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foundations macroeconomics

Questions and Answers of Foundations Macroeconomics

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
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
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
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
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) =
(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
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).
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
(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.
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
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
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
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
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
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
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.
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
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
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
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
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
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
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,
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.
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
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) =
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
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
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
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)
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
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.
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
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
(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?
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
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
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
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
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
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
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
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
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;
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
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
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
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
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
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
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
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
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
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
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.
What are the adjustments required to reduce the twin deficits in an economy?
Explain policy dilemma in the equilibrium of economy.
What is exchange rate overshooting?
Explain the monetary approach to the balance of payments
Explain devaluation in detail.
Explain the role of prices in an open economy.
Explain the term “competitive depreciation”.

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