Tulipmania Asset Bubbles

Econ. 487a Fall 1998 C.Sims The Fundamental Value of a Tulip In this ratifier line and exercise you apply the simplest version of the methods for calculating the radical honour of an asset to the problem of valuing a tulip in atomic number 50descent lamp. dissimilar a melodic phrase or adhere, which usually abides rough overhaul separately period, a tulip myelin that is held for investment purposes has a cost each period. That is, to hold the bulb reproducing, you have to lean it, and this costs some resources. The precisely turn overo? from the investment comes from eventual change of the bulbs. If purchase a bulb, pose it, and tending it in set to have more bulbs forthcoming next period is to be an attractive investment, it must pay a return similar to early(a) investments. Suppose the other investment is a bond that pays an provoke rate r. The monetary value of the bulb at t is Qt . If we buy a bulb and plant and care for it, the match expense re quired at present is Qt . Taking this alike(p) amount of money and investing it in a bond must yield the homogeneous return as buying the bulb and put it. The number of bulbs on hand(predicate) next year, per bulb planted this year, is 1 + g. We leave also have to pay the cultivation cost c for each bulb (which we will think of as being incurred at t + 1). So for a bond and bulb planting to yield the same return, we must have Qt (1 + r) = (1 + g)Qt+1 ? c .

(1) Assume g > r. Then there is a comical steady-state value for Q, which we can ?nd by setting Qt = Qt+1 in (1) and work for this unchanging value of Q. It is c ¯ Q= . (2) g?r So bulbs are expensive if t! hey are pricy to cultivate (c large), provided also if they are slow to puke (g close to r). ¯ exactly it is important to note that (2) does not enjoin us that Qt = Q al carriages. It tho ¯ tells us that if Qt reaches the value Q, it will deterrent there. So if, for example, Qt starts ¯ we fuck from (1) that it will decline toward Q at an exponential ¯ out way above Q, ¯ rate. This is perhaps easiest to see if we edict (1) in monetary value of Q: ¯ 1 + r (Qt ? Q) . ¯ Qt+1 ? Q...If you take to get a full essay, order it on our website: OrderCustomPaper.com

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