Advanced Macroeconomics An Easy Guide Monetary policy An introduction

CHAPTER 19 Monetary policy An introduction The conundrum of money We have reached our last topic monetary policy ( one of the most important topics in policy , and perhaps the most effective tool of management . While among practitioner there is a great deal of consensus over the way monetary policy should be , it always remains a topic where new ideas and raise heated debates . Paul tweeted , Nothing gets people angrier than monetary theory . Say that Trump is a traitor and they yawn say that money works and they scream incoherently . Our goal in these chapters is to try to sketch the consensus , its shortcomings , and the ongoing attempts to rethink for the future , even if people scream ! We will tackle our analysis of monetary policy in three steps . In this chapter we will start with the basics the relation of money and prices , and the optimal choice of . This will be developed first , in a context where output is exogenous . This relative to the New approach we discussed in Chapter 15 , but will provide some of the basic intuitions of monetary policy . The interaction of money and output creates a whole new wealth of issues . Is monetary policy inconsistent ?

Should it be conducted through rules or with discretion ?

Why is targeting so popular among central banks ?

We will discuss these questions in the next chapter Finally , in the last two chapters we will discuss new frontiers in monetary policy , with new challenges that have become more evident in the new period of very low interest rates . In Chapter 21 we discuss monetary policy when constrained by the lower bound , and the new approach of quantitative easing . In Chapter 22 we discuss a series of topics secular stagnation , the theory of the price level , and bubbles . Because these last two chapters are more in referencing this recent work , we do not add the what next section at the end of the chapter , as the references for future exploration are already plenty within the text . But before we jump on to this task , let us note that monetary economics rests on a fairly shaky foundation the role of money why people hold it , and what are its effects on the economy is one of the most important issues in , and yet it is one of the least understood Why is this ?

For starters , in typical micro models and pretty much in all of our macro models as well we did not deal with money the relevant issues were always discussed in terms of relative prices , How to cite this book chapter , and , A . 2021 . Advanced An Easy Guide . 19 . Monetary policy An introduction , London Press . DOI License .

296 MONETARY POLICY AN INTRODUCTION not nominal prices . There was no obvious ( or , at least , essential ) role for money in the that we used throughout this book . In fact , the non plus ultra of micro models , the general equilibrium framework , not only does not need money , it also does not have trading ! Talk about outrageous assumptions . In that model , all trades are consummated at the beginning of time , and then you have the realisation of these trades , but no new trading going on over time . Of course , the world is not that complete , so we need to update our trading all the time . We use money as an insurance for these new trades . However , it is much easier to say people use money for transactions than to model it , because we need to step into the world of incomplete markets , and we do not know how to handle that universe well . The literature has thus taken different paths for introducing money into general equilibrium els . The first is to build a demand for money from . The question here is whether one commodity ( maybe gold , shells , salt ?

may become a vehicle that people may naturally choose for transactions , what we usually refer to as money . and Wright ( 1989 ) for example , go this way While nice , by starting from first principles , this approach is intractable and did not deliver els which are to discuss other issues , so this research has only produced a plausible story for the existence of money but not a workable model for monetary policy The other alternative is to introduce money in our typical overlapping generations model . Money serves the role of social security , and captures the attractive feature that money has value because you believe someone down the road will take it , Unfortunately , the model is not robust . Any asset that dominates money in rate of return will simply crowd money out of the system , thus making it impossible to use this model to justify the use of money in cases in which the rate is minimally positive when money is clearly dominated in rate of return . A third approach is to just assume that money needs to be used for purchases , the cash in advance constraints . In this framework the consumer splits itself at the beginning of each period into a consumer self and a producer self . Given that the consumer does not interact with the producer , she needs to bring cash from the previous period , thus the denomination of cash in advance . This is quite tractable , but has the drawback that gives a very rigid money demand function ( in fact , money demand is simply equal to consumption ) A more version is to think that the consumer has to devote some time to shopping , and that shopping time is reduced by the holdings of money This provides more about thinking in the demand for money Finally , a alternative is just to add money in the utility function . While this is a reduced form , it provides a money demand framework , and , therefore , has been used in the literature . At any rate , it is obvious that people demand money , so we just postulate that it provides utility . An additional benefit is that it can easily be accommodated into the basic framework we have been using in this book , for example , by tacking it to an problem akin to that of the . Thus , we will go this way in this chapter . As you will see , it provides good insights into the workings of money in the economy . I Introducing money into the model Let start with the simplest possible model . Output exogenous , and a government that prints money and rebates the proceeds to the consumer . We will lift many of these assumptions as we go along . But before we start we need to discuss the budget constraints .

