Answer all 3

Consider a small open economy where domestic and foreign financial claims are perfect substitutes and there is perfect mobility of financial capital, but no mobility of labor. The real interest rate in the world financial market is a positive constant The dynamics of the economy are described (at least for some time) by the differential equation = ( ) + + where = ( + )( + ) = ( + )( + + ) Notation: () , () , = national wealth, = technology level, = population, = aggregate consumption, and is the real wage per unit of effective labor. The following parameters are strictly positive: ; the remaining are non-negative. a) Briefly interpret the model, including the parameters. Assume + + b) Draw a phase diagram in ( ) space as well as ( ) space. Illustrate in the diagram the path the economy follows for 0, given the initial condition: 0

c) Sign the long-run current account surplus of the country. Hint: in the balance of payments accounting the current account surplus equals the increase in net foreign assets (whether this increase is positive or negative). d) Suppose that at some point in time an unanticipated shift in the world interest rate occurs. If we imagine that this happens against the background of an international financial turmoil like the one in 2008-2009, what sign should we expect the shift to have? Why? e) Assume agents rightly expect the new interest rate level to last for a long time. Draw a phase diagram illustrating the effects of the shift. Hint: how is affected? Comment. f) Comment on the long-run development of the economy. g) Briefly relate to the evolution of the Chinese economy since 1980. V.2 The Blanchard OLG model for a closed economy is described by the two differential equations = ( ) ( + + ) 0 0 given, (1) = h 0 ( ) i ( + ) (2) and the condition that for any fixed pair ( 0) where 0 0 and 0 lim 0 (0 (())+) = 0 (3) Notation: () and () where and are aggregate capital and aggregate consumption, respectively, is population = labor supply, and is the technology level, all at time Finally, is a production function on intensive form, satisfying (0) = 0 0 0, 00 0 and the Inada conditions. The remaining symbols, except , stand for parameters and we assume all these are strictly positive; is financial wealth at time of a person born at time . Furthermore, 0 a) Briefly interpret (1), (2), and (3), including the five parameters. b) Draw a phase diagram and illustrate the path the economy will follow, given some arbitrary positive initial value of . Can the divergent paths be excluded? Why or why not?

c) Is dynamic inefficiency theoretically possible in this economy? Why or why not? Assume the economy has been in steady state until time 0 Then an unanticipated technology shock occurs so that 0 is replaced by 0 0 0. After this shock everybody rightly expects to grow forever at the same rate, as before. d) Illustrate by the phase diagram (or a new one) what happens to and on impact, i.e., immediately after the shock, and in the long run. e) What happens to the rate of return on impact and in the long run? f) Why is the sign of the impact effect on the real wage ambiguous (at the theoretical level) as long as is not specified further?1 g) What happens to the real wage in the long run? V.3 Fiscal sustainability. Consider the government budget in a small open economy (SOE) with perfect mobility of financial capital, but no mobility of labor. The real rate of interest at the world financial market is a positive constant Time is continuous. Let = GDP at time , = government spending on goods and services at time , = net tax revenue (gross tax revenue transfer payments) at time , = public debt at time All variables are in real terms (i.e., measured with the output good as numeraire). Taxes and transfers are lump-sum. Assume there is no uncertainty and that the budget deficit is exclusively financed by debt issue (no money financing). a) Write down an equation describing how the budget deficit and the increase per time unit in public debt are linked. Suppose grows at a constant rate equal to + where is the rate of (Harrod-neutral) technical progress and is the growth rate of the labor force (= employment) Suppose + 0 Assume = and = , where and are constant over time, 0 1. Let initial debt, 0 be positive.

b) Find the minimum initial primary surplus 0 required for fiscal sustainability. Hint: one possible approach is to derive an expression for where ; another approach is based on the fact that R 0 = 1 for a given constant 6= 0 c) Suppose Is debt explosion possible? d) How does 0 depend on the growth-corrected interest rate? Suppose instead that 0 is negative. e) Is debt explosion possible? f) Answer question b) again. Comment. g) Answer question d) again. Comment. V.4 (Re-exam Febr. 2016) Consider a Blanchard OLG model for a closed economy with a public sector, public debt, and lump-sum taxation. The dynamics of the economy are described by the differential equations = (( ) ) ( + )( + ) (1) = ( ) 0 0 given, (2) = [( ) ] + 0 0 given, (3) the condition lim 0 [()] 0 (4) and a requirement that households satisfy their transversality conditions. Here, is aggregate private consumption, is physical capital, is population = labor supply, is public debt, is government spending on goods and services, is net tax revenue (= gross tax revenuetransfer payments), and is an aggregate neoclassical production function with constant returns to scale and satisfying the Inada conditions. The other symbols stand for parameters and all these are positive; and are positive constants. A dot over a variable denotes the derivative w.r.t. time a) Briefly interpret the equations (1) - (3), the weak inequality (4), and the parameters.

b) Assuming 0 0 and a balanced budget for all 0 derive and construct a phase diagram for the resulting two-dimensional dynamics. Make sure you explain how the curves and arrows you draw are implied by the model. Illustrate the path the economy follows for an arbitrary 0 0. It is understood that and 0 are "modest" relative to the production possibilities of the economy, given this 0. Make sure you explain how the illustrated path is implied by the model. We will first do comparative dynamics. c) Suppose that two countries, Country I and Country II, are both well described by the model. The countries are similar at time = 0 except that Country I has less debt than Country II, that is, 0 0 (and as a consequence the countries possibly also differ w.r.t. 0) The countries have the same 0 Comment on the implied long-run differences between the countries. Now we shift to dynamic analysis of just Country I. Suppose Country I has been in its steady state until time 0 0 Then, suddenly the government changes fiscal policy so that = where is a constant which is smaller than the tax revenue in the old steady state. d) Define what is meant by fiscal policy being sustainable. Is the fiscal policy ( ) sustainable? Why or why not? Hint: there are different approaches; one approach uses that if is a positive constant, then R 0 (0) = 1 Suppose that at time 1 0, taxation in country I again changes such that for 1 the government budget is balanced and people rightly expect it to remain so. Between 0 and 1 we can not precisely pin down the evolution of the economy because the market participants did not know in advance when a fiscal tightening - or debt default - would occur. Yet, qualitatively something can be said about the position of the economy in the ( ) plane immediately after time 1 e) Construct a phase diagram in the ( ) plane to illustrate a possible position of the economy immediately after time 1 as well as the movement of the economy over time afterwards. f) Illustrate by graphical time profiles the corresponding motion over time of and for 0