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Unformatted text preview: Econ 251a Fall 2006 Computing Equilibrium in OLG Economies with Land 1 OLG Economies In real life, the economy lasts much longer than the life of any individual. Indeed many economic institutions survive precisely because they are expected to continue forever. Social security is the chief example. If people understood that there was going to be a last generation, then they would anticipate that this generation would not contribute when it was young, hence that the previous generation would not contribute when it was young, hence that the third to last would not contribute, and so ultimately, that even todays young would not contribute. Maurice Allais and later (perhaps independently) Paul Samuelson invented the overlapping generations model (OLG) to capture this situation. Every period a new generation is born which lives for two periods. Thus at each time period there are two living generations, an old generation and a young generation. A period is thought of as approximately 30 years. Time goes on forever. Allais and Samuelson argued that the in f nity of both time periods and agents radically changed the nature of equilibrium. Samuelson suggested that equilibrium might not be Pareto e cient, and that the real rate of interest might be negative, even if the economy did not shrink over time. They also thought that a second, new kind of equilibrium would emerge in which the real rate of interest is divorced from any of the considerations like impatience that Irving Fisher had stressed. They thought that in this new kind of equilibrium the real rate of interest woud turn out to be equal to the rate of population growth, irespective of the impatience of the consumers or the distribution of their endowments. Furthermore, Samuelson argued that it might not be necessary for an asset to be valued according to the present value of its dividends, contradicting yet another one of Fishers central concepts. Samuelson suggested that a piece of green paper might be worth a lot, even though it pays no dividends, because the holder might think he could sell it to somebody later, who would buy it on the expectation that he could sell it to somebody else later, ad in f nitum. Later authors called this a rational bubble. It turns out that these views are incorrect if one includes in the model in f nitely lived assets like land, that do pay dividends in every period. We shall not discuss this new kind of equilibrium in this chapter, but instead go directly to the overlapping generations model with land. Overlapping generations economies give us the opportunity to study how long- lived assets get priced in a world of certainty in a simple setting. With many periods, one would typically have to calculate equilibrium prices for every time period, which might get too complicated. But with OLG economies, we can assume a stationary stucture, with not only the forward rates, but also the asset prices, constant for all time. In a f nite horizon model prices could never be constant over time, because as 1 the end approaches the value of the asset would have to decline (becoming literally...
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