MONETARY POLICY AN INTRODUCTION Assume there is only one good the price of which in terms of money is given by . The agent can hold one of two assets money , whose nominal stock is , and a real bond , whose real value is given , as in previous chapters , by . Note that we now adopt the convention that real variables take on letters , and nominal variables are denoted by capital letters . The representative agent budget constraint is given by , PI where , is real taxes paid to the government and , as usual , is income and consumption . the real quantity of money as . Taking logs of both sides , and then time derivatives , we arrive at . MI PI MI MI PI , I I I I I it , as the rate of and rearranging , we have , PI The of ( is the real value of the money the government injects into the system . We call this total revenue from money creation , or seigniorage . Notice from the of ( 194 ) that this has two components . The term is the increase in real money holdings by the public . It is sometimes referred to as seigniorage as well well keep our use consistent ) The term , is the tax the erosion , because of , of the real value of the money balances held by the public . We can think of my as the tax base , and Ir , as the tax rate . Using ( in ( we have that , On the we have accumulation by the agent of the two available assets money and bonds . The last term on the is an additional expense taxes paid on the real balances held , Let us consider a steady state in which all variables are constant , then ( becomes . Hence , total income on the must be enough to total expenditures ( including regular taxes and the tax ) A useful transformation involves adding and subtracting the term , to the of ( in , Now at ,

298 MONETARY POLICY AN INTRODUCTION as total assets held by the agent , and ' II , as the nominal rate of interest . Using these two relationships in ( we get , The last term on the shows that the cost of holding money , in an environment , is the nominal rate of interest i , The model Following ( 1967 ) we assume now the representative agent utility function is I ( Here ( my ) is utility from holdings of real money balances . Assume ( and that conditions hold . The agent ( subject to ( 19 . 10 ) which we repeat here for clarity , though assuming , without loss of generality , that output remains constant , plus the standard solvency condition lim aTe , co and the initial condition ac . The is ( i , where , and , are control variables , at is the state variable and , is the . First order conditions for a maximum are ( where the last equality comes from assuming as usual . Equations ( and ( together imply that ) is constant and equal to for all I . Using this fact and combining ( and ( we have ( i , We can think of equation ( as money demand demand for real balances is decreasing in the nominal interest rate it and increasing in steady state consumption This is a way to the traditional money demand functions you all have seen before , where demand would be a positive function of income ( because of transactions ) and a negative function of the nominal interest rate , which is the opportunity cost of holding money

MONETARY POLICY AN INTRODUCTION 299 I Finding the rate of What would the rate of be in this model ?

In order to close the model , notice that , where is the rate of money growth . We will also assume that the money printing proceeds are to the consumer , which means that , Replacing ( and ( into ( using , and realizing the agent has no incentive to hold debt , gives that , so that marginal utility is also constant and can be to . Using ( equation ( becomes ( which substituting in ( gives , Equation ( is a differential equation that the equilibrium . Notice that because ( this is an unstable differential equation . As the initial price level determines the initial point ( is a jump variable in our of Chapter ) the equilibrium is unique at the point where , The dynamics are shown in Figure . This simple model provides some of the basic intuitions of monetary theory . An increase in the quantity of nominal money will leave unchanged and just lead to a jump in the price level . This is the quantitative theory of money that states that any increase in the stock of money will just result in an equivalent increase in prices . Figure The model

300 MONETARY POLICY AN INTRODUCTION . The rate of is the rate of growth of money ( see equation ( is a monetary phenomenon . What happens if , suddenly , the rate of growth of money is expected to grow in the future ?

