Exercise 2. (From Schmitt-Grohe, Uribe and Woodford 2022) Consider two countries, say the U.S. and Japan. Both countries produce tradables and nontradables. Suppose that at some point in time the production technology in the U.S. is described by OTUS US = aT SINUS ; with an" = 0.4 and ONUS USINUS = ON ; with ax = 0.1, where QTUS and ONUS denote, respectively, output of tradables and nontradables in the U.S., as and ay denote, respectively, labor productivity in the tradable and the nontrad- able sector, and LTUS and INUS denote, respectively, the amount of labor employed in the tradable and nontradable sectors in the U.S. The total supply of labor in the U.S. is equal to 1, so that 1 = LTUS and INUS '. At the same point in time, production possibilities in Japan are given by Qr = 0.2LYand QN = 0.2LN, where the superscript J denotes Japan. The total supply of labor in Japan is also equal to 1. Assume that in each country wages in the traded sector equal wages in the nontraded sector. Suppose that the price index in the U.S., which we denote by PUS, is given by Pus PUS PUS where Pro and Py denote, respectively, the dollar prices of tradables and nontradables in the U.S. Similarly, the price index in Japan is given by PJ = 1 Pi PN , where Japanese prices are expressed in yen. 1. Calculate the dollar-yen real exchange rate, defined as e = &PJ / PUS, where & denotes the dollar-yen exchange rate (dollar price of 1 yen). The answer to this question is a number, but show your work. 2. Suppose that the U.S. labor productivity in the traded sector, a?", grows at a 3 per- cent rate per year, whereas labor productivity in the nontraded sector, an, grows at 1 percent per year. Assume that labor productivityes in Japan are constant over time. Calculate the growth rate of the real exchange rate. Provide an intuitive explanation of your result