I have the concept of money multiplier nailed down. To summarize, M = C + D, where C=cD so M = (1 + c)D B = R + C, where R=rD so B= (r + c)D M = [(1+c)/(r+c)] x B So here’s my question: According to the example given in figure 7 on page 369, we figure that the multiplier is 2.5. So a $100,000 increase in additional reserves results in $250,000 of new money. The currency drain was given as 50% (c=0.5). So, solving for C=cD, where M = cD + D, or M= D(1 + c), we divide M by (1 + c). With numbers, 250,000/1.5 = 166,667. Subtracted this figure from 250,000 and we end up with currency, C, of 83,333. Fair enough. But here’s where I’m getting stumped. On the second paragraph of page 369, we have the following: “The magnitude of the U.S. money multiplier depends on the definition of money that we use. For M1, r=0.08 and c = 1.06, so the money multiplier is 1.8. For M2, r=0.01 and c = 0.12 so the money multiplier is 8.6. That is, in the United States, a $1 million increase in the monetary base brings a $1.8 million increase in M1 and an $8.6 million increase in M2. Currency increases by $930,000 and bank reserves increase by $70,000.” How do we get the figures $930,000 and $70,000? What is this based off of, M1 or M2? If it’s M2, why is it when I divide $8.6 million by 1.12 and subtract the result from $8.6 million I end up with 921,428? Any input would be appreciated.
Does your question amount to why when you use 3 significant figures you get an answer which is $921,428 (i.e. 6 sig figs) while the book gets $930,000 (i.e. 2 sig figs)?
I guess my question is, did the author just arbitrarily round this figure? If so, it’s no big deal, except for the fact that I spent 20 minutes last night scratching my head staring at that page wondering how the author arrived at the figure of 930,000. This wouldn’t be the only time I encountered subjective rounding by the author. For instance, on page 399 (reading 26) the author states “Brazil’s president…struggled to contain an inflation that hit a rate of 40 percent per month–or 5600 percent per year.” When converting the nominal rate (40%/month) to an effective annual rate, you get the following: (1.4)^12 - 1 = 5569.39%. Like you said, perhaps the author just felt like rounding up to 2 siginificant digits.