Modeling Monetary Economies 4th Edition Bruce Champ, Scott Freeman, Joseph Haslag - Solutions

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Consider an economy of identical infinitely lived people. Suppose there is a tax cut in period 1 of d goods per person financed by long-term government debt that is never retired but pays the net real interest rate i = r − 1 in every period. Interest payments are financed by lump-sum taxes in
Consider an economy of altruistic two-period–lived people who care about the utility of their children. Children do not care about the utility of their parents. Parents currently leave a bequest worth fifty goods. For each of the following policies, find the size of the bequest in period 1 and
Consider an overlapping generations economy in which people are endowed with 100 goods when young and with nothing when old. Population grows at the rate n.Capital pays the gross rate of return of x. Utility is given by ln(c1,t) + ln(c2,t+1). If people have no income when old, this implies that
Suppose the government debt of 100 goods in period t financed not the tax cut of Example 16.1 but rather a government capital project that will pay off 100xg goods in the following period (t + 1). At that time, the government retires the debt. Assume that the returns from the capital project are
Suppose that there are 100 young rich people born in every period. Government debt and capital both pay real net rates of return equal to 25 percent. The fiat money stock is fixed. Each young rich person wishes to save fifty goods in each period. In period 0, the government issues a total amount of
Consider an overlapping generations economy in which capital pays a 25 percent net rate of return. The population of a generation grows by 10 percent each period. In the initial period (period 1), there are 100 people and a preexisting fiat money stock of M0 = $1 million. Because of a political
Assume that the maximum revenue that can be collected from all taxes, including seigniorage, is 5,000 goods and that the maximum debt is 6,000 goods. The real gross market rate of return is 1.2. Government expenditures currently equal 4,500 goods.The current leaders of the country detest government
Will the bank have enough in currency to meet the needs of the movers in the high-fraction event?c. Decribe how an elastic currency regime would address the answer to part b.
In that simple random-relocation model, each individual is endowed with 50 goods when young and nothing when old. The money stock is constant and equal to $1 million. Each island has a constant population, with 500 people born in each period t. Suppose the fraction of movers takes on either of two
Consider the random relocation economy developed in this chapter. Each person receives an endowment of 500 goods when young and nothing when old. People only want to consume when old. Let Mt = 1.1Mt−1 for every period t. The net rate of return on capital is 15 percent.a. Write down the contract
Suppose you are the sole shareholder of an S&L with deposits of $1.2 million and assets of $1 million. There is no reserve requirement. Your liability in the S&L is limited by law to your investment (if it fails, you need not make up losses to depositors). You are risk neutral.a. What is the net
Consider an economy in which people wish to hold money balances worth a total of 4,000 goods. They are indifferent between money issued by the central bank and money issued by private banks (as long as both offer the same rate of return). The central bank owns a constant stock of capital equal to
Consider an economy in which people wish to hold money balances worth a total of 5 million goods. They are indifferent between money issued by the central bank and money issued by private banks (as long as both offer the same rate of return). In the initial period, the central bank issues $1
Consider an economy in which people wish to hold bank checking deposits worth a total of 5 million goods and currency worth 2 million goods in every period. In addition, there is a stock of unintermediated capital worth 10 million goods. Fiat money is the only asset used as currency. Deposits at
Answer each part of Exercise 8.1 assuming that the central bank allows banks to borrow up to one-half of required reserves at a net interest rate of 8 percent.
Consider an economy with a constant population in which people wish to hold bank checking deposits worth a total of 5,000 goods in every period. The economy has a total endowment of 10,000 goods in each period. There is a total stock of unintermediated capital of 1,000 goods in each period. Bank
Consider an economy in which people live two-period lives in overlapping generations but are endowed only in the first period of life. Capital has a minimum size, k∗, which is greater than the endowment of any single individual but less than the total endowment of a single generation. Capital
Suppose the intermediation of capital goods costs φ units of the consumption good for each unit of capital intermediated (φ
Consider our model of three-period–lived individuals of this chapter. Suppose the two-period real rate of return on capital is X = 1.44, the rate of population growth is n = 1.1, and the rate of fiat money creation is z = 1.2. Find the following net rate for both one and two periods:a. nominal
What will the real fiat money holdings of a typical lender be?
