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214 CHAPTER 7. THE REAL EXCHANGE RATEP ∗ =(PT ∗ )θ (PN ∗ )1−θ , (7.4)where the shares of the traded and nontraded-goods are identical athomeandabroad(θ ∗ = θ). The log real exchange rate can be decomposedasq =(s + p ∗ T − p T )+(1− θ)(p ∗ N − p∗ T ) − (1 − θ)(p N − p T ), (7.5)where lower case letters denote variables in logarithms. We adopt thecommodity arbitrage view of PPP (chapter 3.1) and assume that thelaw-of-one price holds for traded goods. It follows that the Þrst termon the right hand side of (7.5), which is the deviation from PPP forthe traded good, is 0. The dynamics of the real exchange rate is thencompletely driven by the relative price of the tradable good in terms ofthe nontraded good.The Balassa—Samuelson ModelNow, we need a theory to understand the behavior of the relative priceof tradables in terms of nontradables. It turns out if, i) factor marketsand Þnal goods markets are competitive, ii) production takes placeunder constant returns to scale, iii) capital is perfectly mobile internationally,iv) labor is internationally immobile but mobile between thetradable and nontradable sectors, then the relative price of nontradablegoods in terms of tradable goods is determined entirely by theproduction technology. Demand (preferences) does not matter at all.The theory is viewed as holding in the long run and therefore omittime subscripts. To Þx ideas, let there be only one traded good and onenontraded good. Capital and labor are supplied elastically. Let L T (L N )and K T (K N ) be labor and capital employed in the production of thetraded Y T (nontraded Y N )good. A T (A N ) is the technology level in thetraded (nontraded) sector. The two goods are produced according toCobb-Douglas production functionsY T = A T L (1−α T )T K (α T )T , (7.6)Y N = A N L (1−α N )N K (α N )N . (7.7)The balance of trade is assumed to be zero which must be true inthe long run. Let the traded good be the numeraire. The small open