This page intentionally left blank Modeling Monetary Economies The approach of this text for upper-level undergraduates is to teach monetary eco- nomics. This textbook is designed to be used in an advanced undergraduate course. The approach of this text is to teach monetary economics using the classical. Cambridge Core - Economic Theory - Modeling Monetary Economies - by Bruce Champ.

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Cambridge University Press. - Modeling Monetary Economies, Second Edition - Bruce Champ and Scott Freeman. Frontmatter. More information . Modeling monetary economies by Bruce Champ. Modeling monetary economies. by Bruce Champ; Scott Freeman; Joseph H Haslag. Print book. English. Modeling Monetary Economies (3rd ed.) by Bruce Champ. Read online, or download in secure PDF or secure EPUB format.

Hence, the individual will prefer point B to point A. Likewise, point C will be preferable to both points A and B. This is assumption 1. It is often useful to draw an analogy between an indifference map and a contour map that shows elevation. On a contour map, the curves represent points of constant elevation; on an indifference map, the curves represent points of constant utility.

Extending the analogy, if we think of traversing the indifference map in a northeast- erly direction, we would be going uphill. In other words, utility would be increasing.

In fact, an indifference map, like a contour map, is merely a handy way to illustrate a three-dimensional concept on a two-dimensional drawing. The three dimensions here are first-period consumption, second-period consumption, and utility. If an individual prefers bundle B to bundle A and bundle C to bun- dle B, then that individual must also prefer bundle C to bundle A.

Graphically, this implies that indifference curves cannot cross. To do so would violate this property of transitivity and assumption 1. To see this, refer to Figure 1. Indifference curves cannot cross. By our first assumption about preferences, the individual whose preferences are represented by these indifference curves prefers bundle C over bundle B because bundle C consists of more first-period consumption and the same amount of second-period consumption compared with bundle B.

However, because the individual must be indifferent between all three bundles, A, B, and C, a contradiction arises. Our assumptions rule out the possibility of indifference curves that cross. We know that indifference curves represent bundles that give an individual the same level of utility. In other words, the individual whose preferences are represented by Figure 1. Sim- ilarly, the individual must be indifferent between bundles A and C on indifference curve U 1.

We see, then, that the individual is indifferent between all three bundles. However, if we compare bundles B and C, we also observe that they consist of the same amount of second-period consumption, but C contains more first-period con- sumption than B. By assumption 1, the individual must prefer C to B. But this con- tradicts our earlier statement about indifference between the three bundles. For this reason, indifference curves that cross violate our assumptions about preferences. The Initial Old The preferences of the initial old are much easier to describe than those of future generations.

The initial old live and consume only in the initial period and thus simply want to maximize their consumption in that period. The Economic Problem The problem facing future generations of this economy is very simple.

They want to acquire goods they do not have. A Simple Model of Money good only when young but wants to consume in both periods of life. They must therefore find a way to acquire consumption in the second period of life and then decide how much they will consume in each period of life. In the second, decentralized solution, we allow individuals to use money to trade for what they want. We will then compare the two solutions and ask which is more likely to offer individuals the highest utility.

The answer will help to provide a first illustration of the economic usefulness of money. Feasible Allocations Imagine for a moment that we are central planners with complete knowledge of and total control over the economy. Our job is to allocate the available goods among the young and old people alive in the economy at each point in time.

As central planners, under what constraint would we operate? Put simply, it is that at any given time we cannot allocate more goods than are available in the economy. Recall that only the young people are endowed with the consumption good at time t. There are Nt of these young people at time t. A model with many types of goods is introduced in Chapter 2.

We will see, however, that this simple model is all that is needed to illustrate a demand for money. Feasible Allocations 11 Total consumption by young and old is the sum of the amounts in Equations 1.

We are now ready to state the constraint facing us as central planners: In this case, we rewrite Equation 1. Dividing through by N , we obtain the per capita form of the constraint facing us as central planners: A stationary al- location is one that gives the members of every generation the same lifetime con- sumption pattern.

The feasible set. The feasible set, the gray triangle, represents the set of possible allocations that can be attained given the resources available in the economy. Points outside the feasible set, such as point A, are unattainable given the resources of the economy. The golden rule allocation. The golden rule allocation is the stationary, feasible allocation of consumption that maximizes the welfare of future generations.

It is located at a point of tangency between the feasible set line and an indifference curve point A. This is the highest indifference curve in contact with the feasible set.