Consider an overlapping generations model with 200 lenders and 100 borrowers born in every period. Everyone lives for only two periods. Each lender is endowed with twenty goods when young and nothing when old. Each borrower is endowed with nothing when young and forty goods when old. The lenders
Consider an economy of three-period-lived people in overlapping generations. Each person is endowed with y goods when young and old and nothing when middle-aged.The population of each generation born in period t is Nt , where Nt = nNt−1. There are no assets other than loans. Explain how credit
Use the graph in Figure 6.9 to answer the following questions:a. Suppose the government restricts total borrowing to an amount less than L¯. What would the effect be on capital holdings?b. Find the effect of an increase in the supply of loans on capital and the interest rate.What would the effect
What is the expected rate of return on capital? What is the risk premium of capital?
Suppose capital is risky and pays gross real rates of return of 1.2, 1.1, and 0.9 with probabilities .1, .7, and .2, respectively. A risk-free asset pays a safe gross real rate of return of
Suppose people in our overlapping generations model have the opportunity either to hold fiat money with complete safety or to lend to someone who may never repay the loan. The chance of such a default is 10 percent. Assume a stationary monetary equilibrium in which the population grows at a net
Consider the following version of the model of this chapter. The number of young individuals born on island i in period t, Ni t , is random according to the following specification:Assume that the fiat money stock grows at the fixed rate zt = z in all periods:a. Set up the budget constraints of the
Consider two identical countries, a andb, in our standard overlapping generations model. In each country, the population of every generation is 200 and each young person wants money balances worth 50 goods. Assume that the money of country a is the only currency that currently circulates in the two
Consider two identical countries in our standard overlapping generations model. In each country, the population of every generation is 100, and each young person wants money balances worth 10 goods. There are $400 of country a money and £100 of country b money. The exchange rate is fixed at 1.
Suppose that Germany (countrya) and France (countryb) do not have foreign currency controls in effect. The total demand for money is always 2,000 goods in Germany and 1,000 goods in France. The fiat money supplies are 100 marks in Germany and 300 francs in France.a. Find the value of each
(advanced) Suppose the monetary authority prints fiat money at the rate z but now does not distribute the newly printed money as a lump-sum subsidy. Instead, the government distributes the newly printed money by giving each old person α new dollars for each dollar acquired when young. Assume that
(advanced) Consider an economy with a constant population of N = 1,000. Individuals are endowed with y = 20 units of the consumption good when young and nothing when old. All seigniorage revenue is used to finance government expenditures. There are no subsidies and no taxes other than seigniorage.
(advanced, requires calculus) Assume that the utility function of people in the economy described in Exercise 3.6 is log(c1,t) + log(c2,t+1).a. Find the real demand for money (q = vtmt) as a function of z and τ . Hint: See appendix to Chapter 1 for a discussion of solution techniques.b. Find the
Assume that people face a lump-sum tax of τ goods when old and a rate of expansion of the fiat money supply of z > 1. The tax and the expansion of the fiat money stock are used to finance government purchases of g goods per young person in every period.There are N people in every generation.a.
Describe the essential features of a model economy of rational people for which each of the following statements is true (These features might include the pattern of population growth, monetary growth, endowments, and government policies. Note that there may be more than one model that yields the
Consider the following economy: Individuals are endowed with y units of the consumption good when young and nothing when old. The fiat money stock is constant.The population grows at rate n. In each period, the government taxes each young person τ goods. The total proceeds of the tax are then
Consider an overlapping generations mode with the following characteristics: Each generation is composed of 1,000 individuals. The fiat money supply changes according to Mt = 2Mt−1. The initial old own a total of 10,000 units of fiat money(M0 = $10, 000). Each period, the newly printed money is
Consider an economy with a shrinking stock of fiat money. Let Nt = N, a constant, and Mt = zMt−1 for every period t, where z is positive and less than 1. The government taxes each old person τ goods in each period, payable in fiat money. It destroys the money it collects.a. Find and explain the
Let Nt = nNt−1 and Mt = zMt−1 for every period t, where z and n are both greater than 1. The money created each period is used to finance a lump-sum subsidy of a∗t goods to each young person.a. Find the equation for the budget set of an individual in the monetary equilibrium.Graph it. Show an
(advanced) Consider again the model economy described in Exercise 2.2, but suppose there is a second storable good: silver. Silver is as easy to exchange and store as gold.The initial old own a total of 50 units of silver. There can be no additions to the stock of silver. Individuals are
