Fakultät III Univ.-Prof. Dr. Jan Franke-Viebach

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1 Univ.-Prof. Dr. J. Franke-Viebach WS 206-7: International Macroeconomics (2 nd exam period) Universität Siegen Fakultät III Univ.-Prof. Dr. Jan Franke-Viebach Exam International Macroeconomics Winter Semester (2 nd Exam Period) Available time: 60 minutes Solution For your attention:. The exam is made up of 8 pages (including this cover page). Please check and see if the exam you are holding is complete. 2. For your answers, use the designated spaces. Should these not suffice, use the backside of the pages. Please do not use a pencil. 3. Additional materials you may use for the exam: a non-programmable calculator. (Smart phones and mobile phones are not allowed!) 4. ATTENTION: The names for variables have the same meaning as in the lecture. Insofar as you also use the same symbols for the variables as we did in the lecture you will not have to define these any further. Question Sum Mark Points achievable Points achieved Intern Macro / WS 6-7 2T Solution

2 Univ.-Prof. Dr. J. Franke-Viebach 2 WS 206-7: International Macroeconomics (2 nd exam period) Problem : Aggregate Accounting of an Open Economy Suppose you have the following information about an open economy with a flexible exchange rate. Gross domestic product is 50 while gross domestic demand is 20. The net export of services is 30, the imports of goods are 40. There are neither transfers nor payments of factor income between domestic residents and foreigners. Please calculate the following variables using the appropriate equations from the relevant accounting systems of an open economy: a) Balance of trade in goods and services (NX t ) [2 points] NX t = GDP t GDD t = = 30 () () (0.5) b) Exports of goods ( Ex G t ) [3 points] G S G EX t = NX t NX t + IM t = = 40 (0.5) () () (0.5) c) Balance on current account (CA t ) [2 points] CA t = NX t + BPI t + BSI t = = 30 (0.5) (0.5) (0.5) (0.5) d) Balance on financial account (FA t ) [2 points] FA t = CA t + KA t = = 30 (0.5) () (0.5) e) Balance of the non-reserve financial account (FA t NR ) [2 points] FA NR = FA t R t = 30 0 = 30 (0.5) () (0.5) Intern Macro / WS 6-7 2T Solution

3 Univ.-Prof. Dr. J. Franke-Viebach 3 WS 206-7: International Macroeconomics (2 nd exam period) Problem 2: Representative Consumer in a Small Endowment Economy We consider an economy with exogenous incomes (Y < ) where the representative consumer has a two-period horion. There is no initial international investment position (B = 0). The individual has the following budget constraint. = +(+r)(y -C ) a) Please illustrate the budget constraint in -C space. [ point] 0 C () B A () points for (d) : - if twist is in point A - if twist is counter-clockwise () () ()α 0 C D () Intern Macro / WS 6-7 2T Solution

4 Univ.-Prof. Dr. J. Franke-Viebach 4 WS 206-7: International Macroeconomics (2 nd exam period) b) Please denote the following in the graph above: - the endowment point as A - the maximal future consumption point as B - the maximal present consumption point as D - the angle as α, where tan α = +r [4 points] c) Calculate the slope of budget line. Interpret the slope! [4 points] d dc = ( + r) (0.5) (0.5) Opportunity cost of C in terms of (0.5) (0.5) () () d) Assume the representative consumer consumes at the endowment point. Now the interest rate r falls. Illustrate the change (in the graph above) and calculate the effect on the second-period consumption (d ); show your calculation. [4 points] d = Y C dr = 0 (0.5) (0.5) (0.5) (0.5) Intern Macro / WS 6-7 2T Solution

5 Univ.-Prof. Dr. J. Franke-Viebach 5 WS 206-7: International Macroeconomics (2 nd exam period) Problem 3: Consider the following functions: (I) U = ln C + ß ln, ß = /(+b) II C + + r = Y + + r a) Please briefly interpret function (I). [2 points] intertemporal (or: life-time) utility () () b) What does the factor b in function (I) mean? How will the consumption preference of the representative individual change when b falls? [4 points] - Subjective interest rate () () - individual is more patient (or: generates more utility) () () c) Please give an economic interpretation of the left-hand side of equation (II). [2 points] present value of life-time consumption () (0.5) (0.5) Intern Macro / WS 6-7 2T Solution

6 Univ.-Prof. Dr. J. Franke-Viebach 6 WS 206-7: International Macroeconomics (2 nd exam period) d) Derive the so-called Euler equation by using the Lagrange approach. [7 points] L = ln C + ß ln + λ ( Y + + r C + r ) (0.5) (0.5) (0.5) (0.5) (0.5) (0.5) L C = C λ = 0 () = + r ß C (2) L = ß λ + r = 0 () or: C = + r ß e) In general terms, the Euler equation reads like this: u C = + r ß u ( ). Please interpret this equation. [3 points] marginal utility of consumption in period (0.5) (0.5) must be equal (0.5) to marginal utility of consumption in period 2 multiplied by the interest rate factor (0.5) (0.5) (0.5) or: the marginal utility loss of savings in period must be equal to marginal utility gain of consumption in period 2 Intern Macro / WS 6-7 2T Solution

7 Univ.-Prof. Dr. J. Franke-Viebach 7 WS 206-7: International Macroeconomics (2 nd exam period) or: marginal rate of substitution must be equal to interest rate factor Problem 4: Current Account Balance and the Interest Rate in a Two-Country Model with Exogenous Incomes We consider a two-period model of two large open economies H and F that are linked by a perfect international capital market. The intertemporal Euler equation of the representative consumer in country ( = H, F) is given by: I u C = ß + r u C, where u C i = ln C i, i =, 2 ; = H, F Both countries face an exogenous time path of income Y i, i =, 2 ; = H, F II B t+ = + r B t + Y t C t, i =, 2 ; = H, F a) What does equation (II) describe? [3 points] evolution of net international investment position () (0.5) (0.5) (0.5) (0.5) b) Is r in this situation endogenous or exogenous? Explain why! [5 points] - endogenous () - both countries are large (2) - their investment and savings decisions thus affect r (2) (or: r emerges as an equilibrium price in the international capital market) Intern Macro / WS 6-7 2T Solution

8 Univ.-Prof. Dr. J. Franke-Viebach 8 WS 206-7: International Macroeconomics (2 nd exam period) c) Derive B 2 as a function of r. Assume that B = B 3 = 0. [0 points] B 2 = Y C III C = Y B 2 (2) B 3 = 0 = + r B 2 + IV = + r B 2 + (2) Intertemporal Euler equation: V C = ß + r (2) Insert (III) and (IV) into (V): Y B 2 = ß + r +r B 2 + (2) Y B 2 = ß + r [ + r B 2 + ] Y ß +r = + ß B 2 or: = ß+ ß B 2 B 2 = Y ß ß + +ß +r or: = +ß [ ß Y +r ] (2) Intern Macro / WS 6-7 2T Solution