The set of stationary, feasible, per capita allocations — the feasible set, for short — is bounded by the triangle in the diagram. We refer to the triangular region as the feasible set. The thick diagonal line on the boundary of the feasible set is called the feasible set line. The feasible set line represents Equation 1. This is done in Figure 1.

The feasible allocation that a central planner selects depends on the objective. One reasonable and benevolent objective is the maximization of the utility of the future generations, an objective we call the golden rule. The golden rule in Figure 1. Note that the golden rule occurs at the unique point of tangency between the feasible set boundary and an indifference curve. Any other point that lies within the feasible set yields a lower level of utility.

For example, points B and C are feasible because they lie on the boundary of the feasible set. However, they lie on an indifference curve that represents a lower level of utility than the one on which point A lies. Point D is preferable to point A, but it is unattainable. The endowments of the economy simply are not large enough to support the allocation implied by point D. Decentralized Solutions 13 The Initial Old It is important to consider the welfare of all participants in the economy — including the initial old — when considering the effects of any policy.

Although the golden rule allocation maximizes the utility of future generations, it does not maximize the utility of the initial old. The goal of the initial old is to get as much consumption as possible in period 1, the only period in which they live.

You may want to imagine that the initial old also lived in period 0; however, because this period is in the past, it cannot be altered by the central planner, who assumes control of the economy in period 1. This would be accomplished among stationary feasible allocations at point E of Figure 1. This stationary allocation, which implies that people consume nothing when young, would not maximize the utility of the future generations. Faced with this conflict in the interests of the initial old and the future generations, an economist cannot choose among them on purely objective grounds.

Nevertheless, the reader will find that, on subjective grounds influenced by the fact that there are an infinite number of future generations and only a single generation of initial old , we tend to pay particular attention to the golden rule in this book. Decentralized Solutions In the previous section, we found the feasible allocation that maximizes the utility of the future generations.

Such a redistribution requires that the central planner have the ability to reallocate endowments costlessly between the generations. These are strong assumptions about the power and wisdom of central planners. This leads us to ask if there is some way we can achieve this optimal allocation in a more decentralized manner, one in which the economy reaches the optimal allo- cation through mutually beneficial trades conducted by the individuals themselves.

In other words, can we let a market do the work of the central planner? Before we answer this question, we need to define some terms that are used throughout the book.

First, we discuss the notion of a competitive equilibrium. A Simple Model of Money competitive equilibrium has the following properties: Each individual makes mutually beneficial trades with other individuals.

Through these trades, the individual attempts to attain the highest level of utility that he can afford. Individuals act as if their actions have no effect on prices rates of exchange. There is no collusion between individuals to fix total quantities or prices. Supply equals demand in all markets.

In other words, markets clear.

Edited by Michael L. Alosco and Robert A. Stern

Equilibrium Without Money Let us consider the nature of the competitive equilibrium when there is no money in our economy of overlapping generations. Recall that agents are endowed with some of the consumption good when young. Their endowment is zero when old. Their utility can be increased if they give up some of their endowment when they are young in exchange for some of the goods when they are old.

Without the presence of an all-powerful central planner, we must ask ourselves if there are trades between individuals in the economy that could achieve this result.

No such trades are possible. Refer to Figure 1. A young person at period t has two types of people with whom to trade potentially in period t — other young people of the same generation or old people of the previous generation. However, trade with fellow young people would be of no benefit to the young person under consideration. They, like him, have none of the consumption good when they are old. Trade with the old would also be fruitless; the old want the good the young have, but they do not have what the young want because they will not be alive in the next period.

However, in period t, these people have not yet come into the world and so do not want what young people have to trade. Jevons to explain the need for money]. Each generation wants what the next generation has but does not have what the next generation wants. Unable to make mutually beneficial trades, each individual consumes his entire endowment when young and nothing when old. In this autarkic equilib- rium, utility is low.

Both the future generations and the initial old are worse off than they would be with almost any other feasible consumption bundle. A member of the future generations would gladly give up some of his endowment when young in order to consume something when old.

A member of the initial old would also like to consume something when old. The same absence of trade would result if they were separated in space, as in the models of Robert Townsend Finding the Demand for Fiat Money 15 Equilibrium with Money To open up a trading opportunity that might permit an exit from this grim autarkic equilibrium, we now introduce fiat money into our simple economy.

