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First, let me address some incorrect premises in your question Usually economists say that in recession there is deflation, so increasing the money supply does not lead to high level of inflation. This statement is not really correct. First, I dont know many economists who would say that usually recessions are deflationary. For example, according to Romer'...

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It would seem logical that this would result in reverse-inflation or lower prices, but this is actually not the case (at least over time). The banking system has a "supply and demand" market for reserves. When say 1 million dollar is withdrawn and not redeposited, the banking system in the aggregate will bid more for current reserves to replace the ones ...

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Well you do not provide any source for the $dM+dV = dP+dY$ so it is hard to say why someone written that. That is certainly not normal total derivative of QTM. You are right that the correct total derivative of QTM will be given by: $$VdM+MdV=YdP+PdY$$ Possible explanation why you saw it somewhere written differently: Note the above can be divided by $MV=... 3 You're getting two quite different concepts mixed up: Banks earn a spread on loans for serving as an intermediary between savers and borrowers and for holding credit risk. The process of borrowing and lending, of banking, leads people in an economy to have more liquid assets (money in a broader sense), than there is underlying cash. When economists say ... 3 Credit cards are a way of deferring payment in the form of inter-temporal substitution; it helps reduce the household's liquidity constraint that may prevent it from consumption smoothing as much as they would like if their transitory income was much more spread over the household's lifetime. You are right that the amount of money doesn't change. Loans ... 2 The money supply expansion mechanics are interesting, but do not affect loan pricing. Let’s assume that the only assets a bank invests in are loans it extended, and required reserves at the central bank. Furthermore, assume that the rate of interest on required reserves is 0%. We will assume that bank equity is extremely small (close to the truth), and the ... 2 Taking logs of the equation$MV=PY$gives:$ln(M) + ln(V) = ln(P) + ln(Y)$. Next, differentiating with respect to time yields$\frac{dln(M)}{dt} + \frac{dln(V)}{dt} = \frac{dln(P)}{dt} + \frac{dln(Y)}{dt}$. Or, using$\frac{dln(X)}{dt} = \frac{\dot{X}}{X}$, with$\dot{X} = \frac{dX}{dt}$, the derivative of a variable$X$with respect to time, you can ... 2 As I noted in a comment, the description in this question of real world central banks is overly simplistic. Central banks do not make proportional changes to the monetary base to set the price level. However, I will ignore those problems, and just address the core of the question: 1) Will it make sense to change account balances on a pro rata basis to keep ... 2 In the chapter 4 of the graduate textbook Lectures on Macroeconomics there is "The Overlapping Generation with Money". In that case we have a model which is microfounded (i.e. accounts for how our consumers interact with money on the microeconomic level). This is essentially an explanation of Paul Samuelson's 1958 "consumption loan model". You can find a ... 2 M * V = P * Y is not in a form of growth rate, so it needs to be changed into ΔM + ΔV = ΔP + ΔY Because V is constant, then 14 + 0 = ΔP + 5 ΔP = 9% ΔP = Change in price = inflation 2 Money demand is fixed because it depends on the real economy....that's an assumption. So when M changes only P can change. That's the theory. It's not really a theory. Just an accounting equality, since V is never defined exogenously. It's bad economics. :/ 2 The question as currently stated is too long, and contains misleading statements. I will answer the core of the question, which I believe is as follows: why don’t countries use “helicopter money” to replace incomes? (“Helicopter money” is the act of the central bank directly handing out money to households to stimulate the economy.) The answer to that is ... 2 Velocity of money is according to the Fed definition: The velocity of money is the frequency at which one unit of currency is used to purchase domestically- produced goods and services within a given time period. In other words, it is the number of times one dollar is spent to buy goods and services per unit of time. Hence paying taxes/transfers is not ... 2 It is rather other way around. We want to target about$2\%$inflation and to do so money supply should expand faster than real growth. Also, the$2%$target is not commonly interpreted as a target that has to be kept all the time. For example, as explained in this Brookings blog many central bankers advocate targeting the$2\%$over business cycle. During ... 2 There are multiple answers to this question. In any model you can always make a thought experiment where you hold certain variables fixed. So one answer, although not very satisfying one, is that you can view it as a thought experiment. For example, in physics distance traveled equals velocity times time or$D=tv$and you can always make a thought ... 2 Well first if actually the cryptocurrency we are talking about would be created by central bank, then the rules that were used to create it would be by definition monetary policy even if supply of money would be fixed, since monetary policy is central bank’s control of money supply either directly or via interest rate (see Yeyati, Sturzenegger (2010), or ... 1 The two series are linked by an accounting identity, which is why they tend to move together closely. There’s no theoretical limit to how much larger assets can be than the monetary base, though. If you look at the two tables in the H.4.1 Release, you’ll see that the first table is basically the Fed’s assets (what you refer to as its “balance sheet,” but in ... 1 The money supply is in theory interpreted broadly so from that perspective$M2$or even$M3$would be more appropriate. Also empirical studies in this strand usually use$M2$see for example Sargent and Surico (2011). However, you should note that nor the quantity theory of money nor monetarism claims inflation can be predicted solely by change in money ... 1 You may be confusing money velocity with money supply. From Wikipedia, the velocity of money is "measure of the number of times that the average unit of currency is used to purchase goods and services within a given time period." There is indeed more M2 than M1 but the velocity of M1 is often higher than that of M2. The shared portion of M1 and M2 will have ... 1$M\cdot V=P\cdot Y \Leftrightarrow M=\frac{P}{V}\cdot Y\\ \frac{1}{V}=k \Leftrightarrow M=kPY$So suppose we keep$V$and$Y$fixed and vary$M$,$P$varies as well and this means$kPY$also varies (because of P). More specifically when money supply goes up while keeping velocity and output constant, the price level has to rise,(raising money demand to equal ... 1 If one believes that there is a single equilibrium, and that markets will find it whatever the starting position, then money must be neutral in the long run. A monetary intervention, in that world, is a temporary perturbation that will get traded away to zero eventual impact, as everything returns to equilibrium. It is likely that neither of those ... 1 There are multiple ways that a central bank can resort to apply its designated monetary policy. The most common one is called "open market operations (omo)", which is basically selling/buying government securities to/from private individuals or organizations. Through these operations, central bank affects the level of cash reserves in the banking system ... 1 I will try to explain this through ISLM model. Consider you are an employee working for the government and earn \$1000 per month. Government follows expansionary fiscal policy and increases your pay to \$1500. Your purchasing power increases by \$ 500 when prices are held constant. This increase in your income will translate into money demand because ...

