- 1 Consider The Following Unified Monetary Model Of The Exchange Rate Where Time Is Discrete And Runs From Period T 0 1 (192.51 KiB) Viewed 12 times
1. Consider the following unified monetary model of the exchange rate where time is discrete and runs from period t = 0 onwards : iUK,t = ius e£/s₁t+1- €£/s,t (1) MUK exp(-niuk,t)YUK, MUS PUS exp(-nius) Yus (2) PUK,t ∞ S 1 n etR [MUK mus+yus-YUK] (3) 1+n 1+n s=0 in period t = 0 PUK.t {AAN PUK,t-1+ (Pnew - Po) in periods 1 to T (4) pnew in all later periods where P₁ = P > 0 is the given initial UK price level. The UK money supply MUK is given and Mus, YUK, YUS, PUS, N, T are known positive constants. Lowercase versions of variables are natural logarithms (e.g. muk = ln(MUK)). The home exchange rate in period t is e£/$, ti and e£/S,t+1 is the expected future exchange rate. We assume Muk is such that the UK interest rate (iuk) is initially equal to the US interest rate. Agents have rational expectations. (a) Give a brief economic explanation for equations (1) and (4). (b) There is a permanent unanticipated increase in UK money supply from M to Mnew in period 0. The new long run price level is given by pnew x P, and we assume T = 2. Find an analytical solution for the period 0 spot rate. [10%] Mnew = M [10%] (c) We now repeat the experiment in (b) with numerical values: n = 1, P=8, Pus-1.5, Mus-1.5, YUK-YUS-1.5, M = 8, Mnew-8.8. Complete the table below. Does the exchange rate overshoot? [10%] Period PUK UK US e LR e£/$ 0 1.674 → 1 2 -