Advanced Macroeconomics 1st Edition Sanjay Rode - Solutions

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Briefly explain whether each of the following statements concerning a crosscountry regression of income per person on a measure of social infrastructure is true or false:(a) ‘‘If the regression is estimated by ordinary least squares, it shows the effect of social infrastructure on output per
(A different form of measurement error.) Suppose the true relationship between social infrastructure (SI ) and log income per person (y) is yi = a + bSIi + ei . There are two components of social infrastructure, SI A and SI B (with SIi = SI A i + SI B i ), and we only have data on one of the
Increasing returns in a model with human capital. (This follows Lucas, 1988.) Suppose that Y(t) =K(t)α[(1 − aH )H(t)]β , H (t) =BaH H(t), and K(t) = sY(t).Assume 0
Consider the following model with physical and human capital:Y(t) = [(1 − aK )K(t)]α[(1 − aH )H(t)]1−α, 0 0, φ > 0, γ + φ < 1, L(t) = nL(t), A(t) = gA(t), where aK and aH are the fractions of the stocks of physical and human capital used in the education sector.This model assumes that
(This follows Jones, 2002.) Consider the model of Section 4.1 with the assumption that G(E) = eφE . Suppose, however, that E, rather than being constant, is increasing steadily: E(t) = m, where m > 0. Assume that, despite the steady increase in the amount of education people are getting, the
Consider the model in Problem 4.5.(a) What are the balanced-growth-path values of k and h in terms of sk, sh , and the other parameters of the model?(b) Suppose α = 1 3 and β = 1 2 . Consider two countries, A and B, and suppose that both sk and sh are twice as large in Country A as in Country B
(This follows Mankiw, D. Romer, and Weil, 1992.) Suppose output is given by Y(t) =K(t)α H(t)β [A(t)L(t)]1−α−β , α > 0, β > 0, α + β < 1. Here L is the number of workers and H is their total amount of skills. The remainder of the notation is standard. The dynamics of the inputs are L(t)
Suppose the production function is Y = Kα(e φEL)1−α, 0
Suppose output in country i is given by Yi = Ai Q ie φEiLi . Here Ei is each worker’s years of education, Q i is the quality of education, and the rest of the notation is standard. Higher output per worker raises the quality of education. Specifically, Q i is given by Bi (Yi /Li )γ , 0 0.Our
Endogenizing the choice of E. (This follows Bils and Klenow, 2000.) Suppose that the wage of a worker with education E at time t is be gteφE . Consider a worker born at time 0 who will be in school for the first E years of life and will work for the remaining T −E years. Assume that the interest
The golden-rule level of education. Consider the model of Section 4.1 with the assumption that G(E) takes the form G(E) = e φE .(a) Find an expression that characterizes the value of E that maximizes the level of output per person on the balanced growth path. Are there cases where this value
Which of the following possible regression results concerning the elasticity of long-run output with respect to the saving rate would provide the best evidence that differences in saving rates are not important to cross-country income differences? (1) A point estimate of 5 with a standard error of
Delays in the transmission of knowledge to poor countries.(a) Assume that the world consists of two regions, the North and the South.The North is described by YN (t) = AN (t)(1−aL )LN and AN (t) = aL LN AN (t).The South does not do R&D but simply uses the technology developed in the North;
(This follows Rebelo, 1991.) Assume that there are two sectors, one producing consumption goods and one producing capital goods, and two factors of production: capital and land. Capital is used in both sectors, but land is used only in producing consumption goods. Specifically, the production
Learning-by-doing with microeconomic foundations. Consider a variant of the model in equations (3.22) (3.25). Suppose firm i ’s output is Yi (t) =Ki (t)α[A(t)Li (t)]1−α, and that A(t) = BK(t). Here Ki and Li are the amounts of capital and labor used by firm i and K is the aggregate capital
The balanced growth path of a semi-endogenous version of the Romer model. (Jones, 1995a.) Consider the model of Section 3.5 with two changes. First, existing knowledge contributes less than proportionally to the production of new knowledge, as in Case 1 of the model of Section 3.2: A(t) =
(a) Show that (3.48) follows from (3.47).(b) Derive (3.49).
Suppose that policymakers, realizing that monopoly power creates distortions, put controls on the prices that patent-holders in the Romer model can charge for the inputs embodying their ideas. Specifically, suppose they require patentholders to charge δw(t)/φ, where δ satisfies φ ≤ δ ≤
Consider the model of Section 3.5.Suppose, however, that households have constant-relative-risk-aversion utility with a coefficient of relative risk aversion of θ. Find the equilibrium level of labor in the R&D sector, LA.
