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In the description of so-called money market, we have demand,Md, for liquid money from individuals (and firms) and supply,Ms, of liquid money, likely from central banks. Now it is assumed that if interest rate,r, would increase, the demand for money,Md, would decrease due to people's preference of bonds(or other high yield securities) over money at high interest rate.

This doesn't make sense; whereas it is true that "households" would buy bonds in exchange for money at higher r, bonds are simply transfers of money, from households to firms or governments. So the aggregate money in the economy remains constant, as firms/governments would utilize the bonds' money in the economy. Thus, if we consider the economy as a whole, the "demand" for money does not change with people opting for bonds.

If we only consider the households' demand for money, then the analysis in money theory and LM curve would be inaccurate; In the discussion of LM curve, we have MV=PY and M/P =Md(Y,r). M/P essentially denote the "real money" supply from central bank. In the first formula MV=PY derived from money theory, If M/P hold constant, Y, also known as the aggregate income, is also constant; This is consistent if we consider the economy as a whole. However, in the second formula, It is understood that the money demand Md(Y,r) account for only the "households". It is unreasonable to discuss the dynamic between money supply and money demand when we have the whole economy in consideration on one hand and have only a sector of the economy weighted on another hand.

To sum up, I can understand that higher interest rate could encourage people to save up, thus effectively reduced the amount of money in circulation so reducing the "demand" but I do not see how opting for bonds decrease the demand for money unless only a sector of the economy is taken into consideration. Can someone provide some insight into this?

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There are a few sub-questions in this question, and I will not attempt to answer all of them. These “economics 101” models are extremely abstract, and it takes a lot of effort to relate them to observed economic behaviour. (I worked in fixed income research for 15 years, and cannot recall industry research ever referring to them.)

“Households” stand in for the entire private sector. (In these models, firms’ financial asset holdings are normally assumed to be zero, as otherwise, they would also have to solve a multi-period optimisation to maximise profits. This breaks the models, as there are then two sectors with competing multi-period optimisations.)

Financial assets are issued by the government sector (Treasury/central bank), although the models may allow reverse borrowing by households by allowing them to have negative bond holdings (which little literal sense in the real world).

Since you asked about it in comments, I will add some details to the institutional structure. In these models, like in the real world, the Treasury is the financial arm of the government. (In some countries, labelled the Ministry of Finance.) It owns the central bank, and leaves its cash on deposit at the central bank. Since this deposit is a liability between two related entities, it does not show up in the money supply numbers. If we consolidate the accounting, the deposit is money the entire government owes to itself, and so it disappears from the balance sheet. And to repeat: this is not just a model simplification, it is how real world statistical agencies do the accounting for the money supply. Note that governmental liabilities are only the narrowest components of the money supply (“M0”), wider aggregates (“M3”) include private sector instruments - which do not appear in this class of models.

The household money demand equation is just a portfolio allocation decision: given a portfolio size, what is the breakdown between money and bonds? The greater the interest rate, the greater the percentage held in bonds.

The central bank is the counterparty to the household sector portfolio decision. When it buys bonds, money returns to the central bank. Since money is a liability of the central bank, it does not hold it as an asset, so the money is “destroyed” - the stock of money contracts.

The money cannot go to the Treasury or firms, since the model construction does not allow for it.

This site wants to keep opinions out of answers. However, it is clear that there are a lot of issues with how (neo-)classical models handle “money”, as most “money” (broad money supply aggregates) are private sector liabilities (e.g., bank deposits). There is a large post-Keynesian literature on money and finance, the key words to look for is “endogenous money”. These critiques of the classical models might help you relate them to real world behaviour, as the post-Keynesians like to explain the deficiencies of the classical models. I cannot think of any immediate reference, but you could search. In anymevent, it would be easier to find an existing critique than attempt to re-invent your own monetary theory.

