All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
foundations of modern macroeconomics

Questions and Answers of Foundations Of Modern Macroeconomics

3. Compute the steady state values, k*, y* and c*, for the capital-labour ratio, income per worker, and consumption per worker, respectively (use k=0). Explain and compare to the parallel expressions
2. Illustrate the above Solow equation in a Solow diagram with k along the horizontal axis and the curve sBk as well as the ray (n+5)k along the vertical axis. Demonstrate (from the Solow diagram)
1. Show that from k = K/L it follows k/k=K/K-L/L. (Hint: You can do the 'log-dif-trick', that is, first take logs on both sides of k = K/L and then differentiate with respect to time.) Then show that
4. In Chapter 2 it was shown that developed economies have experienced relatively constant positive growth rates in GDP per worker (annual rates around 2 per cent) and relatively constant
3. Show that with the CES production function, the income share of labour under competitive market clearing is: WL Y 1-a (+) =+ (1-a)
2. Find the marginal rate of substitution between capital and labour for the CES production function, and show that the elasticity of substitution is -, independent of r and w. The CES function is
1. Find the marginal rate of substitution between capital and labour (the marginal product of capital divided by the marginal product of labour) for the Cobb-Douglas production function. Show that
Exercise 6. Growth and trade This chapter has presented the stylized facts of growth that are most important for the theoretical developments in subsequent chapters. There is at least one more
Exercise 5. Level convergence among the rich? Commenting on Fig. 2.3 in Section 2.3 we said that it showed a tendency towards convergence to a common growth path with constant growth for the
Exercise 4. Growth against ultimo level In Section 2.3 there were figures showing across countries the log of GDP per worker in an initial year along the horizontal axis, and average annual growth in
Exercise 3. Time to double Assume that in a specific country GDP per capita, or per worker, grows at the rate g each year over many years, where g is written as a percentage, e.g. 2 per cent. Show
Exercise 2. The income distribution for the rich part of the world Table 2.4 shows GDP per worker (in 2000 US dollars) and population size for 1951 and 2003 for the rich part of the world (defined
Exercise 1. GDP per capita versus GDP per worker Give some arguments why GDP per worker, rather than GDP per capita, should be used for a comparison of standards of living between countries.
3. Consider the introduction of leisure to the household’s utility function: U = ∞ 0 e−ρt[ln Ct + β ln(L − lt)]dt, (16.35) where the parameter β > 0 determines the importance of leisure
2. Suppose the government provides R&D subsidies. Derive the equilibrium level of R&D labour in the Schumpeterian growth model without capital.
1. Consider the Schumpeterian growth model without capital. Use the Hamiltonian function Ht = ln At + ln(L − Lr,t) + λtAt(θ ln z)Lr,t, (16.33) to show that the optimal allocation of R&D labour
3. Derive the socially optimal rate of R&D subsidies in the Romer model.
2. Show that the socially optimal allocation of R&D labour in the Romer model is given by L∗ R = L − ρ θ . (15.32) In the Romer model, intertemporal knowledge spillovers are also present
1. Consider the general law of motion for the number of varieties given by N˙ t = θNφ t LR,t. (15.29) Show that the socially optimal rate of R&D subsidies is given by ς∗ = 1 − α ρ + n ρ +
4. Consider the introduction of leisure to the household’s utility function in the Jones model: U = ∞ 0 e−ρt [ln Ct + β ln (1 − lt)] dt, where the parameter β > 0 determines the
3. Show that on the balanced growth path, the saving rate s∗ in the Jones model is given by s∗ = α μ δ + gN + n ρ + δ + gN + n. (14.16)
2. Show that on the balanced growth path, the growth rate of capital, output and consumption is given by gN + n.
1. Suppose the government imposes an upper bound on the monopolistic price given by Pt(i) = μRt < Rt/α, (14.14) where the parameter μ ∈ (1, 1/α) is the markup ratio, capturing the monopolistic
4. Suppose the production function in the Romer model is given by Yt = H1−α−β Y,t Lβ t Nt 0 Xα t (i) di, where HY,t is the number of high-skill production workers, and Lt is the number of
3. Show that on the balanced growth path, the saving rate s∗ in the Romer model is given by s∗ = α μ δ + gN ρ + δ + gN . (13.26)
2. Show that on the balanced growth path, the growth rate of capital, output and consumption is given by gN .
1. Suppose the government imposes an upper bound on the monopolistic price given by Pt(i) = μRt < Rt/α, (13.24) where the parameter μ ∈ (1, 1/α) is the markup ratio, capturing the
4. Suppose the growth rate of labour is L˙ t/Lt = n. Derive the steady-state saving rate in the monopolistic version of the Ramsey model.