(advanced) Suppose the consumption of gold offers people a marginal utility that diminishes as that person consumes more gold. Assume also that gold can be mined in unlimited amounts at the constant marginal costs, χ, units of the nongold consumption good.a. Can the trading value of gold exceed χ
Consider a commodity money model economy like the one described in this chapter but with the following features: There are 100 identical people in every generation.Each individual is endowed with 10 units of the consumption good when young and nothing when old. To keep things simple, let us assume
Consider a fiat money/barter system like that portrayed in this chapter. Suppose the number of goods J is 100. Each search for a trading partner costs an individual 2 units of utility.a. What is the probability that a given random encounter between individuals of separate islands will result in a
Suppose utility equals ln(c1,t) + β ln(c2,t+1) where ln(c) represents the natural logarithm ofc, whose derivative equals 1/c. The parameter β is a positive number.a. Prove that real money balances are q∗ = βy 1 + βb. Derive expressions for the lifetime consumption pattern c∗1,t and
In this chapter, we modeled growth in an economy by a growing population. We could also achieve a growing economy by having an endowment that increases over time.To see this, consider the following economy: Let the number of young people born in each period be constant at N. There is a constant
Consider an economy with a growing population in which each person is endowed with y1 when young and y2 when old. Assume that y2 is sufficiently small that everyone wants to consume more that y2 in the second period of life. Bear in mind that under the new assumptions, the equations and graphs you
Consider two economies, A and B. 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
Consider an economy with a constant population of N = 100. Individuals are endowed with y = 20 units of the consumption good when young and nothing when old.a. What is the equation for the feasible set of this economy? Portray the feasible set on a graph. With arbitrarily drawn indifference curves,
Consider an economy populated by a large number of identical, infinitely lived people. Suppose the government decides to tax the capital stock, but only at date 1. (The only existing capital stock in this period is k0)a. How will lifetime wealth be affected if the government tax is used to finance
Consider an overlapping generations economy in which people are endowed with 100 goods when young and with nothing when old. Population grows at the rate n. Capital pays the gross rate of return of x. Utility is given by In(c1,t) + In(c2,t+1) If people have no income when old, this implies that
Suppose we introduce the following fully funded government pension system in an overlapping generations economy where capital pays the fixed gross rate of return . The government taxes each young person τ goods and invests the tax payments in capital (and only in capital). When old, each person
To be consulted sqib bhai plz(a) To find the equilibrium level of the real interest rate, we need to determine the demand for and supply of loans. Since each lender wishes to save 10 goods, and there are 200 lenders, the total supply of loans is equal to (200) (10) = 2000 goods, independent of the
Consider an economy in which the money growth rate permanently increases from 3 percent to 10 percent. What is the effect of this policy change on the capital stock?
Suppose the monetary authority prints fiat money at the rate but now does not distribute the newly printed money as a lump-sum subsidy. Instead, the government distributes the newly printed money by giving each old person α new dollars for each dollar acquired when young. Assume that there is a
Consider an economy with a constant population of N = 1,000. Individuals are endowed with y = 20 units of the consumption good when young and nothing when old. All seigniorage revenue is used to finance government expenditures. There are no subsidies and no taxes other than seigniorage. Suppose
Assume that the utility function of people in the economy described in Exercise 3.6 is log (c1,t) + log (c2,t+1).a. Find the real demand for money (q = vtmt) as a function of z and τ.b. Find the government budget constraint in a stationary equilibrium. Solve it for as a function of. (The
Assume that people face a lump-sum tax of T goods when old and a rate of expansion of the fiat money supply of z > 1. The tax and the expansion of the fiat money stock are used to finance government purchases of g goods per young person in every period. There are N people in every
Describe the essential features of a model economy of rational people for which each of the following statements is true: (These features might include the pattern of population growth, monetary growth, endowments, and government policies. Note that there may be more than one model that yields the
Consider a pay-as-you-go social security plan that would collect 10 goods from each young person and distribute these goods evenly to old people. Find the effect of this plan on the wealth of future generations, consumption when young and old, private saving by the young, and investment by the
Consider an economy in which the central bank is willing to loan any quantity of reserves to banks. Let the gross real return on capital be x.a. What amount would a bank choose to borrow if the central bank rate of discount window loans is less than ?b. Reconsider your answer to part a but with
Consider an increase in the lump-sum taxes paid by old people. Find its effect on wealth consumption when young and old and on saving by the young. Assume that capital is the only asset in the economy. What effect does the tax increase have on output?
