1.5 International Labor Movements (Text der Folien)

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1 .5 International abor Movements (Text der Folien) in most models labor is much less mobile internationally than either commodities or capital language and cultural barriers, family and ethnic ties, and political barriers low levels of immigration in industrial countries over the past twenty years few major exceptions such as Australia, Canada, and the United States Table.3 s gures for : recent net in ows of foreign workers. developing countries and countries of the former Soviet bloc: substantial outward migration Greece: workers remittances from abroad were 3 percent of GDP in 992 Up until World War, footloose labor owed in massive waves from Europe to former European colonies in North America and Oceania (again see Table.3), as well as to atin America As recently as , Germany and Switzerland let in numerous guest workers from Mediterranean countries France: immigrants from its former African colonies. Goal of this section: close examination of the causes and e ects of international labor movements. immigration is usually a much more emotion-charged issue than capital mobility labor mobility can yield similar e ciency bene ts by equalizing marginal products of labor across countries. we develop a two-period small-country model in which there is no international borrowing or lending (perhaps the result of prohibitive barriers to international capital movements). International emigration and immigration are, however, completely free. How should we think about the gains from trade in such a world?.5. Capital, abor, and the Production Function: A Digression we now make explicit that produced output is a function of capital and labor inputs Production function: Y = F (; ) (33) constant returns to scale (linear homogeneous): F (; ) = F (; ) ; 8 > 0 Some properties of constant-returns production functions gure prominently in the present model First, output equals the sum of factor marginal products multiplied by factor inputs (Euler theorem): F (; ) = F (; ) + F (; ) (; ) F (; ) F (; marginal product of capital marginal product of labor

2 Second, the marginal products depend only on the capital-labor ratio, k = Due to constant returns we have intensive or per-worker production function: marginal products of capital and labor: = ) F ; = F (; ) ) Y = F (; ) = F ; f (k) F (k; ) f (k) F (k; ) ) F (; ) = F F (; ) = f 0 ; = f = f 0 = f 0 (k) (35) F (; ) = f + f 0 = f f 0 = f (k) f 0 (k) k (36) Vollständige onkurrenz auf dem Markt für Realkapital und dem Arbeitsmarkt + Gewinnmaximierung der repräsentativen Firma impliziert: r = F (; ) w = F (; ) r = rental rate of capital (interest rate), w = real wage. Alternative Darstellung: w = f (k) r = f 0 (k) f 0 (k) k Sicht der repräsentativen Firma: r und w gegebene Größen, die sie mit ihren eigenen Aktionen nicht beein ussen kann. Gesamtwirtschaftliche Sicht einer kleinen o enen Volkswirtschaft: immobile capital and perfectly mobile labor: w exogen, r und k endogen perfectly mobile capital and immobile labor: r exogen, w und k endogen.5.2 A Two-Period, Small-Country Model On date 2 (the model s second period), the home economy s output is Y 2 = F ( 2 ; ) where 2 is the capital that domestic residents accumulate during period. 2

3 For simplicity, Y is exogenous, and = 0. Thus production takes place only on date 2. Our small country faces a given world wage rate, w, at which it can export or import labor services on date 2. The representative resident has an inelastically supplied labor endowment of H on date 2, but the economy employs a total of labor units. can be greater or less than H as a result of trade in labor services H > : the representative individual works abroad part-time or, equivalently, of some domestic workers emigrate to work abroad. no government consumption. Because neither international borrowing nor lending is possible, the representative home-country individual maximizes U = u (C ) + u (C 2 ) subject to the constraints C = Y 2 ; C 2 = f( 2 = ) w( H ) + 2 Die Budgetbeschränkung für die Periode folgt aus und der Annahme = 0. Y = C + I = C + 2 The second constraint states that date 2 consumption equals domestic product (a function of the economy s total employment), less the net wage payments on imported labor services, less investment (where we remind you that I 2 = 2 ). Using the two constraints to eliminate C and C 2 from the utility function, we can write the representative individual s problem as max u (Y 2 ) + u f w H + 2 2; First-order conditions with respect to 2 and are u 0 f 0 = u 0 (Y 2 ) ( ) +u 0 2 f w w H + 2 f H + 2 f 0 These conditions can be rewritten as u 0 (Y 2 ) = + f 0 u 0 f or where k 2 = 2 =. f + f 0 f 0 = w w + 2 H + 2 w = 0 u 0 (C ) = [ + f 0 (k 2 )] u 0 (C 2 ) (37) f (k 2 ) f 0 (k 2 ) k 2 = w (38) 3