The dynamics entail a jump in the price level today and a divergent path which places the economy at its new equilibrium when the rate of growth increases . In short , increases in future money affect the price and levels today The evolution of and ! are shown in Figure . Does the introduction of money affect the equilibrium ?

It doesn . Consumption is equal to income in all states of nature . This result is called the neutrality of money . The optimal rate of Let assume now that we ask a central planner to choose the rate in order to maximise welfare . What , and , therefore , what rate would be chosen ?

Figure An anticipated increase in the money growth MONETARY POLICY AN INTRODUCTION We know from ( and ( that the stock of money held by individuals solves the equation ( Ir ) This means that the central bank can choose ' to maximise utility from . This implies choosing I , 1923 ) so that vI ( mI ' This means that is the satiation stock of real balances and you achieve it by choosing a negative rate . This is the famous rule for optimal monetary policy Whats the intuition ?

You should equate the marginal cost of holding money from an individual perspective ( the nominal interest rate ) to the social cost of printing money , which is essentially zero , A zero nominal rate implies an rate that is equal to minus the real interest rate . In practice , we see a lot of central banks implementing policy Why is it so ?

Probably because has a lot of costs that are left out of this model its effect on debtors , on aggregate demand , likely in the case when prices and wages tend to be sticky downwards . We should thus interpret our result as meaning that policy makers should aim for low levels of , so as to keep social and private costs close . In any case , there is a huge literature on the costs of that strengthens the message of this result , we will come back to this at the end of the chapter . I Multiple equilibria in the model In the previous section we analysed the steady state of the model , but , in general , we have always been cautious as to check if other equilibria are possible . In this monetary model , as it happens , they are . Figure shows the possible for equation ( 19121 ) for all We know that din so that the curve crosses the steady state with a positive slope . But what happens to the left of the steady state ?

Figure 193 , shows two paths depending on whether the value of the term ( approaches zero or a positive number as approaches zero . If money is very essential and it marginal utility is very high as you reduce your holdings of money , then ( as approaches zero . This case corresponds to the path denoted by the letter , as then the is of the path leading to A . With this we can now study other equilibria . The paths to the right are paths , where is negative and real balances increase without bound , We do not see these increasing paths , so , from an empirical point of view , they do not seem very relevant ( mathematically they are feasible , and some people resorted to these equilibria to explain the low rates in the in recent years , see Sims ( 2016 ) The paths to the left of the steady state are paths . Paths along the curve are inconsistent , as they require when hits zero , which is unfeasible . However , paths that do end up at zero , denoted A in Figure , are feasible . In these cases money is not so essential , so it is wiped out by a process . In a classical paper , 1956 )

302 MONETARY POLICY AN INTRODUCTION Figure Multiple equilibria in the model speculated on the possibility of these dynamics in which the expectation of higher leads to lower money demand , fuelling even higher . So these feasible paths to the left of the steady state could be called equilibria . The general equilibrium version of the equilibria described here was first introduced by and ( 1983 ) I Currency substitution The model is amenable to discussing the role of currency substitution , that is , the possibility of phasing out the currency and being replaced by a sounder alternative . The issue of understanding how different currencies interact , has a long tradition in monetary economics . Not only because , in antiquity , many objects operated as monies , but also because , prior to the emergence of the Fed , currency in the were issued by commercial banks , so there was an innumerable number of currencies circulating at each time . A popular way to think this issue is Law faced with a low quality currency and a high quality currency , Law argues that people will try to get rid of the low quality currency while hoarding the high quality currency , had money displaces money . Of course while this may be true at the individual level , it may not be so at the aggregate level because prices may increase faster when in units of the currency debasing its value . 1994 ) discusses this issue and makes two points . When there are two or more currencies , it is more likely that the condition ( is ( particularly for the low quality currency ) Thus , the paths are more likely . If the dynamics of money continue are described by an analogous to ( such as ( I 71 ) mia ) notice that if the second currency reduces the marginal utility of the first one , then the tion rate on the equilibrium path is lower less is needed to wipe out the currency .