Suppose people live three-period lives. If the government cuts taxes on the middle-aged, what will happen to the consumption and saving of the young? To the consumption and saving of the middle-aged?
Consider an overlapping generations economy in which endowments increase over time. Let yt = αyt-1, where α> 1 Endowments are received by young people while old people receive no endowment. Preferences are such that a young person always wants to consume half of their endowment. The
Suppose the government debt of 100 goods in period financed not the tax cut of Example 17.1 but a government capital project that will pay off 100 rg goods in the following period (t + 1). At that time, the government retires the debt. Assume that the returns from the capital project are used
Consider an economy of altruistic two-period-lived people who care about the utility of their children. Children do not care about the utility of their parents. Parents currently leave a bequest worth 50 goods. For each of the following policies, find the size of the bequest in period 1 and the
Consider an economy of identical infinitely lived people. Suppose there is a tax cut in period 1 of d goods per person financed by long-term government debt that is never retired but pays the net real interest rate i = r - 1 in every period. Interest payments are financed by lump-sum taxes in each
Explain why a government that must run up a large national debt to finance extraordinary spending over the next several years might choose to surrender the power of money creation to a central bank beyond the government's control.
What will happen to the demand for fiat money, the nominal interest rate, and the real interest rate if the government tries to use inflation to default on the national debt every other year? In randomly selected years? Explain each of your answers.
Suppose the government must borrow 1,000 goods in period 1. Let the gross real marginal product of capital equal 1.07. Assume that people always want to hold fiat money balances worth a total of 100 goods and that the fiat money stock in period 1 is $10,000. Suppose people expect the government to
Consider an economy in which aggregate real money balances is always equal to 1,000,000 goods. What is the maximum amount of seigniorage that a government could generate in this economy in a single period?
Consider an economy in which aggregate real money balances is equal to 1,000,000 goods when the money stock is constant. However, the aggregate demand for real money balances is represented by Nq = 1,000,000 - za. Compute the amount of seigniorage that would be generated if the central bank set the
For a stationary economy, suppose the gross real interest rate on government bonds is equal to the population growth rate; that is, r = n. Assume that the government purchases 1,000 goods per young person. The outstanding stock of government debt is equal to 250 goods per young person. Taxes are
Suppose the economy starts with zero outstanding government bonds. Let government expenditures be goods per young person each period. Neither taxes nor seigniorage are used in periods 1 and 2. So the entire amount of government expenditures is financed through issuing debt.a. Let . Write down the
Consider an overlapping generations economy in which capital pays a 25 percent net rate of return. The population of a generation grows by 10 percent each period. In the initial period (period 1), there are 100 people and a preexisting fiat money stock of M0 = $1 million. Because of a political
Suppose there are 100 young rich people born in every period. Government debt and capital both pay real net rates of return equal to 25 percent. The fiat money stock is fixed. Each young rich person wishes to save 50 goods in each period. In period 0, the government issues a total amount of real
Assume that the maximum revenue that can be collected from all taxes, including seigniorage, is 5,000 goods and that the maximum debt is 6,000 goods. The real gross market rate of return is 1.2. Government expenditures currently equal 4,500 goods. The current leaders of the country detest
Use the same model economy as described in 14.3.Data from 14.3Consider a model economy in which each young person receives 200 units of the consumption good. There are 50 young people born each period. The total stock of fiat money is constant and equal to $10,000. Suppose a
Consider a model economy in which each young person receives 200 units of the consumption good. There are 50 young people born each period. The total stock of fiat money is constant and equal to $10,000. Suppose a person's preferences are such that they only want to consume when old. We assume the
In that simple random-relocation model, each person is endowed with 50 goods when young and nothing when old. The money stock is constant and equal to $1,000,000. Each island has a constant population, with 500 people born in each period t. Suppose the fraction of movers takes on either of two
Consider the random-relocation economy developed in this chapter. Each person receives an endowment of 500 goods when young and nothing when old. People only want to consume when old. Let Mt = 1.1Mt for every period t. The net rate of return on capital is 15 percent.a. Write down the contract
Consider an economy in which each person is endowed with 1,000 goods when young and nothing when old. When young, each person wants to consume 600 goods. The central bank pays interest on reserves equal to the net return on its capital holdings.a. If each person divides savings between fiat money