Learning-by-doing. Suppose that output is given by equation (3.22), Y(t) = K(t)α[A(t)L(t)]1−α; that L is constant and equal to 1; that K(t) = sY(t); and that knowledge accumulation occurs as a side effect of goods production: A(t) = BY (t).(a) Find expressions for gA(t) and gK(t) in terms of
Consider the model of Section 3.3 with β + θ > 1 and n > 0.(a) Draw the phase diagram for this case.(b) Show that regardless of the economy’s initial conditions, eventually the growth rates of A and K (and hence the growth rate of Y) are increasing continually.(c) Repeat parts (a ) and (b) for
Consider the model of Section 3.3 with β + θ = 1 and n = 0.(a) Using (3.14) and (3.16), find the value that A/K must have for gK and gA to be equal.(b) Using your result in part (a ), find the growth rate of A and K when gK = gA.(c) How does an increase in s affect the long-run growth rate of the
Consider the economy described in Section 3.3, and assume β + θ < 1 and n > 0.Suppose the economy is initially on its balanced growth path, and that there is a permanent increase in s.(a) How, if at all, does the change affect the gA = 0 and gK = 0 lines? How, if at all, does it affect the
Consider the economy analyzed in Section 3.3.Assume that θ + β < 1 and n > 0, and that the economy is on its balanced growth path. Describe how each of the following changes affects the gA = 0 and gK = 0 lines and the position of the economy in ( gA, gK) space at the moment of the change:(a) An
Consider two economies (indexed by i = 1, 2) described by Yi (t) = Ki (t)θ and Ki (t) = siYi (t), where θ > 1. Suppose that the two economies have the same initial value of K, but that s1 > s2. Show that Y1/Y2 is continually rising.
Consider the model of Section 3.2 with θ < 1.(a) On the balanced growth path, A = g ∗A A(t), where g ∗A is the balanced-growthpath value of gA. Use this fact and equation (3.6) to derive an expression for A(t) on the balanced growth path in terms of B, aL , γ , θ, and L(t).(b) Use your
Explosive paths in the Samuelson overlapping-generations model. (Black, 1974; Brock, 1975; Calvo, 1978.) Consider the setup described in Problem 2.19.Assume that x is zero, and assume that utility is constant-relative-risk-aversion with θ < 1 rather than logarithmic. Finally, assume for simplicity
The source of dynamic inefficiency. (Shell, 1971.) There are two ways in which the Diamond and Samuelson models differ from textbook models. First, markets are incomplete: because individuals cannot trade with individuals who have not been born, some possible transactions are ruled out. Second,
Assume that x < 1 + n. Suppose that the old individuals in period 0, in addition to being endowed with Z units of the good, are each endowed with M units of a storable, divisible commodity, which we will call money. Money is not a source of utility.(a) Consider an individual born at t. Suppose the
Stationary monetary equilibria in the Samuelson overlappinggenerations model. (Again this follows Samuelson, 1958.) Consider the setup described in Problem
The basic overlapping-generations model. (This follows Samuelson, 1958, and Allais, 1947.) Suppose, as in the Diamond model, that Lt two-period-lived individuals are born in period t and that Lt = (1 + n)Lt−1. For simplicity, let utility be logarithmic with no discounting: Ut = ln(C1t) + ln(C2t
Social security in the Diamond model. Consider a Diamond economy where g is zero, production is Cobb Douglas, and utility is logarithmic.(a) Pay-as-you-go social security. Suppose the government taxes each young individual an amount T and uses the proceeds to pay benefits to old individuals; thus
Depreciation in the Diamond model and microeconomic foundations for the Solow model. Suppose that in the Diamond model capital depreciates at rate δ, so that rt = f(kt) − δ.(a) How, if at all, does this change in the model affect equation (2.60) giving kt +1 as a function of kt ?(b) In the
A discrete-time version of the Solow model. Suppose Yt = F(Kt,At Lt), with F(•) having constant returns to scale and the intensive form of the production function satisfying the Inada conditions. Suppose also that At +1 = (1 + g)At, Lt +1 = (1 + n)Lt, and Kt +1 = Kt + sYt − δKt.(a) Find an
Consider the Diamond model with logarithmic utility and Cobb Douglas production. Describe how each of the following affects kt +1 as a function of kt:(a) A rise in n.(b) A downward shift of the production function (that is, f (k) takes the form Bk α, and B falls).(c) A rise in α.