3. Consider the introduction of leisure to the household’s utility function: U = ∞ 0 e−ρt[ln Ct + β ln(1 − lt)]dt, (12.28) where the parameter β > 0 determines the importance of leisure
2. Suppose Lt = L. Derive the steady-state saving rate in the monopolistic version of the Ramsey model.
1. Suppose the policy parameter μ ∈ (1, 1/α) determines the markup ratio. Compare the steady-state saving rate from the monopolistic version of the Ramsey model to the consumption-maximising
5. Suppose the growth rate of labour is L˙ t/Lt = n and the growth rate of technology is A˙ t/At = gA. Derive the steady-state saving rate and the long-run growth rate of output in the Ramsey model
4. Suppose the growth rate of labour is L˙ t/Lt = n. Derive the steadystate saving rate in the Ramsey model.
3. Consider the introduction of leisure to the household’s utility function: U = ∞ 0 e−ρt[ln Ct + β ln(1 − lt)]dt, (10.24) where the parameter β > 0 determines the importance of leisure
2. Suppose Lt = L. Derive the steady-state saving rate in the Ramsey model.
1. Compare the steady-state saving rate from the Ramsey model to the consumption-maximising saving rate s in the Solow model.Which one is higher? Under what condition would they be the same?
6. Consider an extension of the Solow growth model with human capital accumulation. The production function is Yt = AKα t H1−α t , where Ht is human capital. The level of technology A is
5. Suppose the growth rate of labour is L˙ t/Lt = n and the growth rate of technology is A˙ t/At = gA. What is the long-run growth rate of output per capita in the Solow model?
4. Suppose the growth rate of labour is L˙ t/Lt = n. Derive the steadystate levels of capital per capita and output per capita in the Solow model.
3. Suppose Lt = L. Derive the steady-state levels of capital per capita and output per capita.
2. Derive the steady-state level of consumption. Show that setting the saving rate to s = α maximises the steady-state level of consumption.
1. Use (9.7) and the phase diagram in Figure 9.1 to show the effects of (a) a one-time increase in the level of technology A and (b) a continuous increase in the level of technology A.
3. Suppose monopolistic firms can adjust their capital input Ki in addition to labour input li when yi changes in the short run. How does an increase in the level of money supply affect the capital
2. Given (8.16), show that the profit-maximising price pi = MCi/ε continues to hold. Also, derive the amount of monopolistic profit πi and show that πi → 0 as ε → 1. Explain the intuition.
1. Suppose all the monopolistic firms i ∈ [1, N] can now adjust their capital input Ki in addition to labour input li when yi changes in the short run. Show that the marginal cost of producing yi
4. Suppose the government uses labour income tax to finance its spending and the capital depreciation rate is positive. Derive the steady-state equilibrium levels of {l ∗, K∗, I∗, Y ∗, C∗}.
3. What are the long-run effects of labour income tax τW on consumption and investment?
2. Derive the steady-state equilibrium levels of capital K∗ and output Y ∗
1. Consider a positive capital depreciation rate δ > 0. In this case, the asset-accumulation equation becomes K˙ t = (Rt − δ)Kt + (1 − τW )Wtlt − Ct − Tt. (6.23) Show that the
4. Consider the following government’s budget constraint: Tt = Gt + T Rt = γYt + T Rt, where T Rt is the transfer payment from the government to the household. In this case, the household’s
3. What are the long-run effects of government spending γ on consumption and investment?
2. Derive the steady-state equilibrium levels of capital K∗ and output Y ∗.
1. Consider a positive capital depreciation rate δ > 0. In this case, the asset-accumulation equation becomes K˙ t = (Rt − δ)Kt + Wtlt − Ct − Tt. Show that the steady-state equilibrium level
4. Consider the following household’s lifetime utility function: U = ∞ 0 e−ρt ln Ct − l 1+ϕ t 1 + ϕ dt, where ϕ > 0. Derive the labour supply curve
3. Consider an alternative utility function given by U = ∞ 0 e−ρt (ln Ct − βlt) dt. (4.23) Show that the labour supply curve becomes perfectly elastic. How does an increase in consumption
2. Derive the steady-state equilibrium levels of capital K∗ and output Y ∗.
1. Consider a positive capital depreciation rate δ > 0. In this case, the asset-accumulation equation becomes K˙ t = (Rt − δ)Kt + Wtlt − Ct. (4.21) Show that the steady-state equilibrium level
3. Consider a positive capital depreciation rate δ > 0. Derive the long-run capital supply curve. How does the capital depreciation rate δ affect the long-run capital supply curve?
2. What are the short-run and long-run effects of an increase in the household’s discount rate ρ on {Yt, Kt, Rt, Wt}?
1. What are the short-run and long-run effects of an increase in the level of labour supply L on {Yt, Kt, Rt, Wt}?
4. Suppose the household has the following instantaneous utility function: ut = C1−σ t − 1 1 − σ , where σ > 0 determines the elasticity of intertemporal substitution as 1/σ. This
3. How does an increase in the capital depreciation rate δ affect the steady-state consumption rate C∗/Y ∗? What happens to this effect as α → 0?
2. Consider a positive capital depreciation rate δ > 0. Compute the elasticity of {K∗, Y ∗, I∗, C∗} with respect to technology A.
