answer alll,,,the question is complete

A more flexible specification of the technology than the Cobb-Douglas function. Consider the CES production function3 = + (1 )1 (*) where and are parameters satisfying 0, 0 1 and 1 6= 0 a) Does the production function imply CRS? Why or why not? b) Show that (*) implies = 1 and = (1 ) 1 c) Express the marginal rate of substitution of capital for labor in terms of d) In case of an affirmative answer to a), derive the intensive form of the production function. e) Is the production function neoclassical? Hint: a convenient approach is to focus on expressed in terms of and consider the cases 0 and 0 1 separately; next use a certain symmetry visible in (*); finally use your answer to a). f) Draw a graph of as a function of for the cases 0 and 0 1 respectively. Comment and compare with a Cobb-Douglas function on intensive form, = . 4 g) Write down a CES production function with Harrod-neutral technical progress.

A potential source of permanent productivity growth (this exercise presupposes that f) of Problem I.8 has been solved). Consider a Solow-type growth model, cf. Problem I.6. Suppose the production function is a CES function as in (*) of Problem I.8. Let (0 1) 1 ( + ) and ignore technical progress.

a) Express in terms of where and b) For a given 0, illustrate the dynamic evolution of the economy by a "modified Solow diagram", i.e., a diagram with on the horizontal axis and on the vertical axis c) Find the asymptotic value of the growth rate of for Comment. d) What is the asymptotic value of the growth rate of for e) The model displays a feature that may seem paradoxical in view of the absence of technical progress. What is this feature and why is it not paradoxical after all, given the assumptions of the model?

Consider the government budget in a small open economy (SOE) fully integrated in the world market for goods and financial capital.

Time is discrete, the period length is one year, and there is no uncertainty. Let and be non-negative constants and let = 0(1 + ) (1 + ) = real GDP, = real government spending on goods and services, = real net tax revenue ( = gross tax revenue transfer payments), = real public debt at the start of period = real interest rate in the SOE = world market real interest rate. We assume that any government budget deficit is exclusively financed by issuing debt (and any budget surplus by redeeming debt). a) Interpret and b) Suppose the current inflation rate in the SOE equals Given this inflation rate and given , what is the level of the nominal interest rate, ? You should provide the exact formula, not an approximation. Let = 003 per year and = 002 What is exactly? Instead, let = 004 per year and = 015 (as in many countries in the aftermath of the second oil crisis 1979-80). What is exactly? Compare with the result you get from the standard approximative formula. c) Returning to variables in real terms, write down the real budget deficit and an equation showing how +1 is determined From now on assume that = a constant. Consider a scenario with 0 0 1 + (1 + )(1 + ) and = a positive constant less than one. d) What does government solvency mean and what does fiscal sustainability mean? e) Find the maximum constant which is consistent with fiscal sustainability (as evaluated on the basis of the expected evolution of the debt-GDP ratio). Hint: the difference equation +1 = + where and are constants, 6= 1 has the solution = (0 ) + where = (1 )

Consider a small open economy (SOE) facing a constant real interest rate 0 given from the world market for financial capital. We ignore business cycle fluctuations and assume that real GDP, grows at a constant exogenous rate 0. We assume 11 Time is discrete. Further notation is: = real government spending on goods and services, = real net tax revenue ( = gross tax revenue transfer payments), = real government budget deficit, = real public debt (all short-term) at the start of period . Assume that any government budget deficit is exclusively financed by issuing debt (and any budget surplus by redeeming debt). a) Write down the dynamic identity relating the increase in to the level of Suppose that 0 0 and = = 0 1 , where 0 1 Define the "net tax burden" as b) Find the minimum net tax burden, which, if maintained, is consistent with fiscal sustainability (as evaluated on the basis of the expected evolution of the debt-GDP ratio). Hint: different approaches are possible; one of these focuses on the debt-income ratio and uses the fact that a difference equation +1 = + where and are constants, 6= 1 has the solution = (0 ) + where = (1 ) c) How does depend on and respectively? Comment. II.3 Consider a budget deficit rule saying that 100 percent of the interest expenses on public nominal debt, plus the primary budget deficit must not be above 100 percent of nominal GDP, , where is real GDP, growing at a constant rate, 0 and is the GDP deflator. So the rule requires that + ( ) (*) where 0 0 and = real government spending on goods and services, = real net tax revenue, = (1 + )(1 + ) 1 where is the real interest rate, = 1 1 = the inflation rate, a given non-negative constant. a) Is the deficit rule of the Stability and Growth Pact in the EMU a special case of (*)?

Consider a small open economy (SOE) facing a constant real interest rate 0 given from the world market for financial capital. We ignore business cycle fluctuations and assume that real GDP, grows at a constant exogenous rate 0. We assume 11 Time is discrete. Further notation is: = real government spending on goods and services, = real net tax revenue ( = gross tax revenue transfer payments), = real government budget deficit, = real public debt (all short-term) at the start of period . Assume that any government budget deficit is exclusively financed by issuing debt (and any budget surplus by redeeming debt). a) Write down the dynamic identity relating the increase in to the level of Suppose that 0 0 and = = 0 1 , where 0 1 Define the "net tax burden" as b) Find the minimum net tax burden, which, if maintained, is consistent with fiscal sustainability (as evaluated on the basis of the expected evolution of the debt-GDP ratio). Hint: different approaches are possible; one of these focuses on the debt-income ratio and uses the

fact that a difference equation +1 = + where and are constants, 6= 1 has the solution = (0 ) + where = (1 ) c) How does depend on and respectively? Comment. II.3 Consider a budget deficit rule saying that 100 percent of the interest expenses on public nominal debt, plus the primary budget deficit must not be above 100 percent of nominal GDP, , where is real GDP, growing at a constant rate, 0 and is the GDP deflator. So the rule requires that + ( ) (*) where 0 0 and = real government spending on goods and services, = real net tax revenue, = (1 + )(1 + ) 1 where is the real interest rate, = 1 1 = the inflation rate, a given non-negative constant. a) Is the deficit rule of the Stability and Growth Pact in the EMU a special case of (*)?

