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216 CHAPTER 7. THE REAL EXCHANGE RATE(130)⇒Finally, plug (7.16) into (7.11) to get the solution for relative price ofthe nontraded good in terms of the traded good(1−αP N = A N )(1−α T )TCR (α N −α T )(1−α T )(7.17)A Nwhere C is a positive constant. Now let a =ln(A),r =ln(R), andc =ln(C) and take logs of (7.17) to get the solution for the log relativeprice of nontraded goods in terms of traded goodsp N =µ 1 − αNa T − a N +1 − α TÃ(αN − α T )(1 − α T )!r + c. (7.18)Over time, the evolution of the log relative price of nontradables dependsonly on the technology and the exogenous rental rate on capital.We see that there are at least two reasons why the relative price ofnon-tradables in terms of tradables should increase with a country’sincome.First, suppose that the economy experiences unbiased technologicalgrowth where a N and a T increaseatthesamerate. p N will rise over timeif traded-goods production is relatively capital intensive (α N < α T ). Astandard argument is that tradables are manufactured goods whoseproduction is relatively capital intensive whereas nontraded goods aremainly services which are relatively labor intensive. Second, p N willincrease over time if technological growth is biased towards the capitalintensive sector. In this case, a T actually grows at a faster rate thana N . If either of these scenarios are correct, it follows that fast growingeconomies will experience a rising relative price of nontradables and by(7.5), a real appreciation over time.The implications for the behavior of the real exchange rate are asfollows. If the productivity factors grow deterministically, the deviationof the real exchange rate from a deterministic trend should be astationary process. But if the productivity factors contain a stochastictrend (chapter 2.6) the log real exchange rate will inherit the randomwalk behavior and will be unit-root nonstationary. In either case, PPPwill not hold in the long run.When we take the Balassa—Samuelson model to the data, it is temptingto think of services as being nontraded. It is also tempting to think