The Stock Market in the Overlapping Generations
AbstractThis paper studies a simple OLG model with production under the assumption that capital investment is completely irreversible: installed capital cannot be transformed back into consumption good nor transferred from one firm to another. Since firms cannot be dismantled at each generational change without loosing their value, their ownership is transmitted from generations to generations through a stock market. The paper shows that the financial price of a firm can be lower than the replacement value of its capital without creating arbitrage or dampening the incentives to invest. This possibility changes the long-run behavior of the equilibrium, but only for economies with under-accumulation. In the stock market dynamics these economies have two steady states, the Diamond steady state and the Golden Rule. The Diamond steady stable is locally saddle-point stable and can be reached by only one trajectory on which the financial price and replacement value of firms coincide at all times. All other trajectories on which there is a discount on equity converge (when they converge) to the Golden Rule which is locally stable: the discount on equity has the same effect as an increase of the savings of the young, which lowers the interest rate, and increases investment and wages at the next generation, a virtuous cycle which leads to the efficient long-run steady state. On all these trajectories the equity prices are larger than the fundamental value of future dividends and thus include a bubble component.
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