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I.8 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. I.9 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. 3CES stands for Constant Elasticity of Substitution. 4This function can in fact be shown to be the limiting case of the CES function (in intensive form) for 0

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? I.10 An important aspect of macroeconomic analysis is to pose good questions in the sense of questions that are concise, interesting, and manageable. If we set aside an hour or so in one of the lectures or class exercises, what question would you suggest should be discussed?

II.4 Short questions 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?

II.2 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 (*)?