Therefore increasing the monetary base is a way for the government to get a loan that it will never have to repay and doesn't pay any interest. Indeed, one way to write down the government's budget constraint is: But1 + Port + [MR. - MP] = P.G+ + (1 + it) By (13.5.1) where: . But1 is nominal public debt . Gt is real government spending . it is real government revenue . pt is the price level . it is the nominal interest rate . Me is the monetary base Let's go through the terms in (13.5.1) to see what it means. The right hand side represents all the payments the government must make, in nominal terms. p.G is how much the government mustThis is literally true in some countries and sort-of-true in others. In the US, the Federal Reserve has a mixed governance structure with some influence from the private sector. However, it rebates its profits to the Treasury, so in that sense it's part of the Federal government. If we consolidate the balance sheets of the Treasury and the Central Bank, then the process of money creation looks like this: Before: Central Bank Treasury Consolidated Assets Liabilities Assets Liabilities Assets Liabilities Reserves: pd Bonds Reserves: pd Bonds: Currency: c B Currency: c 0 0 Bonds: B - b b Net Worth Net Worth Net Worth b - pd - c - B b - B - pd - c After: Central Bank Treasury Consolidated Assets Liabilities Assets Liabilities Assets Liabilities Reserves: p(1 - x)d + A Bonds A p+x-px Reserves: p(1 - x)d + p+x-px Bonds: Currency: C + p+x-Px B Currency: C + +x-Px -A 0 O Bonds: B - b- A b+ 4 Net Worth Net Worth Net Worth b - pd - c -B b - B - pd - c so the aggregate balance sheet of the government has exchanged liabilities that pay interest for liabilities that do not.pay for the current period's spending. [1 + it} B: is how much it must pay on the debts it had at the beginning of the period, including the interest that accrued in the current period. The left hand side represents all the resources the government can use to make its payments. pm is how much it raises in taxes, in nominal terms. M31 M? is the increase in the monetary base. This is all the payments the government can make just by virtue of having created extra money. Bt+l is the amount of payments the government can make by virtue of issuing debt that will have to be repaid in the future. We can also rearrange (13.5.1) to express it as: Mair + Bt+1 = P: [G1 Til + (1 +193: + Mtg This formulation makes it easier to see that the monetary base is just like debt (in the sense that it enters the government budget in the same way], except that it doesn't pay interest. Historically, governments have used expansion of the monetary base as a way to satisfy the government budget in various circumstances. Sometimes it's a result of difficulties in collecting regular taxes, due to tax evasion or political indecision about what other taxes to use. Sometimes it's a result of a rapid increase in government spending that leaves no time to increase regular taxes, as in wartime. Sometimes it's the result of the inability to borrow, perhaps because lenders don't trust the government to pay back its debts. In other instances it may have been to a misperception that increasing the monetary base is a way for the government to obtain resources without really taking them away from anyone. Often it could be several of these reasons at the same time. One subtle question is who exactly the government is taxing when it increases the monetary base. It's clear that the government can, at least to some extent, pay for goods and services with monetary expansion. But nobody seems to be paying for this. How does it all add up? The answer is that anyone who holds money is implicitly paying a tax to the govermnent when the monetary base expands. We know that in a money market equilibrium, an expansion of the monetary base leads (through the money multiplier) to an increase in the money supply and then to an increase in the price level. Anyone who holds money while it's losing value is implicitly giving up some of their wealth to the government, just as they would if they were paying a regular tax. That's why seignorage revenue is also sometimes referred to as an ination tax.'1 Figure 12.4.1: Money balances over time in the Baumol-Tobin model. Each time the household goes to the bank, it brings up its money.r balance to 31%;. Then the balance starts to decrease gradually as the household spends the money. Eventually, when the balance reaches zero, the household goes to the bank again to get more money. Itis clear from the picture that the household will, on average, hold less money the more often it goes to the bank have. Indeed, the average money balance is simply _ FY M W (12.4.1) How does the household choose N? Mathematically, it solves the following problem: . .pY mNmpFN + 12? (12.4.2) What does this mean?r The household is trying to minimize the overall cost of having money for transactions. This cost has two parts. First, if it goes to the bank N times, it pays the cost F each time. Expressed in nominal terms, this gives us the term pFN. Second, if it goes to the bank N times it will on average hold 2% dollars in money. Since this money does not earn interest, there is an opportunity cost of holding it: the foregone interest that the household could have earned if it had held less money. If the interest rate is 1', then 13% is the foregone-interest cost of the household's money holdings. The rst-order condition for problem (12.4.2) is pF it? 2 a 2 so we can solve for N to get iY N = 12.4. 