MONETARY POLICY AN INTRODUCTION 303 This pattern seems to have occurred in a series of in Argentina in the late , each new wave coming faster but with . Similarly , at the end of the , also in Argentina , very tight monetary conditions during the exchange regime led to the development of multiple private currencies . Once the exchange rate regime was removed , these currencies suffered and disappeared in a wink ( see and Blackburn 2009 ) I How do these results extend to a model with capital accumulation ?

We can see this easily also in the context of the model ( we assume no population growth ) but where we give away the assumption of exogenous output and allow for capital accumulation . Consider now the utility function I ( where up , um and um , umm , However , we allow the consumer to accumulate capital now . again a , the resource constraint can be written as 11 ' a , The is ( The are , as usual , um ( The first two equations give , once again , a money demand function um , but the important result is that because the interest rate now is the marginal product of capital , in steady state ( where we use the superscript to denote the steady state , We leave the computations to you , assuming , and using the fact that is the marginal product , replacing in ( we that ( But this is the level of income that we would have had in the model with no money ! This result is known as not only does the introduction of money not affect the equilibrium , neither does the rate . Later , we will see the motives for why we believe this is not a good description of the effects of , which we believe in the real world are harmful for the economy

304 MONETARY POLICY AN INTRODUCTION The relation between and monetary policy If originates in money printing , the question is , what originates money printing ?

One ble explanation for lies in the need of resources to public spending . This is called the public approach to and follows the logic of our tax smoothing discussion in the chapter . According to this view , taxes generate distortions , and the optimal taxation mix entails equating these distortions across all goods , and , why , not money . Thus , the higher the cost of other taxes ( the weaker your tax system ) the more you should rely on as a form of collecting income . If the marginal cost of taxes increases with , then you should use more in , Another reason for is to compensate the natural tendency towards . If prices were constant , we would probably have , because we know that price indexes suffer from an upward bias . As new products come along and relative prices move , people change their consumption mix looking for cheaper alternatives , so their actual basket is always cheaper than the measured basket , For the , this bias is allegedly around per year , but it has been found larger for emerging Thus an target of or in fact aims , basically , at price stability . However , the main culprit for , is , obviously , needs regardless of any consideration . The treasury needs resources , does not want to put with the political pain of raising taxes , and simply asks the central bank to print some money which eventually becomes . I The curve The tax collected is the combination of the rate and the money demand that pays that tion tax . Thus , a question arises as to whether countries may choose too high an rate . May the rate be so high that discouraging money demand actually reduces the amount collected through the tax ?

In other words are we on the wrong side of the curve ?

To explore this question let start with the budget constraint for the government , which , in steady state , becomes . Assuming a typical demand function for money , we can rewrite this as I . Note that ( ye ' 77 ) so that revenue is increasing in It for It , and decreasing for . It follows that ! is the revenue maximising rate of . Empirical work , however , has found , fortunately , that government typically place themselves on the correct side of the

MONETARY POLICY AN INTRODUCTION 305 I The and dynamics What are the dynamics of this motivated ?

Using ( 1936 ) we can write , TA ( This in ( implies , log ( log ( Notice that , am , log ( which using ( TA ( to , 19 43 ) am 55 I , I Hence , for the steady state below , and for the steady state mi 55 rate above ' I . This means that the high equilibrium is stable , As is a jumpy variable , this means that , in addition to the equilibrium at low , there are equilibria in which converges to the high equilibria . Most practitioners disregard this high equilibria and focus on the one on the good side of the curve , mostly because , as we said , it is to come up with evidence that tries are on the wrong side . However , the dynamics should be a reminder of the challenges posed by stabilisation , I Unpleasant monetary arithmetic In this section we will review one of the most celebrated results in monetary theory , the unpleasant arithmetic presented initially by Sargent and Wallace ( 1981 ) The result states that a contraction may lead to higher in the future , Why ?

