lecture11

# lecture11 - Lecture XI Economics 202A Fall 2007 Now we are...

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1 Lecture XI Economics 202A Fall 2007 Now we are going to continue to review the usefulness of probabilistic systems such as we saw in the last class in Miller & Orr. Let±s re-begin where we ended last Thursday. I am going to go over the use of Miller & Orr in my own article, ²Irving Fisher on His Head.³ I want to show you that the Miller and Orr model helps us understand the effects of both fiscal and monetary policy. I will begin by discussing some concepts in inventory models of the demand for money. The Miller and Orr model also gives us a convenient way to categorize all standar d models of the demand for money. Those models are inventory models of the demand for money. They can all be written in the form L = L(P, S) where Miller and Orr suggests three bits of terminology. P = autonomous payments flows S = monitoring rules whereby bank accounts are monitored to prevent them from having too high or too low a balance An induced payment is a payment in application of the monitoring rule. Let me illustrate these three bits of terminology in the context of standard models of money demand. Example I. In the standard monetarist story of Irving Fisher persons receive money in their bank account. The flows are proportional to income: T = k T Y. On average these receipts are kept for a period of 8 . Let±s consider an example with some numbers.

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2 8 , the period that receipts are retained is, say, two weeks, or 1/26 year. 8 = 1/26 k T = 10. The ratio of transactions to income is 10. I take this number from the actual ratio of check clearances to income. In this case M = 10/26 Y. Now let&s try to classify the terms in this example. 1. In this example the autonomous flows are k T Y. 2. The monitoring rule is the average lag of two weeks between inpayment and outpayment. 3. Induced payments are the payments made on application of the monitoring rule. Example II is the Baumol-Tobin model. Autonomous payments are the periodic inflow pX. The monitoring rule is: when the bank account has reached the level (1/n*) pX it should be emptied , where n* is the optimal number of transactions per period. Example III is Miller and Orr. autonomous payments flows are: with probability p: gain \$1 with probability q: lose \$1 monitoring rule: if the bank account hits an upper threshold h, buy interest-bearing securities in amount h - z.
3 if the bank account hits the lower threshold of 0, sell securities in the amount z . Most theories of the demand for money say: L = L(P(Y), S(Y, r)) where P are autonomous payments flows and S is the monitoring rule. The following is the most important folk theorem of the demand for money. This is what people&s intuition tells them. If the monitoring rule is constant and income changes, the demand for money will change proportionately, or The implication of this is the belief that the short-run demand for money is proportional to income unless there is a rapid response of the monitoring rule to changes in interest rates or income.

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lecture11 - Lecture XI Economics 202A Fall 2007 Now we are...

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