Fiat money is a nearly costlessly produced commodity that cannot itself be used in consumption or production and is not a promise to anything that can be used in consumption or production. For the purposes of our model, we assume the government can produce fiat money costlessly but that it cannot be produced or counterfeited by anyone else. Fiat money can be costlessly stored held from one period to the next and it is costless to exchange.

Pieces of paper distinctively marked by the government generally serve as fiat money. Because individuals derive no direct utility from holding or consuming money, fiat money is valuable only if it enables individuals to trade for something they want to consume. A monetary equilibrium is a competitive equilibrium in which there is a valued supply of fiat money.

By valued, we mean that the fiat money can be traded for some of the consumption good. For fiat money to have value, its supply must be limited and it must be impossible or very costly to counterfeit.

Obviously, if everyone has the ability to print money costlessly, its supply will rapidly approach infinity, driving the value of any one unit to zero. We begin our analysis of monetary economies with an economy with a fixed stock of M perfectly divisible units of fiat money.

A young person can sell some of his endowment of goods to old persons for fiat money, hold the money until the next period, and then trade the fiat money for goods with the young of that period. Finding the Demand for Fiat Money Of course, this new trading possibility exists only if fiat money is valued — in other words, if people are willing to give up some of the consumption good in trade for fiat money and vice versa.

If it is believed that fiat money will not be valued in the next period, then fiat money will have no value in this period. No one would be willing to give up some of the consumption good in exchange for it.

That would be tantamount to trading something for nothing. A Simple Model of Money Extending this logic, we can predict that fiat money will have no value today if it is known with complete certainty that fiat money will be valueless at any future date T. Working backward in this manner, we can see that fiat money will have no value today if it will be valueless at some point in the future.

Now let us consider a more interesting equilibrium where money has a positive value in all future periods. We define vt as the value of 1 unit of fiat money let us call the unit a dollar in terms of goods; that is, it is the number of goods that one must give up to obtain one dollar. It is the inverse of the dollar price of the consumption good, which we write as pt.

Note also that because our economy has only one good, the price of that good pt can be viewed as the price level in this economy. To answer, we must first establish the constraints on the choices of the individual — why he cannot simply enjoy infinite consumption both when young and when old. As it was for the entire society, the constraints on an individual are that he cannot give up more goods than he has.

In the first period life, an individual has an endowment of y goods. Notice that no one in the future generations is born with fiat money. To acquire fiat money, an individual must trade.

If the number of dollars acquired by an individual by giving up some of the consumption good at time t is denoted by m t , then the total number of goods sold for money is vt m t. The right-hand side of Equation 1. Finding the Demand for Fiat Money 17 In the second period of life, the individual receives no endowment. Hence, when old, an individual can acquire goods for consumption only by spending the money acquired in the previous period.

The only use for these goods is second-period consumption. We can graph this budget constraint as shown in Figure 1. We can easily verify that the intercepts of the budget line are as illustrated. The budget line represents Figure 1.

The choice of consumption with fiat money. At point A individuals maximize utility given their lifetime budget set in the monetary equilibrium. The rate of return on fiat money determines the slope of the budget set line. A Simple Model of Money Equation 1. This is the horizontal intercept of the budget line. This represents the vertical intercept of the budget line.

This point is shown in Figure 1. It is the point along the budget line that touches the highest indifference curve. This must occur at a point where the budget line is tangent to an indifference curve.

And so on. We see that the value of fiat money at any point in time depends on an infinite chain of expectations about its future values. This indefiniteness is not due to any peculiarity in our model but rather to the nature of fiat money, which, because it has no intrinsic value, has a value that is determined by views about the future. Whatever the views of the future value of money, a reasonable benchmark is the case in which these views are the same for every generation.

This is plausible because in our basic model every generation faces the same problem; endowments, preferences, and population are the same for every generation.

We call such equilibria stationary equilibria. Notice that because individuals face different circumstances, depending on whether they are young or old, c1 will not in general be equal to c2 in a stationary equilibrium. People may choose to consume more when young or more when old.

It turns out that the relative mix of first- and second-period consumption depends on preferences and on the rate of return on fiat money. Finding the Demand for Fiat Money 19 We also assume that individuals in our economy form their expectations of the future rationally.

In this special case, we say that people have perfect foresight. This assumption would be less credible in an economy buffeted by random shocks than in our model economy, where preferences and the environment are unchanging and therefore are perfectly predictable.

