Tulipmania Asset Bubbles

Econ. 487a Fall 1998 C.Sims The Fundamental Value of a Tulip In this lector line and exercise you apply the simplest version of the methods for calculating the important honour of an asset to the problem of valuing a tulip in abidedescent lamp. contrasted a melodic phrase or hold, which usually abides close to 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 break a itinerary it, and this costs some resources. The precisely put upo? from the investment comes from eventual bargain of the bulbs. If buy a bulb, pose it, and tending it in battle array to have more bulbs forthcoming next period is to be an attractive investment, it must pay a return corresponding to early(a) investments. Suppose the other investment is a bond that pays an pursuit rate r. The monetary value of the bulb at t is Qt . If we buy a bulb and plant and care for it, the suppl y expense required at present is Qt . Taking this said(prenominal) amount of money and investing it in a bond must yield the alike 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 result 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 declaration for this unchanging value of Q. It is c ¯ Q= . (2) ! g?r So bulbs are expensive if they are pricy to cultivate (c large), precisely also if they are slow to puke (g close to r). ¯ moreover it is important to note that (2) does not enjoin us that Qt = Q always. It but ¯ tells us that if Qt reaches the value Q, it will deterrent there. So if, for example, Qt starts ¯ we get along 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 terms of Q: ¯ 1 + r (Qt ? Q) . ¯ Qt+1 ? Q...If you take to get a full essay, order it on our website: BestEssayCheap.com

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