1. Consider a positive capital depreciation rate δ > 0. In this case, the asset-accumulation equation becomes K˙ t = (Rt − δ)Kt + WtL − Ct. (2.20) Show that the optimal consumption path is
6. How do changes in β in Exercise 4 affect the labour and capital markets when capital supply is elastic?
5. How do changes in β in Exercise 4 affect the labour and capital markets when capital supply is perfectly inelastic (i.e., K = K)?
4. Suppose the supply of labour is chosen by a utility-maximising household with the following utility function: U = C − βL2 2 , where β determines the importance of leisure relative to
3. Suppose the supply of capital is elastic. How does an increase in the supply of labour affect the nominal variables?
2. Show that the neutrality of money holds when the supply of capital and/or labour is elastic.
1. How do changes in the level of technology affect the labour and capital markets when both labour supply and capital supply are elastic?
1.5. Use a calculator to find each of the following:a.b.c.d.e.f.6.50.3 50.350.2(50.25)2(50.550.3)2 50.4 50.2/50.5 5−0.5a. Nominal GDP equals real GDP times the GDP deflator(see Section 2.4 ).
1.4. Suppose that the amount of output, , that a firm can produce depends on its amount of capital, , and the number of workers employed, , according to the functiona. Suppose that . Give the
1. 3. For the function , use Eq. (A.4) to write a general expression for the slope. This expression for the slope will depend on the initial value of , , and on the change in ,. For values of
1. 2. Graph the function . Starting from the point at which , find the slope of the function for and . What is the slope of the line tangent to the function at ? (See Problem 3 .)
1.1. Graph the function . What is the slope of this function?
1. 4.In Section 15.4 , we discuss the potential relationship between government deficits and inflation. In this question, you will investigate the data on government debt as a share of GDP and the
1. 15.5 . What macroeconomic or political factors have caused the changes you observe in the deficit measures?
1. 2. Both transfer programs and taxes affect incentives. Consider a program designed to help the poor that promises each aid recipient a minimum income of $10,000. That is, if the recipient earns
1.1. Why is some state and local spending paid for by grants in aid from the Federal government instead of entirely through taxes levied by states and localities on residents? What are the advantages
1. 9. Consider an economy in which the money supply consists of both currency and deposits. The growth rate of the monetary base, the growth rate of the money supply, inflation, and expected
1.1. The following budget data are for a country having both a central government and provincial governments:Central purchases of goods and services 200 Provincial purchases of goods and services 150
1.10. Define inflation tax (also called seignorage). How does the government collect this tax, and who pays it? Can the government always increase its real revenues from the inflation tax by
1. 9. Discuss four reasons why the Ricardian equivalence proposition isn’t likely to hold exactly.
1. 8. In what ways is the government debt a potential burden on future generations? What is the relationship between Ricardian equivalence and the idea that government debt is a burden?
1. 7. Why do economists suggest that tax rates be kept roughly constant over time, rather than alternating between high and low levels?
1. 6. Give a numerical example that shows the difference between the average tax rate and the marginal tax rate on a person’s income.For a constant before-tax real wage, which type of tax rate most
1. 4. What are the three main ways that fiscal policy affects the macroeconomy? Explain briefly how each channel of policy works.
1. 3. How is government debt related to the government deficit? What factors contribute to a large change in the debt–GDP ratio?
1. 2. Explain the difference between the overall government budget deficit, the current deficit, and the primary current deficit. Why are three deficit concepts needed?
1.1. What are the major components of government outlays? What are the major sources of government revenues? How does the composition of the Federal government’s outlays and revenues differ from
1. Discuss the economic effects of government deficits and debt.
1. Describe how government spending and taxing decisions affect the macroeconomy.
1. Use the measures of government outlays and taxes to measure government surpluses and deficits.
1. Graph the three-month Treasury bill interest rate and the unemployment rate, using monthly data since 1961. If changes in monetary policy are reflected primarily by changes in the short term
1. 3. As discussed in the text, if money demand is unstable, the Fed may prefer to target interest rates rather than the money supply itself. When the Fed follows an interest-rate-targeting policy,
1. 2. During much of the postwar period, the Fed attempted to stabilize nominal interest rates. However, during 1979–1982 the Fed under Paul Volcker greatly reduced its emphasis on interest rate
1.1. Obtain data on currency held by the nonbank public, which is called the currency component of M1 (starting in 1959). Define“deposits” for each year since 1959 to be M2 minus currency, and
1. 4. Why do many governments have policies against negotiating with hostage-taking terrorists? Under what conditions, if any, are such policies likely to reduce hostage taking? Discuss the analogy
1. 3. Use the LR curve to show how each of the following shocks affects output, the real interest rate, and the price level in the short run and the long run, following the Keynesian model. Draw a
1. 2. Suppose that the Fed were committed to following the Taylor rule in Eq. (14.6) . For each of the following types of shocks,determine whether the use of the Taylor rule would tend to be

Showing 1 - 100 of 1938

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved