Real Exchange Rate and Terms of Trade Obstfeld and Rogo, Chapter 4

Transcription

1 Real Exchange Rate and Terms of Trade Obstfeld and Rogo, Chapter 4

2 Introduction Multiple goods Role of relative prices

3 2 Price of non-traded goods with mobile capital 2. Model Traded goods prices obey Law of One Price (LOOP) Constant returns to scale production Traded goods are the numeraire Y T = A T F (K T ; L T ) Non-traded goods Y N = A N F (K N ; L N )

4 Labor Mobilty is perfect within country assuring identical wage across industries Labor is completely immobile between countries Total labor supply is xed L = L T + L N

5 Capital Mobile across countries Costlessly transform tradeables into capital and capital into tradeables Cannot transform non-tradeables into capital or capital into non-tradeables Capital must be in place one period before it is used

6 Firm optimization problem Present value of pro ts in the tradeables sector with no depreciation X s=t + r s t hat;s F K T;s ; L T;s w s L T;s K T;s+ i K T;s+ = K T;s+ K T;s

7 FO conditions K T;s+ h A T;s+ F K KT;s+ ; L T;s+ + i + r divide by L T;s+ and rearrange = 0 A T;s+ f k kt;s+ = r L T;s A T;s F L KT;s ; L T;s = ws

8 use property of CRS that h A T F L (K T ; L T ) = A T;s f (kt ) f 0 i (k T ) k t h A T;s f kt;s f 0 i k T;s kt;s = ws

9 Present value of pro ts in the non-tradeables sector with no depreciation X s=t + r s t hps A N;s F K N;s ; L N;s w s L N;s K N;s+ i FO conditions K N;s+ p s A N;s+ g k kn;s+ = r L N;s p s A N;s h g kn;s g 0 k N;s kn;s i = ws

10 Equilibrium Four equations in four unknowns, k T ; k N ; w; p World interest rate r is given and exogenous

11 2.2 Factor Price Frontier A T f k (k T ) = r solves for k T k T (A T ; r) = f 0 r A T! < 0 Use A T F L (K T ; L T ) = w to solve for w w (r; A T ) = A T f [k T (A T ; r)] rk T (A T ; = k T (A T ; r) implies a negative relationship between the marginal product of labor and marginal product of capital in an industry, given k T de nes factor price frontier

12 Given w can solve for k N and p using equations in non-traded goods industry Graph with p on vertical axis and k N on horizontal MP K = r graph pa N g 0 (k N ) = r as k N increases, its marginal product falls requiring an increase in p MP K = r line is upward-sloping

13 MP L = w graphs pa N h g (kn ) g 0 (k N ) k N i = w as k N increases, the marginal product of labor increases requiring that p fall for xed w MP L = w line is downward-sloping

14 PPP will hold if countries have identical production functions and mobile capital Relative factor quantities and prices are independent of demand conditions holds only if both goods are produced if no traded goods are produced, then the wage cannot be determined in traded goods sector and need another equation for demand

15 2.3 Anticipated Shocks Anticipated in t to occur in t A T increases MPL in tradeables increases increasing w MPK in tradeables increases increasing k T Increase in w shifts MP L = w line upwards, raising p and k N

16 A N increases MP K = r and MP L = w both shift downward in exact proportion to the increase in A N p falls so that marginal product in terms of tradeables is unchanged

17 Analytical results Zero pro t conditions A T f (k T ) = rk T + w; pa N g (k N ) = rk N + w Take natural logs and totally di erentiate with respect to A T ; k T ; r and w da T A T ln A T + ln f (k T ) = ln [rk T + w] + f 0 (k T ) dk T f (k T ) = rdk T + dw + k T dr rk T + w Substitute from the FO condition on capital A T f k (k T ) = r

18 and from zero pro t condition to get da T A T + rdk T A T f (k T ) = rdk T + dw + k T dr A T f (k T ) Write as proportionate rates of change = da T + k T r A T A T f (k T ) rk T A T f (k T ) dk T k T! + dk T k T! w A T f (k T ) dw w + rk T A T f (k T ) dr r Simplifying da T A T = w A T f (k T ) dw w + rk T A T f (k T ) dr r

19 de ne labor s share in traded goods as u LT = wl T Y T ^A T = u LT ^w + ( u LT ) ^r Perform similar steps on zero pro t condition for non-traded goods with ^r = 0 ^p + ^A N = u LN ^w u LN = wl N py N

20 Substitute ^w out to yield ^p + ^A N u LN = ^A T u Lt Solve for the rate of change of the relative price of non-tradeables ^p = u LN u LT ^A T ^A N For u LN u ; faster productivity growth in tradeables raises the LT relative price of non-tradeables the e ect is stronger the more labor intensive are non-tradeables relative to tradeables

21 E ect of world interest rate increase on relative price of non-tradeables since u KT = ^p == u LT (u KN u KT ) ^r = u LT (u LT u LT u LN ) ^r An increase in the relative price of capital raises the relative price of the good that uses capital intensively If tradeables are more capital intensive, then relative price of nontradeables falls Converse of Stolper-Samuelson theorem: change relative product prices bene ts the factor used intensively in the industry with the increased relative price

22 2.4 Empirical Implications Facts u LN u LT productivity growth in non-tradeables, including services, is slower than productivity growth in tradeables Prediction: rising relative price of non-tradeables is con rmed in the data Real exchange rate home and foreign price index P = p = p P = (p ) = (p )

23 home price level relative to foreign price level Home price Foreign price = P P = p p! depends on the relative price of non-traded goods rate of change of home relative to foreign prices ^P ^P = ( ) (^p ^p ) = ( ) " uln u LT ^A T ^A T ^A N ^A N # home experiences real appreciation (increase in home relative to foreign prices, equivalently, home goods purchase more foreign goods) if relative technical progress in tradeables is greater than in nontradeables independent of preferences and demand side

24 Harrod-Balassa-Samuelson proposition: price levels tend to rise with country per capita income rich countries become rich primarily through technical progress which is greater in tradeables than in non-tradeables implying higher price levels Japan and productivity growth Post WWII rapid productivity growth in manufacturing and slow productivity growth in services yielded very high price levels reverse in US

25 3 Consumption and Production in the Long Run (role of demand) 3. Assumptions Homothetic preferences such that the desired ratio between tradeables and non-tradeables depends only on relative price, not on the level of spending Steady state with constant national wealth in terms of the tradeable good Q B + K T + K N B + K

26 Constant labor force of L No productivity growth No government consumption 3.2 Composition of tradeables and non-tradeables Zero pro t in traded and non-traded goods where overbars denote steady state Y T = r K T + w L T = [rk T (r) + w (r)] L T p (r) Y N = r K N + w L N = [rk N (r) + w (r)] L L T

27 GDP line is the PPF between tradeables and non-tradeables when pro tmaximizing international capital ows are allowed Use non-tradeables equation to solve for L T and substitute into the tradeables equation " # rkt (r) + w (r) Y T = p (r) Y N + [rk N (r) + w (r)] L rk N (r) + w (r) When Y N increases, Y T falls by more than p (r) since k T > k N p is the marginal rate of transformation in an autarkic equilibrium additional capital must be borrowed from abroad if the economy is to expand its capital-intensive traded sector with no rise in the rental-to-wage ratio

28 GNP line is economy s steady-state budget constraint locus of best feasible steady-state consumptions of tradeables and nontradeables, C T and C N C T = p (r) C N + w (r) L + r Q as C N increases, C T falls by p (r) Income expansion path for a given relative price p (r)

29 Explanation of diagram Consumers are simultaneously on their income expansion path and their budget line, the GNP line intersection of two determines C T and C N Domestic consumption of non-tradeables equals domestic production of non-tradeables C N = Y N Production of tradeables is above C N on GDP line with Y T > C T ; yielding a positive trade balance