Individuals with wrong beliefs about the future value of money will not choose the money balances that maximize their utility. They therefore have an incentive to figure out the value of money that will actually occur.

Let us now employ the assumptions of stationarity and perfect foresight to find an equilibrium time path of the value of money.

In perfectly competitive markets, the price or value of an object is determined as the price at which the supply of the object equals its demand. This applies to the determination of the price value of money as well as the price of any good. The total supply of fiat money measured in dollars is Mt , implying that the total supply of fiat money measured in goods is the number of dollars multiplied by the value of each dollar, or vt Mt.

A Simple Model of Money which states that the value of a unit of fiat money is given by the ratio of the real demand for fiat money to the total number of dollars.

Because all generations have the same endowments and preferences and anticipate the same future pattern of endowments and preferences, it seems quite reasonable to look for a stationary equilibrium. Then, after some cancelation, Equa- tion 1.

Modeling monetary economies

Because the price of the consumption good pt is the inverse of the value of money, it too is constant over time. Notice that the rate of return on fiat money is also a constant 1 in the stationary equilibrium. Identical people who face the same rate of return will choose the same consumption and money balances over time, a stationary equilibrium.

Therefore, the stationary equilibrium is internally consistent. Our graph of the budget line therefore becomes the one depicted in Figure 1. Be aware that the stationary equilibrium may not be a unique monetary equilib- rium. There also may exist more complicated nonstationary equilibria. In this text, however, we confine our attention to stationary equilibria because there is much that can be learned from these easy-to-study cases. Finding the Demand for Fiat Money 21 Figure 1.

With a constant money supply and population, the rate of return on fiat money is 1, implying the lifetime budget constraint of the diagram. The Quantity Theory of Money The simplest version of the quantity theory of money predicts that the price level is exactly proportional to the quantity of money in the economy.

We would like to investigate whether this theory holds in our basic overlapping generations model. Recall that, in Equation 1. This is evident from the lack of time subscripts on the right-hand side of Equation 1.

As an example, suppose that the initial stock of fiat money in the economy M is doubled but remains constant from then on. This is referred to as a once-and-for-all increase in the fiat money stock. Equation 1. A Simple Model of Money price level in every period will also be twice as high.

This demonstrates that our model is indeed consistent with the quantity theory of money. We see from Figures 1. The rate of return of money is unaffected by the size of the constant stock of fiat money notice in Equation 1. This property of the monetary equilibrium is referred to as the neutrality of money. Why is this the case? All we have done is to introduce intrinsically worthless pieces of paper into an economy. How can this improve welfare? We hinted at the answer earlier.

Without fiat money, people are unable to trade for the goods they desire c2 because they do not own anything that the owners of these goods, the next generation, desire. With fiat money, however, people are able to trade for the goods they desire despite this absence of a double coincidence of wants.

People sell some of the goods they have for fiat money and then use the money to download the goods they want.

In this model economy, therefore, fiat money serves as a medium of exchange. It is not consumed nor does it produce anything that can be consumed. It is valued nevertheless because it helps people acquire goods they otherwise could not have acquired.

Second-period consumption is a market good in the sense that an individual must trade to obtain more of it. In contrast, first-period consumption is a nonmarket good; individuals already possess first-period consumption without needing to trade for it.

We can say then that fiat money provides a means for individuals to download market goods. We have seen that fiat money can provide for second-period consumption, improv- ing the welfare of individuals otherwise unable to trade. We would like to make the 7 Keep in mind that we are discussing here the size of a constant stock of money.

We will allow the stock of money to change over time in Chapter 3. A Monetary Equilibrium with a Growing Economy 23 individuals in our economy not just better off but as well off as possible.

It remains to ask, therefore, whether the monetary equilibrium results in the best possible allo- cation of goods. In particular, we would like to see whether the stationary monetary equilibrium we have just found maximizes the welfare of future generations. In other words, does the monetary equilibrium reach the golden rule?

Compare the budget line of Figure 1. They are identical. The choice of consumption in this monetary equilibrium will be identical to the one we found when we were looking at the stationary allocation that was dictated by a central planner who wanted to maximize the utility of the future generations. This implies that the stationary monetary equilibrium obeys the golden rule. The introduction of fiat money allows the future generations not only to increase their utility through trade but, in this case, actually allows them to reach their maximum feasible utility.