4 The rst of these equations is the Euler equation when the domestic real interest rate equals the marginal product of capital (recall eq. (35) The second states that under free international labor mobility, the marginal product of labor [recall eq. (36)] must equal the world wage rate. Notice that eq. (38) ties down k 2 = 2 = as a function of the world wage rate, so we can write the production capital-labor ratio as a function k(w). Genauer: Durch (38) ist implizit die Funktion de niert. Di erenziert man die Gleichung k 2 = k (w) w = f (k (w)) f 0 (k (w)) k (w) total nach w, so erhält man = f 0 (k (w)) k 0 (w) f 00 (k (w)) k 0 (w) k (w) f 0 (k (w)) k 0 (w) = f 00 (k (w)) k 0 (w) k (w) Aus diesem Ergebnis und der Annahme f 00 < 0 folgt: dk 2 dw = k0 (w) = f 00 (k (w)) k (w) > 0 i.e. die inländische apitalintensität hängt positiv vom Weltreallohn ab. By implication, the domestic interest rate also is a function of w alone: it is given by r(w) = f 0 [k(w)] Genauer: Der inländische Zinssatz r, der bei Verwendung des representative consumer-producer nicht explizit im Modell aufscheint, stimmt im Gleichgewicht mit der Grenzproduktivität des apitals überein, d.h. r 2 = f 0 (k 2 ). Es gilt daher: Durch Di erenzieren nach w erhält man Unter Berücksichtigung von erhält man r 0 (w) = r 2 = r (w) f 0 (k (w)) r 0 (w) = f 00 (k (w)) k 0 (w) k 0 (w) = f 00 (k (w)) f 00 (k (w)) k (w) f 00 (k (w)) k (w) = k (w) < 0 Dies bedeutet, daßder inländische Zinssatz r negativ vom Weltreallohn w abhängt. The model s negatively sloped functional relation between r and w [r (w) with r 0 (w) < 0] is called the factor-price frontier A rise in the world wage w raises the optimal capital intensity of production, lowering the domestic marginal product of capital. As long as w doesn t change, however, neither k nor r can change, no matter what else in the economy does change (other than the production function itself). Given w, net labor exports adjust to ensure that k and r remain constant. 4

5 5.3 Pattern of Trade and Gains from Trade Figure.2: The concave locus is the autarky PPF autarky PPF describes the home economy s intertemporal consumption trade-o when the labor used in second-period production is restricted to the domestic endowment, H. autarky PPF is described by C 2 = F (Y C ; H ) + Y C Its slope = F (Y C ; H ) = + F ( 2 ; H ) < 0 ap P F 2 C 2 = F (Y C ; H ) ap P F and the assumption that F < 0 it follows that the autarky PPF is strictly concave Its horizontal intercept is at C = Y, and its vertical intercept is at C 2 = F (Y ; H ) + Y. Point A is the economy s autarky equilibrium. The straight line tangent to the autarky PPF at B is the representative domestic resident s intertemporal budget constraint when there is trade in labor services: C 2 = [ + r (w)] 2 + w H and its linearity is due to the constancy of r(w), given w. We call this line the GNP line because it equates second-period consumption plus investment to domestic output plus net factor payments from abroad. Point B is generated by an investment level at which the marginal product of capital is r(w) when employment equals H. Genaue Ableitung der GNP line Schritt : Die Euler Gleichung F (; ) = F (; ) + F (; ) kann unter Verwendung von F (; ) = f F (; ) = f 0 F (; ) = f f 0 auch in der folgenden Form dargestellt werden: f = f 0 + f f 0 5

