > 0, the Pareto optimal allocation involves a constant growth rate of

which is strictly greater than the equilibrium growth rate g∗ given in (13.20).

Reference no: EM131135714

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