30 Current account balance must be zero implying agents must pay interest on debt they accumulated to invest in production of tradeables income expansion path implies that the country prefers more tradeables than would be provided in autarky at the world interest rate therefore, agents must borrow to invest in tradeables production (since tradeables are relatively more capital intensive) Flatter income expansion path would indicate a preference for nontradeables and agents would lend abroad since non-tradeables are not capital intensive

31 Higher steady-state wealth Q vertical upward shift of GNP (income) line by rd Q consumption of both goods rises and production of tradeables falls to produce more non-tradeables and less tradeables,country must send some capital abroad lower trade surplus and smaller interest payments on debt

32 Higher government spending on tradeables G T GNP line shifts downward by G T consumption of both goods falls production of non-tradeable falls implying an increase in production of tradeables larger current account surplus to pay interest on debt

33 Higher government spending on non-tradeables G N goods market equilbrium in non-traded goods Y N = C N + G N to maintain xed ratio of by the increase in G N C T C N income expansion path must shift right production of non-tradeables expands and production of tradeables contracts send capital abroad and have smaller current account surplus and smaller debt payments

34 3.3 Productivity Trends and the Size of the Traded Goods Sector Can we explain decline in manufacturing employment by a relatively more rapid rise in productivity in traded relative to non-traded sector? Assume tastes are unchanged Rise in productivity in traded should imply that can produce more goods with fewer workers in traded sector Workers switch to non-traded,yielding a fall in employment in traded sector

35 Model Cobb-Douglas prodution with xed total labor supply [L] Y N = A N K N L N = A Nk N L N Factor shares u KN rk N py N = u LN = wl N py N = Take logs of the production function and di erentiate ^A N + ^kn + ^L N = ^Y N

36 Set productivity growth in non-traded sector to zero and solve for rate of growth of labor ^L N = ^Y N ^kn implying that higher output in N requires higher employment in N unless capital intensity rises since non-traded goods consumption must equal non-traded goods output ^L N = ^C N ^kn

37 Derive demand for non-tradeables ^C N CES utility " CT + ( ) C N # 0 < < > 0 Total spending Z = C T + pc N Maximize utility subject to the constraint on total spending C T " CT + ( ) C N # C T =

38 C N " CT + ( ) C N # ( ) C N = p Take the ratio! C T! C N! C N C T! = p = p where is the elasticity of substitution

39 Demand for tradeables and non-tradeables: guess and verify C T = Z + ( ) p C N = p ( ) Z + ( ) p show that this guess satis es ratio of FO conditions and sum satis es spending constraint Take logs of non-tradeables and di erentiate ln C N = ln p + ln ( ) + ln Z ln + ( ) p totally di erentiate ^C N = ^Z ^p ( ) ( ) p + ( ) p dp = ^Z ^p ( ) ( ) p + ( ) p ^p

40 simplify by setting p = ^C N = ^Z ^p ( ) ( ) ^p = ^Z ^p [( ) + ] tradeables consumption is increasing in total expenditure (Z) and decreasing in the relative price of non-tradeables (p) Compute ^Z Expenditure equals output Z = wl + r Q

41 Take logs ln Z = ln wl + r Q Di erentiate with respect to Z and w ^Z = where L is labor s share wl wl + r Q ^w L ^w Use relation between wage and technology from before ^A T = u LT ^w Solve for ^w and substitute ^Z = L u LT ^A T

42 Use ^p from above with ^A N = 0 ^p = u LN ^A T = u LT u LT ^A T using the Cobb-Douglas production function for non-tradeables Write expression for ^C N as a function of exogenous productivity growth in tradeables ^A T ^C N = ^Z ^p [( ) + ] L = ^A T [( ) + ] u LT u LT ^A T = f L ( ) [( ) + ]g ^A T u LT