2F ( 3) Equation (12.4.3) tells us that the household will go more times to the bank if t' is high and if F is low. What's the economic logic of this?r If i is high, then the opportunity cost of holding money is high and the household will be willing to go to the bank many times in an effort to hold low amounts of money. On the other hand, if F is low going to the bank is cheap and the household will, other things being equal, be willing to go to the bani: more times. Replacing (12.4.3) into (12.4.1) and rearranging, we get an expression for the average money balances or, dividing by the price level, for average \"real\" money balances M_ YF p 2, {12.4.4} M YF _ = __ (12.4.4) p 2% \"Real money balances\" are the answer to the question: \"how many goods would the household be able to buy with the amount of money it holds?" Equation {12.4.4} is telling us that real money balances will be higher when: a Y is high. If the household wants to spend more, this will involve more payments and therefore the household will choose to carry higher real money balances. a i is low. 2' is the opportunity cost of holding money. If this is low, the household will choose to hold higher money balances to save on trips to the bank. a F is high. If going to the bank is costly, the household will choose to hold higher money balances to save on trips to the bank. The Baumol-Tobin model makes very specific assumptions about how exactly households manage their money: every trip to the bank costs the same, spending is spread out exactly over time and 218 Updated caravan-15 12.5. EXERCISES CHAPTER 12. MONEY perfectly predictable, etc. We will sometimes want to think about the basic economic forces that the Baumol-Tobin model captures while not expecting the exact formula (12.4.4) to hold. For this purpose, we will sometimes want to think of a generalized money-demand function 7313 {Y, 3'), increasing in Y and decreasing in i. 1313 (Y, i} = 1 lg is just a special case of this more general formula. 13.1 Equilibrium in the Money Market In Chapter 12 we looked at the money supply and the money demand separately. An equilibrium in the money market requires that supply equals demand: all the money that is created jointly by the central bank and the private banks must be held by someone, voluntarily. We can write the money-market equilibrium condition as: M3 = m3 (111') -;1} (13.1.1) The left hand side of (13.1.1) is the money supply. We are going to imagine that the central bank simply chooses the money supply, by choosing the monetary base and understanding the money multiplier. The right hand side of (13.1.1) is the money demand. This is the result of households1 decisions of how much money to hold. How does a money market equilibrium come about? Suppose that the central banlc increases MS, what changes to induce households to increase their money holdings? The right hand side of {13.1.1} gives us a list of the things that could possible change to restore equilibrium: a p. The price level could rise. If the price level is higher, then the same amount of real transactions requires more money, so households would want to hold extra money. a 1'. Nominal interest rates could fall. If interest rates are lower, the opportunity cost of money is lower and households would be willing to hold more of it. a Y. GDP could go up. If GDP is higher, there are more real transactions to carry out, which requires more money. There are different views on which of these three variables tends to respond and why. This turns out to be an extremely important issue and it's an area of quite a bit of disagreement. 1We'll start by looking at the socalled \"classical" view. The socalled classical view postulates that the real side of the economy is separate from anything having to do with money. Real variables like real GDP and real interest rates are determined purely by real factors (technology, preferences, etc.) that do not change when the money supply changes. One way of stating this view is to say that money is neutral. In everything we have done so far we have implicitly adopted this classical View: we studied the forces that determine real variables without any reference to the money supply. Later on in the course we'll think about reasons why money might not be neutral. Let's see how prices and ination behave if the classical view is correct. An economy in steady state with a constant money supply Imagine rst that the economy is in a steady state where Y and r are constant and the central bank holds the money supply MS constant as well. We'll conjecture that in this economy the price level will be constant as well, and then verify that this is consistent with an equilibrium in the money marketfl If indeed the price level is constant, then the nominal interest is equal to the real interest rate. Therefore, solving for p in (13.1.1) we get: MS ,, = m3 (Y, T) (13.2.1) which indeed is constant. Equation (13.2.1) tells us that an economy where the money supply is higher will, other things being equal, have higher prices. People want a certain level of real money D S balances given by m , so the price level will be such that :1: corresponds to these desired real money balances. An economy in steady state with a growing money supply Maintain the assumption that Y and r are constant but now assume that the money supply grows at a constant rate ,u, i.e. Mi, = [1 + p.) M,3 . In this economy the price level will also grow at rate ,u. Letis check that this is consistent with equilibrium in the money market. If Pt+1 = {1 + H} Pt then inflation At+1 is Pt+1 - 1 = / Pt This method of figuring out the equilibrium of a model is sometimes called "guess and verify". 