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Even in simplest of models I don't think it is enough info to constrain the fx rate. Even if velocity can be worked out we can't get m0. In the simplest model all islanders are equally capable or some equilibrium arises where everyone gets the same proportions of resource. Then if resource x has $a$ units per person and total of all resources or sum of all ...

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The velocity should just be the amount of times the average unit of currency exchanges hands per year. That is $10$ if we take the highest possible number. Money supply is $100$ units of island currency ($IC$), so that the left side of $$MV=PY$$ turns into $100*10$ Nominal GDP, so $YP$, is \$$100 per Islander, or$$\$100/XR*n$$in$IC$, where$XR$... 1 The level of a price index (like the GDP deflator) is essentially arbitrary. The usual choice is to set the reference date to 100, but it could just as easily be set to 1. So the level of the real money balance is essentially an arbitrary number. If you were using it in an economic model, you would need to adjust the scaling in the functions to account for ... 1 You may have misunderstood the endogenous money-creation argument. The endogenous money growth theory is a useful explanation of how monetary expansion works: but note that it describes the aggregate effect across the whole banking system; not the effect within a single bank. When a bank takes deposits of 100, it can't lend more than that. Indeed, because ... 1 Amongst central bankers there is no controversy, the money multiplier is plain wrong, see this definitive paper from the Bank of England here. So assuming that loans create deposits... Imagine a bank lends (i.e. creates) 1000 dollars for person A to buy second hand car from person B (for simplicity imagine they both are customers of the same bank). Person ... 1 Assume there are two agents in an economy,$A$and$B$, (and some costless transaction mechanism). Per time period, agent$A$produces alone quantity of intermediate good$q_A$. Agent$B$, thorugh a company where it is shareholder, buys this quantity, the company inputs also some other intermediate good , say$q_B\$, and the two together through a production ...

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