This will not always be the case. The budget set and the feasible set answer different economic questions. The budget set depicts the constraint on an individual, whereas the feasible set describes the constraint on the society as a whole.

We will later find cases in which these two constraints differ and the monetary equilibrium does not obey the golden rule. The initial old are also better off in the monetary equilibrium than they were with the autarkic equilibrium. This means their consumption will be positive. In the autarkic equilibrium, their consumption would be zero. They are certainly better off in the monetary equilibrium.

Because we concentrate on stationary monetary equilibria in this book, it may be useful to summarize the features of such equilibria. A stationary consumption bundle of a monetary equilibrium satisfies two basic properties: A Monetary Equilibrium with a Growing Economy In the example we just considered, we found that a constant value of money constant prices led to an equilibrium that maximized the welfare of future generations.

Is this always the case? Are there cases in which a changing value of money maximizes the utility of future generations? To answer these questions, we now complicate our example by allowing the economy to grow over time. We accomplish this by assuming that the population is increasing over time. This implies that the total amount of the consumption good available in the economy will grow over time.

A Simple Model of Money In a monetary equilibrium, the assumption of a growing population also implies a growing demand for fiat money. This says that the number of people born in any period is always n times the number born in the previous period.

The gross rate is the net rate plus 1. To test your understanding of population growth rates, try Example 1. Example 1. Trace out the number of young and old people alive in periods 1 and 2. What is the growth rate of the total population? The Feasible Set with a Growing Population First, as before, consider the case of an all-powerful central planner who determines allocations of the available goods in each generation.

We consider the case of a monetary equilibrium later. As we determined earlier, the total amount of goods available for allocation in period t is Nt y. Although this will not occur here, we can simplify Equation 1. The golden rule allocation with a growing population. When the population grows at the rate n, the feasible set line has a horizontal intercept of y and a vertical intercept of ny.

As before, the golden rule allocation is determined at a point of tangency between the feasible set line and an indifference curve. We can easily graph this constraint, as is done in Figure 1. You should verify that the intercepts are as shown in the diagram. Why is this vertical intercept greater than it was in the case of a constant population? With a growing population, there are n young people for each old person.

Therefore, if we divide the entire endowment of the young equally among the old, there will be ny goods for each old person. It is easier for the planner to provide for consumption by the old because they are relatively few in number.

As always, this occurs at a point of tangency between the feasible allocations line and an indifference curve. If the central planner were to give this combination of c1 and c2 to each member of future generations, his welfare would be maximized.

The Budget Set with a Growing Population Now that we have determined the optimal allocation for future generations, let us turn to the case of a stationary monetary equilibrium. As before, we will eliminate the central planner and introduce fiat money into the economy. We again require that markets clear.

A Simple Model of Money supply. Earlier we found that this condition implies see Equation 1.

Modeling Monetary Economies Solutions Manual

The equation tells us that the value of fiat money in any period is determined by the relative demand for fiat money and its supply. A higher real demand for fiat money will raise its value, and a higher supply of fiat money will lower its value. If we update the time subscripts in Equation 1. Previously, with a con- stant population, the N terms also canceled. This implies that the price of the consumption good is falling over time.

Note that our earlier constant- population example is merely a special case of the one just considered. With a constant population, n is equal to 1. We therefore conclude that the rate of return on money is also equal to 1 in that case. This implies that an omnipotent, omniscient, and benevolent central planner could do no better than individuals acting within their budget sets.

In such a case, the value of money falls over time, implying a rising price level. However, much of the previous analysis would still apply. The monetary equilibrium with a constant fiat money stock would still attain the golden rule.

Summary In this chapter, we introduced the basic overlapping generations model. We found that fiat money, intrinsically worthless pieces of paper, can have value by providing a means for individuals to acquire goods that they do not possess.

In addition, we saw that the introduction of a fixed stock of fiat money into an economy enables fu- ture generations to attain the maximum possible level of utility given the resources available.

So far, we have concentrated on factors that affect the demand for money. We found that, in a growing economy where the demand for money increases over time, a constant fiat money stock enables individuals to attain the golden rule.


We might also be interested in knowing what effects a growing supply of fiat money has on an economy. We turn our attention to the case of an increasing fiat money stock in Chapter 3. Before doing so, in Chapter 2 we consider two alternative trading ar- rangements to using fiat money — the use of barter and the use of commodity money.