b) Let (1) Derive the law of motion (difference equation) for assuming the deficit ceiling is always binding. Hint: GBD = + ( ) Suppose is such that 0 1 + (1 ) (1 + )(1 + ) c) For an arbitrary 0 0 find the time path of Briefly comment. Hint: the difference equation +1 = + where and are constants, 6= 1 has the solution = (0 ) + where = (1 ) d) How does a rise in affect the long-run debt-income ratio? Comment. e) Let the steady-state value of be denoted and assume 0 Illustrate the time path of in the ( ) plane. Comment. f) How does depend on ? Comment. g) How does depend on ? Comment. h) What could the motivation for having

a) What is meant by the No-Ponzi-Game condition of the government? b) The No-Ponzi-Game condition of the government and the intertemporal budget constraint of the government are closely related. In what sense? c) "A given fiscal policy is sustainable if and only if it maintains compliance with the intertemporal budget constraint of the government." True or false? Briefly discuss. d) In the absence of uncertainty and credit frictions, if a government can run a permanent debt rollover without experiencing solvency difficulties (standard notation). Briefly explain. e) How is the inequality in d) modified in the presence of uncertainty and credit frictions? II.5 The Ricardian equivalence issue. What is meant by Ricardian equivalence? Under the assumption of rational expectations and at most a "weak" bequest motive, overlapping generations models refute Ricardian equivalence. How?

We consider the same economy as that described by (1) - (5) in Problem I.6. a) Find the long-run growth rate of output per unit of labor, . b) Suppose the economy is in steady state up to and including period 1 Then, at time (the beginning of period ) an upward shift in the saving rate occurs. Illustrate by a transition diagram the evolution of the economy from period onward c) Draw the time profile of ln in the ( ln ) plane. d) How, if at all, is the level of affected by the shift in ? e) How, if at all, is the growth rate of affected by the shift in ? Here you may have to distinguish between temporary and permanent effects. f) Explain by words the economic mechanisms behind your results in d) and e). g) As Solow once said (in a private correspondence with Amartya Sen2): "The idea [of the model] is to trace full employment paths, no more." What market form is theoretically capable of generating permanent full employment? h) Even if we recognize that the Solow model only attempts to trace hypothetical time paths with full employment (or rather employment corresponding to the "natural" or "structural" rate of unemployment), the model has at least one important limitation. What is in your opinion that limitation? the question is complete plz

A more flexible specification of the technology than the Cobb-Douglas function. Consider the CES production function3 = + (1 )1 (*) where and are parameters satisfying 0, 0 1 and 1 6= 0 a) Does the production function imply CRS? Why or why not? b) Show that (*) implies = 1 and = (1 ) 1 c) Express the marginal rate of substitution of capital for labor in terms of d) In case of an affirmative answer to a), derive the intensive form of the production function. e) Is the production function neoclassical? Hint: a convenient approach is to focus on expressed in terms of and consider the cases 0 and 0 1 separately; next use a certain symmetry visible in (*); finally use your answer to a). f) Draw a graph of as a function of for the cases 0 and 0 1 respectively. Comment and compare with a Cobb-Douglas function on intensive form, = . 4 g) Write down a CES production function with Harrod-neutral technical progress.

A potential source of permanent productivity growth (this exercise presupposes that f) of Problem I.8 has been solved). Consider a Solow-type growth model, cf. Problem I.6. Suppose the production function is a CES function as in (*) of Problem I.8. Let (0 1) 1 ( + ) and ignore technical progress.

a) Express in terms of where and b) For a given 0, illustrate the dynamic evolution of the economy by a "modified Solow diagram", i.e., a diagram with on the horizontal axis and on the vertical axis c) Find the asymptotic value of the growth rate of for Comment. d) What is the asymptotic value of the growth rate of for e) The model displays a feature that may seem paradoxical in view of the absence of technical progress. What is this feature and why is it not paradoxical after all, given the assumptions of the model?

Consider the government budget in a small open economy (SOE) fully integrated in the world market for goods and financial capital.

Time is discrete, the period length is one year, and there is no uncertainty. Let and be non-negative constants and let = 0(1 + ) (1 + ) = real GDP, = real government spending on goods and services, = real net tax revenue ( = gross tax revenue transfer payments), = real public debt at the start of period = real interest rate in the SOE = world market real interest rate. We assume that any government budget deficit is exclusively financed by issuing debt (and any budget surplus by redeeming debt). a) Interpret and b) Suppose the current inflation rate in the SOE equals Given this inflation rate and given , what is the level of the nominal interest rate, ? You should provide the exact formula, not an approximation. Let = 003 per year and = 002 What is exactly? Instead, let = 004 per year and = 015 (as in many countries in the aftermath of the second oil crisis 1979-80). What is exactly? Compare with the result you get from the standard approximative formula. c) Returning to variables in real terms, write down the real budget deficit and an equation showing how +1 is determined From now on assume that = a constant. Consider a scenario with 0 0 1 + (1 + )(1 + ) and = a positive constant less than one. d) What does government solvency mean and what does fiscal sustainability mean? e) Find the maximum constant which is consistent with fiscal sustainability (as evaluated on the basis of the expected evolution of the debt-GDP ratio). Hint: the difference equation +1 = + where and are constants, 6= 1 has the solution = (0 ) + where = (1 )