221 Updated 03/04/2018 13.2. THE CLASSICAL VIEW CHAPTER 13. THE PRICE LEVEL AND INFLATION and therefore the nominal interest rate is If the money market is in equilibrium in period t, then: M5 =m ( Y,r + /) Pt ME (1 + 1 ) = m ( Y,r + p) P. (1 + 1) MS1 = m ( Y,r+ 1 ) Put1 which implies that the money market is also in equilibrium in period t + 1. Economically, what's going on is the following. Since GDP and nominal interest rates are constant, people want to hold constant real money balances. Since the money supply is growing, prices must be growing too in order to keep money balances constant. Figure 13.2.1 looks at data on inflation and money growth over many years. The data shows that inflation is, indeed, almost exactly proportional to the growth rate of the money supply.Now suppose that the economy is in a steady-state-with-growth, with Y growing at a constant rate g and a constant real interest rate r. The money supply grows at a constant rate /. Let's try to find the inflation rate in this economy. Start from (13.1.1) and take the derivative with respect to time: dMS am? (Y, i) dy ,Om (Y,i) di] dt OY dt + Oi dt . ptm (Y, i ) Now divide by (13.1.1) on each side: dMS dt am? ( Y, i ) Y am" (Y,i) di di MS + OY m! ( Y, i ) V + m? (Y, i) dt am" (Y, i) Y am? (Yl) di di OY m" (Y, i ) g + m" (Y, i ) dt + 7 Let n = om" (Yi) Y ay m (vij . n represents the elasticity of money demand with respect to GDP. It is the answer to the question: if GDP rises 2%, by what percent does the demand for real money balances increase? Assume the function m" is such that this elasticity is constant, so: am (Y,i) 1 = ng + di m' ( Y , i ) dt + 71 If inflation is constant, then i = r + 7 will be constant so # = 0. Then the equation reduces to: H = ng + 7 and therefore T= U - ng (13.2.2)A one-time increase in the money supply Suppose that, starting from a steady state with a constant money supply, at time t there is a sudden, unexpected increase in the money supply, from MS to M5\". After this, the money supply is expected to remain constant at MS' forever. 1What's going to happen to the price level? Before time t we had that p = \"13%.After that, the money supply will again be constant, except that the level will be higher. Therefore we are going to be back in a constant-money-supply steady state, where p' = g!_ The effect on prices is therefore: M3 Pi MS: 3 In other words, prices jump immediately to their new level, and the size of the jump is proportional to the size of the increase in MS. Note that one condition for this reasoning to be correct is that prices must be exible, reacting inmlediately to changes in the supply of money. Later on in the class we'll think about the possibility that prices might be \"sticky\" and react slowly to changes in the money supply. This will be a source of monetary nonneutrality, i.e. of interaction between money and the real economy. A change in the rate of growth of the money supply. Now let's do a slightly more subtle exercise. Suppose we start at a steady state with the money supply growing at rate it and, therefore, an ination rate of a. At time t there is a sudden, unexpected increase in the rate of growth of the money supply, form ,a to n'. After this, the rate of growth of the money supply is expected to remain at ,u." forever. "Whats going to happen? A naive guess would be to say that inf lation would simply increase from ,u. to ,u'. This guess is not wrong, but it's incomplete. If the ination rate changes from p; to pf, then the nominal interest rate rises from i = r + n to 3' = 'r + a\". Using {13.1.1}, this implies that real money balances must fall: MS D r =m ,r-l- p (1' a) Higher nominal interest rates increase the opportunity cost of holding money, so people want to hold less of it. But the fever? of M3 does not change at time t: it simply starts growing at a different rate. 1What makes the money market clear? The price level must rise! Economically, this is what's going on. People are all simultaneously trying to reduce their money balances because the opportunity cost of holding them has gone up. Since the total [nom- inal) supply of money has not changed, money loses value, which is the same thing as saying the prices rise. Figure 13.2.2 shows how the price level evolves over time in the different examples above. 