Exercises 1. What is the equation for the feasible set of this economy? Portray the feasible set on a graph. With arbitrarily drawn indifference curves, illustrate the stationary combination of c1 and c2 that maximizes the utility of future generations. Now look at a monetary equilibrium.

Write down equations that represent the con- straints on first-and second-period consumption for a typical individual. Combine these constraints into a lifetime budget constraint. What condition represents the clearing of the money market in an arbitrary period t? Use this condition to find the real rate of return of fiat money. For the remaining parts of this exercise, suppose preferences are such that individuals wish to hold real balances of money worth y goods.

What is the value of money in period t, vt? Use the assumption about preferences and your answer in part c to find an exact numerical value. What is the price of the consumption good pt? If the rate of population growth increased, what would happen to the rate of return of fiat money, the real demand for fiat money, the value of a unit of fiat money in the initial period, and the utility of the initial old?

Explain your answers. Answer these questions in the order asked. Suppose instead that the initial old were endowed with a total of units of fiat money. How do your answers to part d change? Are the initial old better off with more units of fiat money? Both economies have the same population, supply of fiat money, and endowments. In each economy, the number of young people born in each period is constant at N and the supply of fiat money is constant at M. Furthermore, each individual is endowed with y units of the consumption good when young and zero when old.

The only difference between the economies is with regard to preferences. Other things being equal, individuals in economy A have preferences that lean toward first-period consumption; individual preferences in economy B lean toward second- period consumption.

We will also assume stationarity. More specifically, the lifetime budget constraints and typical indifference curves for individuals in the two economies are represented in the following diagram.

Will there be a difference in the rates of return of fiat money in the two economies? If so, which economy will have the higher rate of return of fiat money?

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Give an intuitive interpretation of your answer. Will there be a difference in the value of money in the two economies? If so, which economy will have the higher value of money? Assume that y2 is sufficiently small that everyone wants to consume more than y2 in the second period of life. Bear in mind that under the new assumptions the equations and graphs you find may differ from the ones found previously. Using Calculus 29 a.

Apply the steps taken in Equations 1. Assume that all individuals within a generation will be treated alike and graph the set of stationary per capita feasible allocations. Draw arbitrarily located, but correctly shaped, indifference curves on your graph and point out the allocation that maximizes the utility of the future generations. Turning now to the monetary equilibrium, find the equation representing the equality of supply and demand in the market for money.

Assume a stationary solution and a constant money supply. Draw the budget set for an individual in this monetary equilibrium. Does this mon- etary equilibrium maximize the utility of future generations?

We could also achieve a growing economy by having an endowment that increases over time. Unlike static PDF Modeling Monetary Economies solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn.

You can check your reasoning as you tackle a problem using our interactive solutions viewer. Plus, we regularly update and improve textbook solutions based on student ratings and feedback, so you can be sure you're getting the latest information available. How is Chegg Study better than a printed Modeling Monetary Economies student solution manual from the bookstore? Our interactive player makes it easy to find solutions to Modeling Monetary Economies problems you're working on - just go to the chapter for your book.

Hit a particularly tricky question? Description and Table of Contents. Golub, Money, Credit, and Capital. Goldfeld and Daniel E. Sichel, Sriram, International Monetary Fund. Townsend, Kareken and Neil Wallace, ed. Barnett , Determinants and Effects of Changes in the Stock of Money, Foreword by Milton Friedman, pp.

Table of Contents. Review, Allan H. Meltzer , J of Business, 44 3 , pp. Spindt, Belongia, Bernanke , Bridel, Smith , Minsky , Reprinted in M. Tool, ed. O'Connell, Mendoza, Moore, Calvo and Enrique G. Palgrave MacMillan. Keynes , Santomero and John J.Finding the Demand of Fiat Money 17 Figure 1. However, exchange costs with a commodity money system are typically not equal to zero.

It must be easy to recognize and measure. The authors have added in this third edition new material on money as a means of replacing imperfect social record keeping, the role of currency in banking panics and a description of the policies implemented to deal with the banking crises that began in Mishkin, ed. We hope individual instructors will build on our foundations to fill any gaps.

Consistent with its statutory mandate, the Committee seeks to foster maximum employment and price stability. In the second, decentralized solution, we allow individuals to use money to trade for what they want.

The average costs associated with money and barter are summarized in Table 2. This does not mean that the equivalence results in only a theoretical curiosity.

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