Homework 2 Answers. Ricardo Cavazos and Robert Santillano University of California at Berkeley. September 28, 2006

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1 Question 1. Speciic Factors and Trade Hoework Answers Ricardo Cavazos and Robert Santillano University o Caliornia at Berkeley Septeber 8, 006 Finland is capital abundant relative to potential trading partners in the rest o the world. Telecounications is a capital intensive industry relative to the business services industry. Businesses in Finland have ade investents in both industries, creating stocks o capital that are devoted to either telecounications or business services. (a) Suppose that Finland is not trading. Draw the speciic actors diagra or Finland, indicating how labor is divided between the two industries, and showing the prevailing wage w 0. K BS capital: speciic to business services K T capital: speciic to telecounications sector L labor: obile actor P BS price o business services P T price o telecounications (K F /L F )> (K ROW /L ROW ) Finland (F) is capital abundant relative to potential trading partners in the Rest o the World (ROW) thereore (P T /P BS ) F < (P T /P BS ) International < (P T /P BS ) ROW (K T /L T )> (K BS /L BS ) Telecounications is a capital intensive industry relative to the business services industry w P BS x MPL BS P T x MPL T w 0 L T L 0 L BS Figure 1 In Figure 1, we see the initial allocation o labor L 0 and initial wage w 0. The Business services sector has relatively ore labor eployed because it is a labor intensive industry in coparison to Telecounications which as stated in the proble is a capital intensive industry.

2 (b) Modiy your diagra to show how Finland s labor allocation and wage change when it opens to trade with the rest o the world. w P 1 T x MPL T P BS x MPL BS P T x MPL T w 1 w 0 L T L 0 L 1 L BS Figure Fro Figure we can see the eects o Finland opening up to trade. In irst place, the price o telecounications (P T ) will increase given that Finland will now ace a World deand or Telecounications instead o only the doestic one. The increase in P T will cause the Value o Marginal Product o Labor in the Telecounications sector to shit to the North-East (up and to the right). The shit in this curve will cause the allocation o labor in both sectors to change. The eployent o labor in the Telecounications sector will increase and eployent in the Business services sector to decrease since there is a liited aount o total labor available. (c) How does the opening o trade aect capital owners in Finland s telecounications industry? Describe and show in your graph. The shit o the Value o Marginal Product o Labor in Telecounications, described in question b, will cause the ollowing changes in the arginal productivities o capital in the Telecounications and Business Services, respectively. MPK T will increase (i.e. shit up since there are now ore workers per unit capital) MPK BS will decrease (i.e. shit down since there are now less workers per unit land) Noinal returns to capital in the Telecounications sector, r T : r T P T x MPK T (assuing perectly copetitive arkets) P T increases due to the opening up to trade, this provides the irst shit o the curve, and then MPK T increases, a second shit o the curve, this only eans that r T ust increase. Real returns to capital in Telecounications sector: r T /P T MPK T : increased since MPK T in addition we can say the increase in r T has been greater than the increase in P T r T /P BS has increased because r T has increased and P BS has reained constant.

3 Since returns have increased in ters o both goods, real returns to capital in the Telecounications sector have risen unabiguously. Noinal returns to capital in business services, r BS : r BS P BS x MPK BS (assuing perectly copetitive arkets) Since P BS has reained constant and MPK BS has allen, r BS ust all. Real returns to capital in business services: r BS /P BS MPK BS : decreased since MPK BS has decreased r BS /P T has decreased because r BS has decreased and P T has increased Since returns have allen relative to both goods, real returns to capital in the business services sector have allen unabiguously. r r T r T1 r T0 P 0 T x MPK 0 T P 1 T x MPK 1 T P 1 T x MPK 0 T K 0 K T Figure 3 Figure 3 above presents the outcoe or capital owners in the Telecounications sector in Finland. r BS r 0 P BS x MPK 0 BS r 1 P BS x MPK 1 BS K 0 K BS Figure 4 Figure 4 above presents the outcoe or the capital owners in the business services sector.

