1UNIVERSITY OF SOUTHAMPTON ECON3008W1 SEMESTER 2 EXAMINATIONS 2018-19 ECON3008 Macro Policy 3 Duration: 120 mins (2 hours) This paper contains 4 questions Answer ALL questions. An outline marking scheme is shown in brackets to the right of each question. Only University approved calculators may be used. A foreign language direct ‘Word to Word’ translation dictionary (paper version) ONLY is permitted. Provided it contains no notes, additions or annotations. Copyright 2019 v01 c University of Southampton Page 1 of 4 2 ECON3008W1 1. Consider the following one-period model of sovereign default. The government has borrowed an amount L from abroad at an interest rate rL. If the government decides to repay, lump-sum taxes T are collected from households to finance the repayment. If the govern- ment does not repay, a fraction 0 < f < 1 of output is lost. The government aims to maximize national utility, U(C) = C. Output, Y , is a random variable that takes on positive values. There is no government expenditure or investment, so all output is consumed. The government decides whether to repay after output is revealed. (a) Find analytical expressions for consumption under repayment, consumption under default, and the threshold level of output. [10%] (b) The model is given the parameters: f = 0.2, rL = 0.1, L = 0.4. Output is drawn from the following probability distribution: Output (Y ) Prob (Y ) 1 0.1 2 0.2 3 0.6 4 0.1 Find the probability of default. Would this result change if the utility function were U(C) = 2ln(C) Explain. [10%] (c) Now suppose the cost of default, f , is not known before the default decision is taken. It has two possible values: either f = 0.05 with probability 1/4, or f = 0.25 with probability 3/4. The probability distribution of output and the other parameter values are the same as in part (b). Find the probability of default when the utility function is: i. U(C) = C ii. U(C) = 2ln(C) [10%] Copyright 2019 v01 c University of Southampton Page 2 of 4 3 ECON3008W1 2. Consider the following short run monetary exchange rate model: iUK = iUS + e e ￡/$ e￡/$ MUK P = exp( ηiUK)YUK , MUS P = exp( ηiUS)YUS ee￡/$ = e where P = 1 and η, e are known positive constants. The variables MUK andMUS are the given money supplies at home and abroad. YUK and YUS are the given levels of real income in each country. The home exchange rate is e￡/$ (pounds per dollar, in natural logs), and ee￡/$ is its expected future value. (a) Find an analytical solution for the spot rate, e￡/$. [10%] (b) We now give the model parameter values: η = 0.95, MUS = 2, e = 0.5, YUK = YUS = 5. UK money supply, MUK, has the values shown below. Find the blanks in the table. [10%] Period MUK iUK iUS e￡/$ 0 2 1 2.5 2 2 3. Consider the following two-period model of the current account: U = C 1/3 1 + βC 1/3 2 C1 = Y1 CA1, C2 = Y2 + (1 + r)CA1 CA1 + CA2 = 0 where C is consumption, CA is the current account balance, and r is the given world interest rate. Y1, Y2 are given endowments and β > 0 is the discount factor. (a) Show that the lifetime budget constraint is C1+ C21+r = Y1+ Y2 1+r , and set up the economy’s utility maximization problem. [10%] Copyright 2019 v01 c University of Southampton TURN OVER Page 3 of 4 4 ECON3008W1 (b) Find analytical solutions for C1, C2, CA1, CA2. [10%] (c) We now set Y1 = 1, Y2 = 2, r = 0.1, β = 1. Find numerical so- lutions for C1, C2, CA1, CA2, and U . How would these results differ, if at all, if the economy faced a borrowing constraint of the form CA1 ≥ 0.1Y1 Comment on the results. [10%] 4. Consider the following long run monetary model of exchange rates: PUK,t = E￡/$,tPUS,t (1) MUK,t PUK,t = exp( ηiUK,t)YUK,t, MUS,t PUS,t = exp( ηiUS)YUS,t (2) iUK,t = iUS + e e ￡/$,t+1 e￡/$,t (3) e￡/$,t = 1 1 + η ∞∑ s=0 ( η 1 + η )s [ meUK,t+s meUS,t+s + yeUS,t+s yeUK,t+s ] (4) where η, iUS > 0 are constants, and lowercase versions of variables are natural logarithms (e.g. mUK = ln(MUK)). The variables MUK , MUS, YUK , YUS are the given money supplies and real incomes at home (UK) and abroad (US). The home exchange rate in period t is e￡/$,t (pounds per dollar, in natural logs), and ee￡/$,t+1 is its expected value in period t + 1. Agents have rational expectations based on information up to and including period t. (a) Name the equations in (1) to (4). Provide a brief economic interpretation for Equation (3). [10%] (b) We now give the model parameter values: η = 0.5, iUS = 0.10. We also set MUS, YUS, YUK to 1 so that mUS = yUS = yUK = 0. Suppose the UK money supply is: mUK,t = (1 + η)mUK,t 1, with initial value mUK,0 = 1 in period 0. Find numerical solutions for mUK, iUK, e￡/$ in periods 0,1,2. [10%] END OF PAPER Copyright 2019 v01 c University of Southampton Page 4 of 4 Social Sciences Examination Feedback 2018/2019 Module Code & Title: ECON3008 Macroeconomic Policy 3 Module Coordinator: Michael Hatcher Mean Exam Score: 62.2% Percentage distribution across class marks: UG Modules 1 st (70% +) 35.5% 2.1 (60-69%) 26.6% 2.2 (50-59%) 23.2% 3rd (40-49%) 11.8% Fail (25-39%) 1.0% Uncompensatable Fail (<25%) 2.0% PGT Modules 70% + 60-69% 50-59% <50% Overall strengths of candidates’ answers: Most students did well on basic definition and calculation questions. Students performed best on those questions which were similar to those covered in problem sets. Overall weaknesses of candidates’ answers: Answers were sometimes incomplete. This was especially the case for parts 3b and 3c. In general, students struggled with questions that were not familiar from lectures or problem sets. Pattern of question choice: All questions were compulsory. Issues that arose with particular questions: Q1c: Some students answered the question under the assumption that output could not be observed before the default decision was taken (although the question states otherwise). Q2a,b: A minority of students applied the wrong solution method (exchange rate overshooting), ignoring the fact that the economy has a fixed price level and fixed exchange rate expectations. Q3c: The solution under the binding borrowing constraint was often computed incorrectly. Few students linked the binding borrowing constraint to the lower calculated value of utility. Q4b: Students found this question very challenging. The number of students who got all calculations in this part correct was in single figures. Further comments not covered above: None. Discipline vetting completed By (Name): E Mentzakis Date: 24/06/2019