Because , if the amount of ment spending is exogenous and is not with seigniorage , it has to be with bonds . If eventually seigniorage is the only source of revenue , the higher amount of bonds will require more seigniorage and , therefore , more , Of course , seigniorage is not the only , so you may interpret the result as applying to situations when , eventually , the increased cost of debt is not , at least entirely , by other revenue sources . Can it be the case that the expected future leads to higher now ?

If that were the case , the monetary icy would be ineffective even in the short run ! This section discusses if that can be the case . The tools to discuss this issue are all laid out in the model discussed in section , even though the presentation here follows ( 1985 ) Consider the evolution of assets being explicit about the components of , in ,

306 MONETARY POLICY AN INTRODUCTION Where we assume as we ve done before . The evolution of real money follows in , Replacing ( into ( we get lat , where the term can be interpreted as the Call this expression Replacing ( in ( we get ' a ( Equations ( and ( will be the dynamic system , which we will use to discuss our results . It is easy to see that the la equation slopes upwards and that the is an horizontal line . The dynamics are represented in Figure . A reduction in ' shifts both curves upwards . Notice that the system is unstable . But 17 is not a jump Variable . The system reaches stability only if the rate of money growth is such that it can the stabilising the debt dynamics . It is the choice of money growth that will take us to the equilibrium . 17 here is not the decision variable . Our exercise considers the case where the rate of growth of money falls for a certain period of time after which it moves to the value needed to keep variables at their steady state . This exercise represents well the case studied by Sargent and Wallace . To analyse this we compute all the steady state combinations of and for different values of on Making la and in equal to zero in ( and ( and substituting in ( using ( we get I ' This is the locus in Figure . We know that eventually the economy reverts to a steady state along this line . To the analysis , show that the equation for the accumulation of assets can be written as 17 at pa , Figure The dynamics of and mA

MONETARY POLICY AN INTRODUCTION 307 Figure Unpleasant arithmetic ' notice , however , that if 61 this equation coincides with ( This means that above the steady states locus the dynamic paths have a slope that is less than one ( so that the sum of and la grows as you move ) and steeper than one below it ( so that the total value of assets falls ) We have now the elements to discuss our results . Consider first the case where ( log ( In this case the tax is constant and independent of the rate . Notice that this implies from ( that the line is vertical . In this case , the reduction in the growth rate of money implies a jump to the lower rate , but the system remains there and there is no unpleasant monetary arithmetic . A lowering of the rate of growth of money , does not affect the collection of the tax and thus does not require more debt , so the new lower equilibrium can sustain itself , and simply jumps back to the original point when the growth rate of money reverts to its initial value . Now consider that case where the demand for money is relatively inelastic , which implies that , in order to increase seigniorage , a higher rate is required and the slope of the curve is Now the policy of reducing seigniorage collection for some time will increase in the long run as a result of the higher level of debt . This is the soft version of the result . But the interesting question is whether it may actually increase even in the short run , something we call the hard version of the unpleasant arithmetic , or , in words , the spectacular version . Whether this is the case will depend on the slope of the curve . If the curve is then a jump in is required to put the economy on a path to a new steady state . In this case , only the soft , and not the hard , version of the result holds ( an upwards jump in happens only if falls ) However , if the curve is steeper than negative one ( the case drawn in ( 195 ) only a downwards jump in can get us to the equilibrium . Now we have Sargent and Wallace spectacular , unpleasant monetary result lowering the rate of money growth can actually increase the rate in the short run ! The more inelastic money demand , then the more likely this is to be in this case . Of course these results do not carry to all bond issues . If , for example , a central bank sells bonds , to buy foreign reserves Re , where , is the foreign currency price in domestic currency units ) the central bank income statement changes by adding an interest cost , but also adds a revenue equal

308 MONETARY POLICY AN INTRODUCTION to ' Re , where i and i stand for the local and foreign interest rates . If AB Re , to the extent that i i ( uncovered interest parity ) there is no change in net income , and therefore no change in the equilibrium rate . This illustrates that the result applies to bond sales that compensate money printed to the government ( ie . with no backing ) In fact , in Chapter 21 we will discuss the policy of quantitative easing , a policy in which Central Banks issue , substantial amount of liquidity in exchange for real assets , such as corporate bonds , and other instruments , with interest bearing reserves . To the extent that these resources deliver an equilibrium return , they do not change the monetary equilibrium . I Pleasant monetary arithmetic Let imagine now that the government needs to a certain level of government expenditure , but can choose the rates over time . What would be the optimal path for the tax ?