43 Use rst order condition on capital to derive ^kn FO condition Take logs r = pa N k N ln r = ln p + ln A N + ln + ( ) ln k N Di erentiate with ^r = ^A N = 0 ^k N = ^p Substitute for ^p ^k N = ^A T u LT

44 Substitute ^C N and ^kn into expression for ^L N ^L N = ^C N ^kn = f L ( ) [( ) + ]g ^A T u LT as ^A T occurs, wages increase and incomes increase, raising the demand for tradeables and non-tradeables relative price of non-tradeables (p) increases, reducing demand for nontradeables capital intensity in production of non-tradeables increases since w=r increases if =, ^L N falls, and employment in tradeables rises reverse result only if

45 very small so do not substitute our of nontradeables much as their relative price rises very large labor share ( L ) due to high national debt and low national income productivity growth in manufacturing (tradeables) does not explain the decline in manufacturing (tradeables) employment

46 4 Short-run Analysis with Current Account Imbalance 4. Consumer s problem Consumption-based price index Utility U t = X s=t s t u (C s ) C is a linear homogeneous function of C T and C N C = (C T ; C N )

47 C is an index of consumption, sometimes called real consumption De nition: P (consumption-based price index) is the minimum expenditure Z = C T + pc N such that C = (C T ; C N ) = ; given p: P measures the least expenditure in terms of tradeables which buys a unit of C on which utility depends CES index C = " CT + ( ) C N # Write consumption index in terms of Z using expressions for tradeable and non-tradeable demandderived earlier C T = Z + ( ) p C N = p ( ) Z + ( ) p

48 Substitute C = 8 >< >: " Z + ( ) p # + ( ) " p ( ) Z + ( ) p # 9 >= >; Since P is the minimum Z such that C =, set C = and solve for Z = " Z + ( ) p # + ( ) " p # ( ) Z + ( ) p Factor Z out = 8 >< >: " + ( ) p # + ( ) " p ( ) + ( ) p 9 # >= >; Z

49 Collect terms on and and simplify ( h + ( ) p i + ( ) p h + ( ) p i ) Z = h + ( ) p i h + ( ) p i Z = h + ( ) p i Z Solve for Z Z = h + ( ) p i Z = h + ( ) p i

50 Since the consumption-based price index is the Z for which we have solved P = h + ( ) p i Total consumption in terms of P C = Z P Z P is the ratio of spending, measured in tradeables, to the minimum price in tradeables of a single unit of the consumption index

51 Demand functions Tradeables C T = Z + ( ) p P C P = P C Nontradeables C N = p ( ) Z + ( ) p = ( ) p P C P = ( ) p P C Demand for consumption of each type is proportional to real consumption with a coe cient that is an isoelastic function of the ratio of the good s price (in terms of the numeraire) to the price index

52 Price index for Cobb-Douglas case! 8 < ln h + ( ) p i = P = exp : ; ( ln ([ + exp fln ( ) + ( ) ln pg]) = exp l Hopital s rule: take derivative of numerator and derivative of denominator inside the exp term [+( )p ] and take limit as! [ ln p exp fln ( ) + ( ) ln pg] = ln p ( ) 9 )

53 take the results to the exp P = exp (ln p ( )) = p

54 4.2 Reformulate Consumer s Problem Present value budget constraint X s t CT;s + p s C N;s = ( + r) Qt + X s t (w s L s G s ) s=t + r s=t + r C T;s + p s C N;s = Z = P s C s Flow budget constraint Q s+ Q s = rq s + w s L s G s P s C s Solve ow budget constraint for consumption and substitute into utility U t = X s=t s t u Q s+ ( + r) Q s + w s L s G s P s!