An interesting situation in the Ramsey Cass Koopmans model.(a) Consider the Ramsey Cass Koopmans model where k at time 0 (which as always the model takes as given) is at the golden-rule level: k(0) = kGR.Sketch the paths of c and k.(b) Consider the same initial situation as in part (a), but in the
Using the phase diagram to analyze the impact of unanticipated and anticipated temporary changes. Analyze the following two variations on Problem 2.11:(a) At time 0, the government announces that it will tax investment income at rate τ from time 0 until some later date t1; thereafter investment
Using the phase diagram to analyze the impact of an anticipated change.Consider the policy described in Problem 2.10, but suppose that instead of announcing and implementing the tax at time 0, the government announces at time 0 that at some later time, time t1, investment income will begin to be
Capital taxation in the Ramsey Cass Koopmans model. Consider a Ramsey Cass Koopmans economy that is on its balanced growth path. Suppose that at some time, which we will call time 0, the government switches to a policy of taxing investment income at rate τ . Thus the real interest rate that
A closed-form solution of the Ramsey model. (This follows Smith, 2006.)Consider the Ramsey model with Cobb Douglas production, y(t) = k (t)α, and with the coefficient of relative risk aversion (θ) and capital’s share (α) assumed to be equal.(a) What is k on the balanced growth path (k∗)?(b)
Derive an expression analogous to (2.40) for the case of a positive depreciation rate.
Describe how each of the following affects the c = 0 and k = 0 curves in Figure 2.5, and thus how they affect the balanced-growth-path values of c and k:(a) A rise in θ.(b) A downward shift of the production function.(c) A change in the rate of depreciation from the value of zero assumed in the
Growth, saving, and r − g. Piketty (2014) argues that a fall in the growth rate of the economy is likely to lead to an increase in the difference between the real interest rate and the growth rate. This problem asks you to investigate this issue in the context of the Ramsey Cass Koopmans model.
Consider a household with utility given by (2.2) (2.3). Assume that the real interest rate is constant, and let W denote the household’s initial wealth plus the present value of its lifetime labor income (the right-hand side of [2.7]). Find the utilitymaximizing path of C, given r, W, and the
Assume that the instantaneous utility function u(C ) in equation (2.2) is ln C. Consider the problem of a household maximizing (2.2) subject to (2.7). Find an expression for C at each time as a function of initial wealth plus the present value of labor income, the path of r(t), and the parameters
(a) Suppose it is known in advance that at some time t0 the government will confiscate half of whatever wealth each household holds at that time. Does consumption change discontinuously at time t0? If so, why (and what is the condition relating consumption immediately before t0 to consumption
The elasticity of substitution with constant-relative-risk-aversion utility.Consider an individual who lives for two periods and whose utility is given by equation (2.43). Let P1 and P2 denote the prices of consumption in the two periods, and let W denote the value of the individual’s lifetime
Consider N firms each with the constant-returns-to-scale production function Y =F (K,AL), or (using the intensive form) Y = ALf (k). Assume f(•) > 0, f (•) < 0.Assume that all firms can hire labor at wage wA and rent capital at cost r, and that all firms have the same value of A.(a) Consider
Derive equation (1.50). (Hint: Follow steps analogous to those in equations [1.47]and [1.48].)
(a) In the model of convergence and measurement error in equations (1.39) and(1.40), suppose the true value of b is −1. Does a regression of ln(Y/N )1979 −ln(Y/N )1870 on a constant and ln(Y/N )1870 yield a biased estimate of b?Explain.(b) Suppose there is measurement error in measured 1979
Consider a Solow economy on its balanced growth path. Suppose the growthaccounting techniques described in Section 1.7 are applied to this economy.(a) What fraction of growth in output per worker does growth accounting attribute to growth in capital per worker? What fraction does it attribute to
Embodied technological progress. (This follows Solow, 1960, and Sato, 1966.)One view of technological progress is that the productivity of capital goods built at t depends on the state of technology at t and is unaffected by subsequent technological progress. This is known as embodied technological
Go through steps analogous to those in equations (1.29) (1.32) to find how quickly y converges to y∗ in the vicinity of the balanced growth path. (Hint: Since y =f (k), we can write k = g(y), where g(•) = f −1(•).)