0 Ann produces an. apricot and sells it to Bob for 31. Bob produces a blackberry and. sells it to Arm for $1 In the example, nominal GDP is $6, the money supply is $2 and and each dollar changes hands 3 times, so the velocity of money is 3. In general, we have that: M V E Y 13.3.1 Money Supply Velocity Price Level Real GDP Nominal GDP Equation (13.3.1), sometimes known as the quantity equation, is a definition. It's true because this is the way we dene the velocity of money. How does equation (13.3.1) relate to the money-market equilibrium condition (13.1.1)? We can use {1311) to replace % in (13.3.1) and rearrange to obtain: V = _ (13.3.2) Equation {13.32) says that any theory of money demand, summarized by a function 7313 (Y, i), is also a theory of velocity. Once we have a mD (Ki) function, we can simply plug it into (13.3.2) to obtain velocity as a function of Y and 1'. Our theory of money demand implies that velocity is an increasing function of the nominal interest rate. We can see this in equation (13.3.?) by noting that mD is decreasing in i, which implies V is increasing in i. Economically, what this is saying is that if interest rates are higher, people will hold less money, so in order to carry out the same amount of real transactions, each dollar will have to change hands more times. Figure 13.3.1 shows how the velocity of money has evolved over time. Notice that the velocity of M1 is higher than the velociy of M2. Recall from the denitions of M1 and M2 that M2 includes more things than M1. Using (13.3.1), this implies that the velocity of M2 must be lower. Ination is generally seen as undesirable. There are several reasons for this. One reason can be understood directly from the Baumol-Tobin model of money demand. Other things being equal, more ination implies higher nominal interest rates, which means that people will \"go to the bank\" more times to avoid holding high money balances. Each of those trips to the bank has a cost of 17.2 Using {12.4.3} we can compute the total cost of trips to the bank as: Cost = NF (13.4.1) My dad told me that at the times of high ination in Argentina in the late 19805 he would literally go to the banl-r twice a day, once before work and once after work just to make sure that he had exactly enough money for the day's expenses and no more. That time spent dealing with the problem of how much money to hold has a real opportunity cost. On the basis of a reasoning like this, Milton Friedman advocated keeping nominal interest rates at or very near zero, a policy known as the \"Friedman Rule\". The idea of the Friedman Rule is to eliminate the opportunity cost of holding money. In formula (13.4.1), having 1' = B would make the cost equal to zero, because it would mean that you donit ever need to go to the bank: since it has no opportunity cost, you can just hold all your wealth in money. Notice that in order to have i = 0, one would need to have a" = r. Since the real interest rate is usually positive, this means that implementing the Friedman Rule requires deation. The Friedman Rule is usually seen as a theoretical extreme, more valuable for the underlying logic than as a concrete policy proposal. Economists sometimes refer to \"menu costs\" as part of the cost of ination. Sometimes there are real resources that need to be dedicated to put in place a change in prices. For instance, restaurants need to print new menus, shops need to print new signs, etc. When ination is high this needs to be done more often, which is a real cost. Minimizing menu costs would require keeping ination at zero, rather than running deation as implied by the Friedman Rule. Even this would not eliminate menu costs: zero ination means that the price index would stay constant, but the 2. Ricardian Equivalence VS Government with Money (30 Points). This exercise will show you the difference between a government that can attempt to stimulate the economy by financing through taxes and borrowing and a government that can print money. a) (5 points, easy) Consider the following government budget constraint between two periods where government could print the money PIG1 + Mi + (1 + i)B1 = PIT1 + B2 + M2. What are the ways the government could finance its deficit in this economy? b) (5 points, easy) Suppose the government plans to print money at a rate of u: M2 = (1 + Me) M1. Re-write the government deficit as a function of money demand where in equilibrium m(Y, i) = M. Since the government doesn't plan to borrow, you could drop Be from the budget constraint. c) (7 points, moderate) Suppose that people make N trips to the bank each year. Each trip cost them F for transportation cost. And the nominal interest rate is i. The average money balance is PY M =- 2N Explain why people want to hold money in this economy. Derive the demand for money when people want to minimize the cost of holding money by choosing the number of trips they make to the bank each year. min PFN + iM Is the demand for money increasing or decreasing in the following variables: income, nominal interest rate? d) (10 points, moderate) Now, suppose the household knows that the government will increase the money supply every period at the rate of u. Substitute the money demand that you derived in (c) to the government budget constraint in (b) and replace i = r + . e) (3 points, moderate) What is the implication of government fiscal policy in this model, and how does it compare to the Ricardian Equivalence result we established earlier in this class