55 Di erentiate with respect to Q s+ for s t to obtain Euler equation in consumption u 0 (C s ) P s = ( + r) u0 (C s+ ) P s+ De ne consumption based real interest rate as the own rate of interest on the consumption index + r C s+ = ( + r) P s P s+ loan one unit of C on date s and receive + r C s+ of C on date s + di ers from r when expect change in relative price of tradeables, which determines P

56 Rewrite Euler equation u 0 (C s ) = + r C s+ u 0 (C s+ ) Optimal consumption Rewrite intertemporal budget constraint in terms of date t real consumption by dividing both sides by P t

57 left-hand side X s t P s C s! = = s=t " X s=t X s=t + r P t+ P t # "" # P t+2 ( + r) P t ( + r) P t+ sy v=t+ C s + r C v ::::: " ## P s C s ( + r) P s

58 right hand side ( + r) Q t + = ( + r) Q t + X s=t X s=t + r s t (w s L s G s ) (w s L s G s ) + r C v sy v=t+ de ne R C t;s = sy v=t+ + r C v intertemporal budget constraint becomes X s=t R C t;sc s = ( + r) Q t + X s=t R C t;s (w s L s G s )

59 let utility be CRRA u (C) = C = = yielding an Euler equation as C = s = + r C s+ C = s+ solving for future consumption in terms of initial consumption C s+ = h + r C s+ i Cs C t+ = h + r C t+ i Ct C t+2 = h + r C t+2 i Ct+ = h + r C t+2 i h + r C t+ i Ct

60 left-hand side of budget constraint becomes X Rt;sC C s s=t = C t h + R C t;t+ h + r C t+ i + R C t;t+2 h + r C t+2 2 i + ::: i = C t + R C t;t+ + R C t;t :::: = C t 2 4 X s=t R C t;s (s t) 3 5

61 substitute into the intertemporal budget constraint to yield a solution for consumption C t = ( + r) Q t + P s=t R C t;s (w sl s G s ) P s=t R C t;s (s t) 4.3 Equilibrium Current Account Since non-traded sector always clears, write model in terms of traded goods Intertemporal budget constraint in terms of traded goods assuming nontraded goods market clears s t CT;s X s + I s + G T;s = ( + r) Bt + X t Y T;s s=t + r s=t + r

62 Traded goods Euler equation begin with Euler equation for composite good C " # ( + r) Ps C s+ = C s relationship between C T and C P s+ C T = P C C = C T P

63 substitute into Euler equation C T;s+ P s+ = " # ( + r) Ps C T;s P s+ Ps simplify C T;s+ = ( + r) P s P s+! C T;s e ect of in ation depends on an intertemporal and an intratemporal e ect intertemporal: as in ation rises, the real interest rate on C falls, decreasing C t+ relative to C t with elasticity intratemporal: as P s+ rises, the relative price of non-tradeables rises, increasing C T;t+ with elasticity

64 Solve for traded goods consumption using budget constraint and traded goods Euler equation C T;t = ( + r) B t + P s t s=t +r YT;s I s G T;s P h s=t ( + r) i (s t) P t P s

65 Current account CA t = B t+ B t = rb t + Y T;t C T;t I t G T;t Presence of non-tradeables a ects path of the current account through e ect of P Consider a rising value for p and P over time Case : > Traded goods consumption is initially higher than in model without traded goods Traded goods consumption falls over time due to low real interest rate Initial current account de cit followed by a current account surplus

66 Case 2: < Traded goods consumption is initially lower Rises over time as substitute away non-traded goods whose relative price is rising

67 5 Terms of Trade in a Dynamic Ricardian Model 5. Model Assumptions Continuum of goods in the world, indexed by z 2 [0; ] Two countries: home and foreign Labor is only factor of production L (L )

68 Countries have di erent technologies Home produces z with a (z) Foreign produces z with a (z) Utility U t = X s=t s t log C s C = exp " Z 0 log c (z) dz # Numeraire is z = ; so that wages and commodity prices are expressed in terms of good

69 5.2 Consumption based price index Problem Minimize expenditure on goods min c(z) Z 0 p (z) c (z) dz Subject to " Z # C = exp 0 log c (z) dz = Take logs of both sides Z 0 log c (z) dz = 0

