e During the Tulip mania of 1634 7 the price of Gouda tulip bulbs rose

E during the tulip mania of 1634 7 the price of gouda

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e. During the Tulip mania of 1634-7, the price of Gouda tulip bulbs rose approximately sixtyfold over a three-year period and then collapsed to virtually nothing (the fundamental price). What value of 𝜋 in part d. is consistent with these numbers? (Treat a period as a year, the percentage increase in bulb prices between late-1634 and the peak in early-1637 as 6400% and the discount rate, 𝑟 as negligible.) What is the probability of the bubble lasting more than three years? f. What do you think of this explanation of asset-price bubbles? 2 . Pricing a Central Bank Lender of Last Resort facility Suppose banks can fund themselves either with short-term debt that has to be rolled over or with long- term debt that does not. The rate of interest on short debt is 𝑖 ? and the rate of interest on long debt is 𝑖 𝑙 , with 𝑖 𝑙 > 𝑖 ? . There is a probability (1 − 𝜋) per period that a bank will find itself unable to roll its short- term debt (say because some of its loans sour and the bank’s creditors take fright). In that case, it must turn to the central bank for emergency support. The central bank charges 𝑖 ?? on its loans. a. If the central bank announces its lending terms publicly in advance, what rate should it charge if it is to dissuade banks from funding only with short-term debt? Interpret your condition. b. Can you think of reasons why a central bank might not want to pre-announce its lending terms and instead maintain “constructive ambiguity” about the terms on which it will provide assistance? c. Can you think of reasons why a central bank might want to offer different terms if many banks need support than if only one needs it? If so, how would the terms differ? d. Can you think of why there might be a time inconsistency problem associated with announcing the terms in advance?

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