4 (d) Are Finnish workers likely to beneit or lose ro the opening o trade? Fro Figure we can see: Since L BS decreased, equilibriu MPL BS increases. Since L T increased, equilibriu MPL T decreases. Thereore: w/p BS MPL BS has increased w/p T MPL T has decreased The returns have allen relative to Telecounications and risen relative to business services. The overall ipact on real returns to labor is abiguous. (e) Suppose Finnish workers consuer as uch telecounications as they can, while they buy very ew business services. How does this aect the agnitude o worker gains or losses? I we assue that ost o labor s consuption is on Telecounications, then it is likely that real returns to labor decrease, although it is still abiguous. Question. The HO Fraework (a) Mexico produces two goods, GM cars and corn. There are two actors o production, labor and capital. Total available hours o labor and capital are 100 labor and 100 capital. The unit labor requireents or the production o each good are given below. What does the production possibility rontier look like? Labor Requireent (Hours) Capital Requireent (Hours) GM Cars 5 0 Corn 10 5 Since we are given unit requireents (ixed) rather than a unction speciying arginal productivities (variable), we know that the PPF will be linear with a kink. The boundaries o the PPF will be deterined by the line showing ull eployent o labor (the labor constraint) and the line showing ull eployent o capital (the capital constraint). Labor constraint: Intercept car axis where all labor in car production cars L/a LC 100/5 0 Intercept corn (ood) axis where all labor in corn production corn L/a LF 100/10 10 Capital constraint: Intercept car axis where all capital in car production cars L/a KC 100/0 5 Intercept corn (ood) axis where all capital in corn production corn L/a KF 100/5 0

5 Q(cars) 0 Labor constraint 10 B PPF PPF 1 A Capital constraint: K100 Capital constraint: K Q(corn) Figure 5 The PPF looks like PPF 1 in Figure 5. (b) Following NAFTA, Mexico receives an inlux o oreign direct investent ro the US, raising the available pool o capital ro 100 to 00. What happens to the relative production o GM cars and corn? Please show graphically. The capital constraint will shit out. Production will ove ro point A to point B on Figure 5. The production o cars will increase and the production o corn will decrease. Thereore, the relative production o cars will increase. (c) What is likely to happen to the pattern o exports in Mexico (o cars versus corn)? How is this related to the Heckscher-Ohlin Theore? We do not know which way trade lows go unless we know the endowents o a trading partner. Depending on how relatively well endowed with capital Mexico s trading partners are, dierent things ay happen. However, it is likely that relative to at least soe o its trading partners, Mexico will now becoe relatively well endowed with capital. This eans that Mexico ay switch ro exporting corn to exporting cars to these partners. This is an exaple o the Heckscher-Ohlin Theore because Mexico will export the good (cars) that uses its newly relatively ore abundant actor (capital) ore intensively. Note that we can see that cars use capital relatively ore intensively because (K/L) cars 0/5 4 > (K/L) corn 5/10 ½. (d) I the United States continues to lose capital to Mexico, what will happen to its pattern o exports? The pattern o exports or the United States will be such that the country will export the good that uses the actor that is relatively ore abundant. I the United States keeps losing capital to Mexico so that it becoes a labor abundant country then it is highly likely that it will export corn and iport GM cars.

6 (e) Assue Mexico has 100 labor and 00 capital. Using your knowledge o Stolper-Sauelson, what will happen to the returns to wages and capital in Mexico ater trade liberalization? What i the endowent o labor and capital is reversed? Again, i we are assuing that Mexico is relatively well endowed with capital when copared to its trading partner, then the Stopler-Sauelson theore says that real wages will decrease and the real return to capital will increase with trade. Question 3. More on the Speciic-Sector Model and Trade Hoe can produce achinery and lowers in bundles o The production o the two industries are given by QK 1/ L 1/ and QT 1/ L 1/. K is capital, T is land, and L is labor, Prices o achinery P and o ood P are both equal to 1. Factor supply is L + L 100 and TK100. (a) Derive the arginal products o labor MPL and MPL or the two industries. The Marginal Product o Labor is the contribution to output o the last worker hired. In atheatical ters we deine the Marginal Product o Labor as the derivative o the production unction with respect to labor. In this case the Marginal Product o Labor or achinery and lowers are the ollowing, respectively: Q The Marginal Product o Labor in the achinery sector is the ollowing: L Q 1 Marginal Product o Labor in the lower sector is the ollowing: L L T L 1 1 K and the (b) Autarky wage: graph the labor deand curves in the achinery and lower sectors, and calculate the equilibriu wage rate in autarky. w P MPL P MPL w w 0 L L * L Figure 6 We are given the ollowing inoration to calculate the initial wage level in autarky and the labor allocations: L + L 100; TK100. We know that noinal wages have to equal the Value o the Marginal Product o Labor in achinery and also equal the Value o the Marginal Product o Labor in lowers. Building those conditions w L K and w L T Set the equal to each other and solve or L or L.