70 Form Lagrangian L = Z 0 p (z) c (z) dz Z 0 log c (z) dz FO condition with respect to c (z) p (z) c (z)! = 0 p (z) c (z) = Every good receives equal weight in expenditure

71 Solve for using FO condition and constraint Z [log log p (z)] dz = 0 0 log = Z 0 [log p (z)] dz raising both sides to the exp yields = exp Z 0 [log p (z)] dz Consumption based price index P = min c(z) Z Z Z p (z) c (z) dz = dz = = exp [log p (z)] dz 0 0 0

72 Demands When C = c (z) = p (z) = P p (z) Since intratemporal preferences are homothetic, for other values of C c (z) = P C p (z) Expenditure on any interval of goods [z ; z 2 ] [0; ] is Z z2 z p (z) c (z) dz = (z 2 z ) P C

73 5.3 Wages, prices, and production Relative home labor productivity schedule A (z) = a (z) a (z) where A 0 (z) < 0 as z increases foreign labor domestic labor falls home is relatively good at producing on interval [0; ~z] foreign is relatively good at producing on interval [~z; ]

74 Wages: produce good more cheaply at home when wa (z) < w a (z) w w < a (z) a (z) = A (z) goods produced more cheaply abroad when w w > A (z) cut-o value for z w w = A (~z)

75 Derive equilibrium wages World goods market equilibrium P (C + C ) = wl + w L If home produces (0; z) own demand for home goods is zp C foreign demand for home goods is zp C

76 Market clearing in market for home goods zp (C + C ) = wl = z (wl + w L ) Solve for w w = z z L! L! = B z; L L Relative home wage rises with an increase in z and with an increase in relative foreign labor

77 Comparative Statics: increase in L L shifts B inward as need reduction in z for unchanged w w relative home wages w w rise and z falls for all goods produced in home before and after, purchasing power of wage over each good is unchanged at = a (z) is unchanged w p(z) similarly for all goods produced in foreign before and after, a (z) is unchanged w p(z) = home real wages in terms of the goods foreign, produced before and after the increase in relative foreign labor supply, rise w 0 p (z) 0 = w 0 a > (z) w 00 w a (z) w = w p (z)

78 foreign s real wage must fall in terms of goods initiall produced at home and still produced at home wage in terms of goods which move from home to foreign these goods can be produced more cheaply in foreign than in home p (z) 0 = w 0 a (z) < w 0 a (z) using the two ends of the above equation w p (z) = a (z) < w0 p (z) 0 home s real wage in terms of goods that become imports rises because foreign costs now are lower than domestic costs get opposite for foreign

79 Summary rise in relative foreign labor supply lowers its real wage and raises home s real wage making home relatively better o happens even as foreign produces a wider range of goods (increased competitiveness) Terms of Trade = Price of Exports Price of Imports any good home still exports %p = log p (z) 0 log p (z) = log w 0 log w > 0 for goods that were originally foreign exports and still are %p = log p (z) 0 log p (z) = log w 0 log w < 0

80 goods that home used to produce which foreign now produces and exports w 0 a (z) wa (z) < 0 home country sees its terms of trade improve

81 5.4 Current Account Permanent disturbances do not a ect current account Transitory ones do Foreign productivity increase Temporary CA surplus as agents save to smooth consumption after productivity returns to normal Consumption is permanently higher and the CA is balanced

82 5.5 Transport cost and non-traded goods Assumptions A fraction of any good shipped between countries evaporates in transit Cost of good produced at home is wa (z) Cost of imported good is w a (z)

83 Good will be produced at home if wa (z) < w a (z) w w < a (z) a (z) ( ) = A (z) Foreign country will produce good locally if w w > ( w a (z) < ) a (z) a (z) wa (z) = ( ) A (z)

84 Plot A(z) and ( ) A (z) with z on horizontal axis Relative wages will determine range of goods produced in each country Home will produce goods 0 to z H Foreign will produce goods z F to Goods z F to z H are non-traded

