Tulipmania Asset Bubbles

Econ. 487a

Fall 1998

C.Sims

The Fundamental Value of a Tulip
In this subscriber line and exercise you apply the simplest version of the methods for calculating the fundamental honour of an asset to the problem of valuing a tulip incandescent lamp. Unlike a melodic phrase or bond, which usually abides some overhaul separately period, a tulip bulb that is held for investment purposes has a cost each period. That is, to hold the bulb reproducing, you have to tend it, and this costs some resources. The precisely payo? from the investment comes from eventual sale of the bulbs. If buying a bulb, pose it, and tending it in order to have more bulbs forthcoming next period is to be an attractive investment, it must pay a return comparable to early(a) investments. Suppose the other investment is a bond that pays an interest rate r. The monetary value of the bulb at t is Qt . If we buy a bulb and plant and care for it, the total expense required at present is Qt . Taking this same amount of money and investing it in a bond must yield the same 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 will 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 solving 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), but also if they are slow to puke (g close to r). ¯ But it is important to note that (2) does not enjoin us that Qt = Q always. It only ¯ tells us that if Qt reaches the value Q, it will deterrent there. So if, for example, Qt starts ¯ we know 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: Ordercustompaper.com



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