To out , we assume a Ramsey planner that consumer utility , the optimal behaviour of the consumer to the tax itself , much in the same way we did in the previous chapter in our discussion of optimal taxation and , of course , subject to it own budget constraint . The problem is then to maximise I ( i , where we replace for and for ( i , as per the results of the model . The governments budget constraint is a , where , is the real amount of liabilities of the government , is the government and we ve replaced The Ramsey planner has to the optimal sequence of interest rates , that is , of the rate . The are , i , i , plus , 1953 ) The second show that A is constant , Given this the shows the nominal interest is as well . Optimal policy smooths the tax across periods , a result akin to our tax ing result in the previous chapter ( if we include a distortion from taxation , we would get that the marginal cost of should equal the marginal cost of taxation , delivering the result that tion be ) What happens now if the government faces a decreasing path for government expenditures , that is , doe ?

The solution still requires a constant rate but now the seigniorage needs to satisfy do i pao ( MONETARY POLICY AN INTRODUCTION 309 Integrating ( 1951 ) gives the solution for , a , Notice that debt increases over time the government smoothes the tax by running up debt during the high period . This debt level is higher , of course , relative to a policy of the with in every period ( this would entail a decreasing path pari with the ) At the end , the level of debt is higher under the smoothing equilibrium than under the policy of full , leading to higher steady state . This is the arithmetic at work . However , far from being unpleasant , this is the result of an optimal program . The higher long run is the cost of smoothing the in other periods . The costs of The model shows that does not affect the equilibrium . But somehow we do not believe this result to be correct . On the contrary , we believe is harmful to the economy . In their celebrated paper , Bruno and Easterly ( 1996 ) found that , beyond a certain threshold was negatively correlated with growth , a view that is well established among of monetary policy This result is by the literature on growth . always has a negative and effect on growth . In these it may very well be that is capturing a more fundamental weakness as to how the political system works , which may suggest that for these countries it is not as simple as choosing a better rate of . However , to make the point on the costs of more strongly , we notice that even tion programs are expansionary This means that the positive effects of lowering are strong , so much so that they even undo whatever potential costs a may have . Figures 196 and show all recent programs for countries that had reached an rate equal to or higher than 20 in recent years . The is split in two panels , those countries that implemented with a regime and those that used some kind of nominal anchor ( typically the exchange rate ) and shows the evolution of ( monthly ) in and ( quarterly ) in 197 since the last time they reached 20 . The evidence is conclusive are with higher growth . So what are these costs of that did not show up in the model ?

There has been a large literature on the costs of . Initially , these costs were associated with what were dubbed costs the cost of going to the bank to get cash ( the idea is that the higher the , the lower your demand for cash , and the more times you needed to go to the bank to get your cash ) This was never a thrilling story ( to say the least ) but today , with electronic money and credit cards , simply no longer makes any sense . On a more benign note we can grant it tries to capture all the increased transaction costs associated with running out ( or low ) of cash . Other stories are equally disappointing . Menu costs ( the idea that there are real costs of changing prices ) is as uneventful as the story . We know distorts tax structures and tributes incomes across people ( typically against the poorest in the population ) but while these are undesirable consequences they on their own do not build a good explanation for the negative impact of on growth .

MONETARY POLICY AN INTRODUCTION Figure Recent ( and exchange rate regimes ) Inflation in countries with floating regimes so 40 ?