7 1 1 L K L T Ater soe algebra we are able to deterine the ollowing relationship: L T L K Substitute in the values o T and K and to obtain L50 and L50. Substitute these values into the Value o Marginal Product o Labor in achinery or into the Value o Marginal Product o Labor o lowers to obtain wages. w (c) The pattern o trade: ater opening up to ree trade, hoe aces a relative price o P/P. How do the allocation o labor and wages change? When the ratio o relative prices changes to P/P labor allocations change because producers realize the production o achinery is ore proitable than the production o lowers. There is a need or reoptiization, i.e. set the new value o arginal products equal to each other and solve or L and L. Proceeding in such anner and ater soe algebra we obtain the ollowing relationship: 4L L T K Substitute the values or T and K and solve or L and L. Thereore, L80 and L0. We obtain wages by substituting the new values or the labor allocations into the Value o Marginal Product or achinery or into the Value o Marginal Product or lowers. The new level o wages is equals to the ollowing: 5 w (d) Using the general deand relationships or the two sectors, show that the production possibilities rontier is given by MPL/MPL -P/P There are several ways to approach this question. One way to show the relationship posed above is to equate the Value o Marginal Products and play with those expression to obtain MPL/MPL -P/P. In this case, we would go about in the ollowing way: w PMPL w P MPL P MPL P MPL P MPL P MPL It is also possible to axiize a Value unction o the ollowing type:

8 Max V P Q + P Q Q V P P P Q Fro the above expression we see that the slope at the optial value is equal to P P (e) Draw the production possibilities rontier. How does the change in relative prices ater trade aect production? Depict the gains ro trade. Q Slope Q c U 1 iports Q 0 Slope1 Q p U 0 Q c Q 0 Q p Q exports Figure 7 Figure 7 presents the Production Possibilities Frontier and the initial autarky point as Q 0 and Q 0 where production and consuption in the closed econoy occur. We see that the ratio o relative prices is equal to 1 at that point and the econoy has a utility level o U 0. Once the econoy opens up to trade, the ratio o relative prices increases to. Thereore, we observe a shit in the slope o the budget line, i.e. it becoes steeper to denote the increase in the ratio o relative prices. Once the econoy starts trading, observe that production and consuption decisions becoe disjoint, i.e. the production point is dierent ro the consuption point. The production point when the econoy is trading is denoted Q p and Q p. The econoy now produces ore achinery and less lowers. This is a result o the increase in the ratio o relative prices. Producers realize that achinery is ore proitable and thereore want to increase production o that good. This iplies a reduction in the production o lowers. On the other hand, the consuption point is denoted by Q c and Q c. We observe that at the consuption point the econoy attains a utility level o U 1 which is greater than U 0. Thereore, this country is better o. Finally, we see this country is exporting achinery. The aount o exports is denoted by the dierence between Q p and Q c. Likewise, the aount o iports o lowers is given by the dierence between Q c and Q p.

9 Question 4. The HO Fraework. We are given the ollowing input requireents to produce ood and coputers: Labor To produce One Unit Capital to Produce One Unit Food a LF 6 a KF 3 Coputers a LC 4 a KC 10 Chile is well endowed with labor, and consequently has a coparative advantage in labor-intensive goods. Chile is considering joining a ree trade area with the United States. Prior to joining the ree trade area, the price o ood (P) is 15 and the price o coputers (Pc) is 4. Ater joining the ree trade area, the price o ood is 1 and the price o coputers in Chile is 30. (a) What happens to the returns to labor and capital in Chile ater it joins the ree trade area? Calculate exactly using equations please, not just diagras or qualitative answers. The relevant equations here are the zero proit conditions or beore and ater trade. They are: P c w x a LC + r x a KC (1) P F w x a LF + r x a KF () Substituting the nubers into equations (1) and () beore trade we get: 15 6w + 3r r 5-w ro (1) 4 4w + 10r ro () Which we solve to give r 4 and w 1/ Substituting the nubers into equations (1) and () ater trade we get: 1 6w + 3r r 7-w ro (1) 30 4w + 10r ro () Which we solve to give r and w 5/ Thereore noinal returns to labor (w) increase, and to capital (r) decrease. Real returns to labor: w/p C increases because w increases and P C decreases. w/p F? w /P F > w 1 /P 1 F i and only i w /w 1 > P F /P 1 F substituting our beore and ater trade values we see that w /w 1 5 > 7/5 P F /P 1 F So ater trade, w has risen relatively ore than the price o ood, thus real returns have increased in ters o ood as well. So real returns to labor have increased unabiguously. Real returns to capital: r/p F decreases because r decreases and P F increases r/p c? r /P c < r 1 /P 1 c i and only i r /r 1 < P c /P 1 c substituting our beore and ater trade values we see that r /r 1 1/ < 5/7 P 1 c /P c So ater trade, r has allen relatively ore than the price o coputers, thus real returns have decreased in ters o coputers as well. So real returns to capital have decreased unabiguously. (b) Which theore is consistent with this result? Why or why not? This result is consistent with the Stolper Sauelson Theore because opening up to trade leads to an increase in the return to Chile s abundant actor (labor) and a all in the return to its scarce actor (capital).