Consider the same setup as at the start of Problem 1.10: the economy is described by the assumptions of the Solow model, except that factors are paid their marginal products and all labor income is consumed and all other income is saved. Show that the economy converges to a balanced growth path,
Consider Problem 1.10.Suppose there is a marginal increase in K.(a) Derive an expression (in terms of K/Y, δ, the marginal product of capital FK, and the elasticity of substitution between capital and effective labor in the gross production function F (•)) that determines whether a marginal
This question asks you to use a Solow-style model to investigate some ideas that have been discussed in the context of Thomas Piketty’s recent work (see Piketty, 2014; Piketty and Zucman, 2014; Rognlie, 2015). Consider an economy described by the assumptions of the Solow model, except that
Factor payments in the Solow model. Assume that both labor and capital are paid their marginal products. Let w denote ∂F (K,AL)/∂L and r denote[∂F (K,AL)/∂K ] − δ.(a) Show that the marginal product of labor, w, is A[ f (k) − kf (k)].(b) Show that if both capital and labor are paid
Suppose that investment as a fraction of output in the United States rises permanently from 0.15 to 0.18.Assume that capital’s share is 1 3 .(a) By about how much does output eventually rise relative to what it would have been without the rise in investment?(b) By about how much does consumption
Find the elasticity of output per unit of effective labor on the balanced growth path, y∗, with respect to the rate of population growth, n. If αK(k∗) = 1 3 , g = 2%, and δ = 3%, by about how much does a fall in n from 2 percent to 1 percent raise y∗?
Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of population growth falls.(a) What happens to the balanced-growth-path values of capital per worker, output per worker, and consumption per worker?
Suppose that the production function is Cobb Douglas.(a) Find expressions for k∗, y∗, and c∗ as functions of the parameters of the model, s, n, δ, g, and α.(b) What is the golden-rule value of k?(c) What saving rate is needed to yield the golden-rule capital stock?
Consider an economy with technological progress but without population growth that is on its balanced growth path. Now suppose there is a one-time jump in the number of workers.(a) At the time of the jump, does output per unit of effective labor rise, fall, or stay the same? Why?(b) After the
Describe how, if at all, each of the following developments affects the break-even and actual investment lines in our basic diagram for the Solow model:(a) The rate of depreciation falls.(b) The rate of technological progress rises.(c) The production function is Cobb Douglas, f (k) = kα, and
Suppose that the growth rate of some variable, X, is constant and equal to a > 0 from time 0 to time t1; drops to 0 at time t1; rises gradually from 0 to a from time t1 to time t2; and is constant and equal to a after time t2.(a) Sketch a graph of the growth rate of X as a function of time.(b)
Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative of its log to show:(a) The growth rate of the product of two variables equals the sum of their growth rates. That is, if Z(t) = X(t)Y(t), then Z(t)/Z(t) = [X(t)/X(t)] + [Y(t)/Y(t)].(b) The
Explain the following lags in detail.a) Inside lagsb) Outside lagsc) Monetary and fiscal policy lags
What is the “rule versus discretion” concept? Explain.
Write a note on following:a) the Polak fund model;b) the Bank Model;c) the gradualism policy;d) credibility
Explain the merged bank fund model in detail.
The size of debt matters in an economy. What is the role of welfare programs in a government‘s budget?
Write a note on the burden of debt. What policies are required to get rid of this debt?
What is the Barro-Ricardo problem?
Explain the dynamics of debt and deficit.
Write a note on the debt management of government.
How can a deficit be financed? What is the mechanism for such financing?
Write a note on the Laffer curve.
Explain the relationship between the budget deficit and public debt.
What is the relationship between the deficit and hyperinflation?
Inflation tax reduces the inflation in an economy. Explain in detail.
Explain the government’s budget constraints.
Why are implicit contracts criticized by policy makers?
What is the implicit contract? How does it help firms to decide the wages?
Explain the term “Ricardian equivalence”.
Why is the Lucas supply curve criticized?
Explain the Lucas supply curve in detail.
What is the rational expectation hypothesis? Explain.
Examine the primary deficit and its stability.
Debt and gross domestic product are related to interest rate. Explain.
Explain the government budget constraints.
What is the concept of the staggered wage contract?
How does the efficiency wage hypothesis help to achieve equilibrium in output and employment?Discuss.
Explain the efficiency wage hypothesis.
Write a note on the following:a) The Mundell-Fleming modelb) Perfect capital mobility and a flexible exchange ratec) Policy effect of the Mundell-Fleming modeld) Goods market equilibrium in an open economye) Exchange rate system
Explain the relationship between currency appreciation and depreciation and the interest rate. How will it help to achieve equilibrium in the balance of payments?
Export-led policies help to achieve the balance of payment equilibrium. How can the disequilibrium in the capital account of a county be corrected?
The devaluation of a currency helps to reduce the trade deficit. Discuss.
Exchange rate depreciation leads to an increase in the price level in a country. Explain.
What is the macroeconomic stabilization approach? Explain.
Explain the external sector equilibrium in detail.
Exchange rate overshooting reduces the trade deficit of a country. Explain.

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Advanced Macroeconomics 1st Edition Sanjay Rode - Solutions

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