In each of the following instances, an exogenous change is described. Use a graph to show how the particular exogenous change can result in an increase in the equilibrium return on deposits.a. A permanent increase in the money growth rate.b. A permanent increase in the productivity of capitalc. A
Suppose the central bank sets the reserve requirement ratio at 5 percent. The maximum the central bank is willing to lend is 25 percent of required reserves, charging the gross real return of 1 on discount window loans. We assume the gross real return on fiat money is 1.02 and the gross real return
Consider an economy in which the reserve requirement is increased from 10 percent to 20 percent.a. Explain why the increase in the reserve requirement ratio causes welfare to decline.b. Construct a graph in c1 – c2 space (the axes) showing how the increase in the reserve requirement
Answer each part of Exercise 9.1 assuming that the central bank allows banks to borrow up to one-half of required reserves at a net interest rate of 8 percent.Data from Exercise 9.1Consider an economy with a constant population in which people wish to hold bank checking deposits worth a total of
Consider an economy with a constant population in which people wish to hold bank checking deposits worth a total of 5,000 goods in every period. The economy has a total endowment of 10,000 goods in each period. There is a total stock of un intermediated capital of 1,000 goods in each period. Bank
Suppose the inter mediation of capital goods costs ϕ units of the consumption good for each unit of capital intermediated (ϕ < X0.5). Assume that transaction costs occur when agents withdraw from banks (when they are middle-aged). What will the equilibrium rate of return offered by
Consider our model of three-period-lived individuals of this chapter. Suppose the two-period real rate of return on capital is X = 1.44, the rate of population growth is n = 1.1, and the rate of fiat money creation is z = 1.2. Find the following net rate for both one and two periods:a. Nominal rate
Use the graph in Figure 7.9 to answer the following questions: a. Suppose the government restricts total borrowing to an amount less than L̅. What would the effect be on capital holdings?b. Find the effect of an increase in the supply of loans on capital and the interest rate. What would the
Suppose people in our overlapping generations model have the opportunity either to hold fiat money with complete safety or to lend to someone who may never repay the loan. The chance of such a default is 10 percent. Assume a stationary monetary equilibrium in which the population grows at a net
Suppose a version of the model economy in which the money growth rate is a random variable. Let the probability be 4/5 that zt = 1 and the probability be 1/5 that zt = 2. The realization of monetary policy (the realized value of zt) is kept secret from the young until all purchases have occurred
Consider the following version of the model of this chapter. The number of young people born on island i in period , t, Nit is random according to the following specification:Nit = 4/5 N with probability .5 = 1/5 N with probability .5Assume that the fiat money stock grows
Suppose there are two islands. The total population on the two islands is 500 people. The initial stock of fiat money is $500. The money stock increases according to Mt = 1.1Mt-1. The probability that a person is on Island 1 is 1/4 and the probability that a person is on Island 2 is 3/4. Let l
Consider a standard overlapping generations economy in which Euroland is the name given to area over which the euro is the regional currency. Suppose the population of Euroland is 1,000 people born each period. Each young person wants money balances worth 50 goods. There are 2,000 euros
Consider two identical countries in our standard overlapping generations model. In each country, the population of every generation is 100 and each young person wants money balances worth 18 goods. Each member of the initial old starts with $3 of country α money and £3 of country b money,
Consider a two-country economy with no currency restrictions.a. Write down the money market-clearing condition.b. Discuss the exchange rate in this economy. In particular, discuss why the exchange rate may exhibit greater volatility in this economy.
Consider two identical countries, α and b, in our standard overlapping generations model. In each country the population of every generation is 200 and each young person wants money balances worth 50 goods. Assume that the money of country α is the only currency that currently circulates in the
Consider two identical countries in our standard overlapping generations model. In each country, the population of every generation is 100 and each young person wants money balances worth 10 goods. There are $400 of country α money and £100 of country b money. The exchange rate is fixed at 1.
Suppose that Japan (country α) and China (country b) do not have foreign currency controls in effect. The total demand for money is always 2,000 goods in Japan and 1,000 goods in China. The fiat money supplies are 100 yen in Japan and 300 yuan in China.a. Find the value of each country’s money
Consider the following economy: Individuals are endowed with y units of the consumption good when young and nothing when old. The fiat money stock is constant. The population grows at rate n. In each period, the government taxes each young person τ goods. The total proceeds of the tax are then

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Modeling Monetary Economies 4th Edition Bruce Champ, Scott Freeman, Joseph Haslag - Solutions

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