20 10 20 30 40 50 60 Months after disinflation started Dominican Inflation in countries with nominal anchor 100 Inflation ( YoY ) 10 20 30 ' 50 60 Months after disinflation started Czech Russian MONETARY POLICY AN INTRODUCTION Figure growth during Index ( 01 100 ) Index ( 01 ) in countries with floating regimes 150 140 130 120 110 100 15 ' Quarters after disinflation started in countries with nominal anchor 160 140 120 100 15 Quarters after disinflation started Czech 990 Russian

MONETARY POLICY AN INTRODUCTION I The model and competition So the problem with has to be and deep . An elephant in the room that seems to see . 1994 ) provides what we believe is a more plausible story based on the role of in messing up the price system , focuses on a fact increases in tion increase the volatility in relative prices ( this occurs naturally in any model where prices adjust at different times or speed ) argues that relative prices changes , not only generate economic but also change the relative power of sellers and purchasers pushing the economy away from its competitive equilibrium , To see this , lets draw from our analysis of search discussed in Chapter 16 . Imagine a consumer that is searching for a low price . Going to a store implies a price , the value of which can be described by ) Having a price implies obtaining a utility If relative prices were stable , the consumer could go back to this store and repurchase , but if relative prices change , then this price is lost , This occurs with probability If this event occurs , the consumer is left with no offer ( value ) The parameter will change with and will be our object of interest . If the consumer has no price , he needs to search for a price with cost and value as in rU aJ max ( Working analogously as we did in the case of job search , remember that the optimal policy will be determined by a reservation price . As this reservation price is the one that makes the customer indifferent between accepting or not accepting the price offered , we have that ( rU , which will be handy later on . Rewrite ( as it pU ( 1959 ) Subtracting from both sides ( and using rU ) we have ( We can now replace rU and ( to obtain a I ) a ( or , 75 ( mi ( The intuition is simple . The consumer is willing to pay up to his valuation of the good plus the search cost that can be saved by purchasing this unit . However , the reservation price falls if there is expectation of a better price in a new draw .

MONETARY POLICY AN INTRODUCTION I The equation delivers the result that if higher implies a the higher , then the higher is the reservation price . With , consumers search less thus deviating the economy from its competitive . Other stories have discussed possible other side effects of . There is a well documented negative relation between and the size of the sector ( see for example Levine and ( 1991 ) and Levine and ( 1992 ) Another critical feature is the fact that high implies that long term nominal contracts disappear , a point which becomes most clear if may change abrupt . Imagine a budget with an investment that yields a positive or negative return or , in a nominal contract this may happen if moves strongly Imagine that markets are incomplete and agents can not run negative net worth ( any contract which may run into negative wealth is not feasible ) The of eventually running into negative wealth increases with the length of the contract . The disappearance of long term contracts has a negative impact on productivity . I Taking stock We have seen now money and are linked in the long run , and that a simple monetary model can help account for why central banks would want to set at a low level . We haven really talked short run , in fact , in our model there are no real effects of money or monetary policy . However , as you anticipate by now , this is due to the fact that there are no price . To the extent that prices are in the long run , the main concern of monetary policy becomes dealing with , and this is how the practice has evolved in recent decades . If there are , as we have seen previously , part of the effect of monetary policy will translate into output , and not just into the price dynamics . It is to these concerns that we turn in the next chapter . Notes I de and ( 2012 ) a 45 annual bias for Brazil in the . and ( 2018 ) a whopping bias for in Argentina , and for the period . You may know this already , but the curve describes the evolution of tax income as you increase the tax rate . Starts at zero when the tax rate is zero , and goes back to zero when the tax rate is 100 , as probably at this high rates the taxable good has disappeared . Thus , there is a range of tax rates where increasing the tax rate decreases tax collection income . See and ( 1995 ) and as there are no tax resources , it indicates the value of the . We disregard the equilibria where the elasticity is so high that reducing the rate of money growth increases the collection of the tax . As in the previous section , we disregard these cases because we typically the tax to operate on the correct side of the curve . This section follows ( 2016 ) For a contract delivering a positive or negative return with equal probabilities in each period , the possibility of the contract eventually hitting a negative return is if it lasts one period and if it lasts periods . This probability is bigger than 75 after nine periods , so , quickly long term contracts become unfeasible . See ( 1998 ) for a model along these lines .

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