6 Schritt 2: Die Budgetbeschränkung für die zweite Periode, C 2 = f w H + 2 kann unter Verwendung von f = f 0 + f f 0 auch in der folgenden Form geschrieben werden: C 2 = f f = f f f 0 f 0 3. Schritt: Bei optimaler Wahl von k 2 = 2 = gilt (wie oben gezeigt): w H + 2 w + w H + 2 f (k 2 ) k 2 f 0 (k 2 ) = w Durch Einsetzen erhält man f 0 (k 2 ) = r (w) C 2 = [ + r (w)] 2 + w H 4. Schritt: Unter Berücksichtigung von 2 = Y C erhält man die GNP line: C 2 = [ + r (w)] (Y C ) + w H 5. Schritt: Interpretation: Die GNP line beschreibt den onsum, den das repräsentative inländische Individuum in der zweiten Periode erreicht, wenn es in der ersten Periode einen onsum von C wählt, aufgrund dieser Wahl der am Beginn der Periode 2 vorhandene apitalstock durch 2 = Y C gegeben ist und der Arbeitsinput bei freiem Zugang zum Weltarbeitsmarkt optimal, d.h. gemäßder Regel = k (w) 2 = k (w) (Y C ) gewählt wird. Wandert man auf der GNP line nach links oben, so sinkt der onsum C, steigt der apitalstock 2, steigt der Arbeitsinput, bleibt die apitalintensität 2 = konstant. The economy does not have to consume and produce at point B, however: By importing labor services from abroad [and doing enough extra investment to maintain f 0 (k 2 ) = r(w)], residents can move consumption up and to the left along the GNP line from B; by exporting labor services (and investing less) they can move down and to the right. 6

7 Because 2 can t be less than zero (and by assumption there is no foreign borrowing), C 2 can never be less than w H. At this lowest point on the GNP line, the country consumes all its rst-period output, has a domestic product of zero in the second period, and exports all its labor services abroad to generate a GNP of w H. In Figure. 2 the economy s preferred consumption point is C. At C, the economy is investing more than it would at B. To hold the marginal product of capital at r(w), the economy imports labor services from abroad, raising above H Also passing through point B on the autarky PPF is the GDP line, which shows how the sum of second-period GDP and 2 changes with rst-period consumption decisions. (Remember that 2 is eaten after date 2 production.) Recalling eq. (34) and noting that = 2 =k(w), we see that the GDP line is described by Bemerkungen: Y = F ( 2 ; ) + 2 = F ( 2 ; ) 2 + F ( 2 ; ) + 2 = r (w) 2 + w + 2 = [ + r (w) 2 ] 2 + w k (w) 2 = + r (w) + w = k (w) + r (w) + w k (w) 2 (Y C ) Beim Übergang von der ersten zur zweiten Zeile wird das Euler Theorem verwendet Beim Übergang von der zweiten zur dritten Zeile wird berücksichtigt, daßbei optimaler Wahl von (für gegebene Werte von 2 ) F ( 2 ; ) = w; F ( 2 ; ) = r (w) gilt. Beim Übergang von der dritten zur vierten Zeile wird berücksichtigt, daßdie optimaler Wahl von (für gegebene Werte von 2 ) durch beschrieben wird. = k (w) 2 Beim Übergang von der vierten zur fünften Zeile wird berücksichtigt, daßin diesem Modell 2 = Y C gilt, weil annahmegemäß = 0 gilt, und die Wirtschaft keinen Zugang zu einem Weltkapitalmarkt hat. The GDP line passes through point B because there, net labor imports are zero and GDP = GNP. The GDP line is steeper than the GNP line, however: As investment rises, so does immigration, and net payments to foreigners place a wedge between GDP and GNP. Thus GDP exceeds GNP above B but is less than GNP below B. 7

8 At the autarky point A in Figure. 2, the marginal product of capital is less than r(w). The factor-price frontier therefore implies that the autarky wage rate, w A, is greater than the world wage, w. It is straightforward to show that any country with w A > w will recruit foreign workers abroad, as in Figure.2. Countries with w A < w will export labor instead. The autarky wage depends on a number of factors: For example, an increase in a country s labor endowment, H, lowers its autarky wage rate and raises its net exports of labor. Countries that save more in the rst period will tend to have higher autarky wages and higher net immigration. The usual gains from trade are apparent in the gure: the GNP line lies above the autarky PPF except at B, where it is tangent. This result is based, however, on a representative-agent setup in which international labor-market integration has no distributional e ects. When the real wage falls as a result of trade, for example, the representative agent gains more in his role as a capitalist than he loses in his role as a laborer. Even in an economy of heterogenous individuals, everyone can gain from trade provided lumpsum side payments are made to redistribute its bene ts. Such side payments are rarely made in reality, so some economic groupings are likely to lose from international labor movements. These losses explain the erce opposition immigration usually arouses in practice. We will return to immigration again in Chapter 7. 8