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  • $\begingroup$ Hi Brian, thanks for the insight but I still can not explicate this process,or I have a different understanding of this process. I am aware that the central bank can issue bonds , thus effectively reduce the real money supply, and I also have no issue with the assumption that firms have 0 financial holding. If the central bank is the only entity who can issue bonds, I would not have a quarrel with the model. $\endgroup$ – Luminia Qs Apr 19 '18 at 15:28
  • $\begingroup$ since in this case, central bank can "sell" bonds or "buy" money at the "price" of a higher interest rate. In this case, the cause is the central bank's willingness/involvement to reduce M/p, the real money supply and the increase in intrest rate is only a method by which the central bank can manipulate money demand and ,indirectly, money supply. So if interest rate is raised in this way, the aggregate money supply, or M/p, must decrease. This reflects well in the market equilibrium forumla M/p=Md(Y,r). $\endgroup$ – Luminia Qs Apr 19 '18 at 15:29
  • $\begingroup$ However, central bank is not the only entity who can issue bonds and neither is it the only source of causes for increases in interest rate. If central banks are not involved, then the bonds are issued by firms or government and the interest rate can still effectively increase due to increase in the influx of more bonds relative to money. In this case, bonds only function as a money transfer within the private sector, matter not if the financial holdings of firms are 0; It is unequivocally true that your loss of money is someone-else's gain of money. $\endgroup$ – Luminia Qs Apr 19 '18 at 15:29
  • $\begingroup$ So, in this case, interest rate has no correspondence,negative or positive, with the aggregate money demand. In fact, changes in interest rate would affect Md(Y,r) if and only if the central bank is the entity who elicited these changes. $\endgroup$ – Luminia Qs Apr 19 '18 at 15:29
  • $\begingroup$ It it not impossible to come up with this example. Imagine John is a fervent money lover and he just want to keep money piled in his backyard. So he issued high interest bonds, assume he somehow miraculously allowed to do so; So the interest rate in the money market increased but the total money demand remains constant because John himself is also a constituent of the private sector. $\endgroup$ – Luminia Qs Apr 19 '18 at 15:29
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One thing to consider is that, when the Federal Reserve in the United States tries to manipulate the money supply, it does so through either putting more of its money into the market through bond purchases (supplying banks with money to lend) or holding money from the market through bond sales (leaving the money essentially dormant). It is not so much that bond creators receive money when people turn to bonds with higher interest rates but rather that the bonds change hands to people (households, firms, banks) who would have actually circulated money in some way if they held it in liquid form. The missing link is the central bank's money holdings.

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  • $\begingroup$ Hi thanks for the insight. I am aware that the central bank can manipulate the money market; in fact it is them who supply the real money, M/P, to the market. However, it would still not explain why the money demand, Md(Y,r), is inversely related to r, which is the interest rate. As far as I can tell, the interest rate will only reduced the money lay dormant in the hands of either households or firms. $\endgroup$ – Luminia Qs Apr 19 '18 at 4:44
  • $\begingroup$ in other words, the total money demand has two aspects: Me, denoting the money in circulation and Ms,the money in dormant. Clearly, Me is positively related to Y, GDP, as the increase of productivity spike the amount of transaction ,and Ms is negatively related to interest rate as higher interest rate would encourage people opting to bonds, so that the debtor would invest the money from bond sales into circulation. $\endgroup$ – Luminia Qs Apr 19 '18 at 4:58
  • $\begingroup$ The key point is that even if Ms decreases because of bond sales Me would most like increase from these sales, as bonds only function as a money transfer in this sense, so the aggregate demand Md(Y,r) remains constant. Then although interest rate is inversely related to Ms, it does not imply Md(Y,r) is inversely related to interest rate as well, unless we define Md as Ms. $\endgroup$ – Luminia Qs Apr 19 '18 at 5:02
  • $\begingroup$ If we do not complicate the issue and just analyze the impact of Y,GDP, on interest rate, It is clear that if money supply is kept at constant, an increase in Y will result an up in Me and thus less Ms for bond trading; This effectively increase the value of money and thus increase the interest rate. This is, in my opinion, the natural or reasonable way of interpreting the LM curve but all the literature I found invariably claim a negative relationship between Md and r which makes no sense to me at all. $\endgroup$ – Luminia Qs Apr 19 '18 at 5:14

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