85 Prices of non-traded goods are di erent in the two countries p (z) = a (z) w p (z) = a (z) w Prices of traded goods are no longer equal due to transport costs home price of import must be higher than foreign price of same good w a (z) = p

86 Real exchange rate Price index in terms of numeraire as units of good delivered in foreign ( Z z H Z " w P = exp log [w (a (z))] dz + log a # ) (z) dz 0 z H P = exp ( Z z F 0 log " wa (z) # dz + Real exchange rate is the ratio P P = exp exp ( Z z F ( Z z F log [w (a (z))] dz Z z H " w (a (z)) log ( ) dz + log 0 z F w (a dz (z)) log ( ) z F + z H Z z H " w (a (z)) + log z F w (a (z)) # Z z # ) H log ( ) dz ) d

87 Depends on the ratio of non-traded goods prices in the two countries Also depends on the range of production Increase in z F reduces P P since log ( ) < 0 range of goods foreign must import increases spending on transport cost increase increasing foreign price relative to domestic price

88 Joint determination of relative wages and patterns of specialization World demand equals world supply P C + P C = wl + w L Equilibirum supply of home output (wl) equals demand for it wl = z H P C + z F P C = z H P C + z F (wl + w L P C) Home trade balance is production less spending T B = wl P C

89 Solve for w w wl = z H P C + z F (wl + w L P C) = z H P C + z F (wl + w L + T B wl) = z H P C + z F (w L + T B) wl = z H (wl T B) + z F (w L + T B) wl z H = z F w L + T B z F z H w = zf w L + T B z F L z H z H

90 w w = = L L z F L L z F z H + T B w L z H 2 z H z H 4z F + T B z F w L z H 3 5 Since good is the numeraire w = p () a () = a () Substitute for w w w = L L z H 2 4z F + T B z F L =a () z H 3 5

91 Need two cut-o values, z H and z F ; both equal to w w ; and they are related by ( ) A z F = A z H = ( ) Assume a speci c functional form A (z) = exp ( 2z) = a (z) a (z) = exp ( z) exp z Substitute into relationship between z H and z F ( ) exp 2z F = exp 2z H = ( ) Take logs 2 log ( ) = 2z H + 2z F z H = z F log ( )

92 Substitute into the expression for w w to get an expression in z F alone w w = L L z F + log ( ) " z F + Note that w w, named ~B z F, is increasing in z F # T B log ( ) L =a () Intersection of ~B z F with A(z) and z H and ( ) A (z) determines zf The less is produced in foreign (rightward movement along horizontal axis) the more is produced in home and the higher is relative demand for home labor and home relative wage

93 Permanent shock increasing L ; setting T B = 0 ~B z F = w w = z F L L z H ~B z F shifts upwards home s relative wage increases the range of goods produced at home is smaller and the range produced in foreign is larger due to its lower wageforeign exports some goods previously non-traded goods previously exported by home become non-traded relative price of foreign goods falls so that trade balance is unchanged

94 even as home exports fewer goods and foreign exports more home bene ts at foreign s expense

95 Classical transfer problem: Consider an increase in T B from initial value of zero T B up reduces w w shifting ~B z F down [remember log ( ) < 0] the increased trade balance transfers spending from home to foreign and foreign spends some on non-traded goods traded sector contracts as labor is drawn into nontradeables excess demand for foreign labor raises foreign relative wages and reduces range of goods foreign produces country with a positive trade balance has a lower terms of trade trade balance up reduces relative spending

96 demand for non-tradeables falls reducing relative wages the fall in relative wages reduces relative prices

97 Permanent e ects from a temporary increase in foreign productivity (fall in a (z)) A (z) falls so w w falls relative prices in foreign country fall, wa (z) w a (z) rises improving home terms of trade and making home better o agents smooth consumption so foreign has trade surplus while home has trade de cit range of production abroad rises and at home falls In the long run, home has a permanent trade balance surplus to pay

98 for the initial de cit transfer e ects country with trade balance surplus has a lower terms of trade