P C. w a US PT. > 1 a US LC a US. a US

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2 And let s see hat happens to their real ages ith free trade: Autarky ree Trade P T = 1 LT P T = 1 PT > 1 LT = 1 = 1 rom the table above, it is clear that the purchasing poer of ages of American orkers stays the same hen it comes to computers but increases in terms of T-shirts. Note hoever that the assumptions of the Ricardian model are very strong. The consequences of trade on ages might be different if, for example, there are more factors of production. In this particular context, the strongest assumption of the Ricardian model - or the one that seems to not hold in reality - is that there is perfect labor mobility, that is, that orkers can costlessly move from one sector to the other hen countries open up to trade. ( ) US ( ) or example, assume that U.S. T-shirt orkers are stuck in their sector. Given that the PT > PT > ( ) PT hina, if American T-shirt producers ants to keep on selling T-shirts, they ill have to loer their prices. But note that from the age equation e kno that = (P T ) US 1 so that a drop in T-shirt prices LT ill entail a drop in ages for T-shirt orkers, ho are stuck in their sectors. Thus, if this is the case, importing T-shirts from hina ill also import a drop in ages. Exercise 2 Part 1 To figure out absolute advantage, look at columns IV and V on the table. or example, U.S. labor productivity in omputing is hereas German labor productivity is only When looking at the list of all industries, one can see that the U.S. has absolute productivity in all sectors except for uel and Building. Part 2 To anser in hich industries the U.S. exports more to the U.K. than Germany, look at column VI. All the industries in hich the ratio of U.S. exports to the U.K. to German exports to the U.K is greater than one, are industries in hich the U.S. exports more. Those industries are: omputing, Medical, Other, Metals, Aircraft, and Pharmaceuticals. 2

3 To look at hether U.S. productivity advantage is particularly large, one can look at column VII. irst, note that the ratio of U.S. labor productivity to German labor productivity has a mean of 1.5, and a standard deviation of One can first notice that the productivity ratio in the industries in hich the U.S. exports more to the U.K. than Germany, is not necessarily greater than the mean or median productivity ratio. The productivity ratio for Pharmaceuticals is 2.78, for omputing it is 1.80, and for Medical it is 1.59; in all these industries the ratio is higher than the mean labor productivity ratio. The labor productivity ratio in Other is 1.49, for Aircraft it is 1.43, and for Metals it is 1.11, the three of hich are belo the mean. Thus, the sectors in hich the U.S. exports more than Germany to the U.K. are not necessarily those in hich the U.S. productivity advantage is particularly large. Part 3 The correlation beteen the columns is This number says that, on average, the U.S. exports relatively more than Germany to the U.K. in those industries in hich the U.S. s productivity is relatively larger. Part 4 When regressing exports on productivity e find the folloing output (I did it in Stata): Table 1: Dependent variable is ratio of U.S. to German exports Variable oefficient (Std. Err.) Ratio of U.S. to German productivity (0.440) onstant (0.686) N 21 R Significance levels : : 10% : 5% : 1% The coefficient is significant at the 10% level so that although the effect of relative productivity on relative export volumes is positive, it is not very statistically significant. Note hoever that given the small number of observations, the eak statistical significance of the result shouldn t be taken as conclusive evidence to reject the model. 3

4 In the picture belo, you see the correct positive slope of the regression line: Ratio of U.S. Exports to German Exports to the U.K Regression of export ratios on productivity ratios Metals Aircraft Other Medical omputing Wood Electrical Machinery Telecom. Transport Paper Plastic Metal Minerals products uel Textile Building IronMotors ood Pharma Ratio of U.S. Labor Productivity to German Labor Productivity urthermore, note that if e eliminate the aircraft industry from the sample, the output becomes: Table 2: Dependent variable is ratio of U.S. to German exports (no Aircraft data) Variable oefficient (Std. Err.) Ratio of U.S. to German productivity (0.289) onstant (0.453) N 21 R Significance levels : : 10% : 5% : 1% This suggests that there is an important role for Ricardian forces in shaping trade flos. Exercise 3 The technology in each country can be summarized by means of the unit labor requirements of each country and each sector: = 4 man-hours; = 4 man-hours = 1 man-hours; = 2 man-hours In the Ricardian model, because e assume constant returns to scale in production, these four countryindustry pair completely describe the technology of the model. Part 1 Note that: < 4

5 and: < It follos that anada has the absolute advantage in the production of both food and clothing. Part 2 We can rite: = 1 and: = 1 2 so it follos that: > aan The US has a comparative advantage in the production of food and anada in the production of clothing. Part 3 The PP of an economy is the set of all combinations of output (, ) that make full use of the economy s factor of production. Given that the production function has constant returns to scale and that labor is the only factor of production, the PP of each country dran on a - space ill be a straight line. The PP ill intersect the y axis (ood) at the level of food the country produces if all of its labor is allocated to the ood sector. Similarly, the PP ill intersect the x axis (lothing) at the level of clothing the country produces if all of its labor is allocated to the lothing sector. If the country is endoed ith L units of labor, the y intercept of the PP is L/ and the x intercept of the PP is L/a. Both countries are endoed ith 40 units of labor, measured in man-hours. It follos that L US = L AN = 40 and that the intercepts for each country are: The PP for the U.S. is: U.S. s PP x intercept = LUS anada s PP x intercept = AN = 10; y intercept = LUS = 10 = 40; y intercept = AN = 20 ********* I still haven t learned ho to dra decent graphs, if you have questions about the PPs, please let me kno ****************** The PP for anada is: ********* I still haven t learned ho to dra decent graphs, if you have questions about the PPs, please let me kno ****************** 5

6 To interpret the slope, look at the folloing PP. Assume that current production is at point Q 0 = ( 0, 0 ). No assume that e decide to increase the production of clothing by one unit. To produce an extra unit of clothing, e need a units of labor. Given that e only have to sectors, to increase production e ill need to reallocate a units of labor from the sector to the sector. As a result of this reallocation, production of clothing increases by 1 and production of food decreases by a / (in, each unit of labor can produce 1/ units of food). It follos that the slope a / measures the opportunity cost of producing clothing in terms of food. or example, if a is very high relative to the labor necessary to produce a unit of clothing is very high hich means that to increase production of clothing the country has to give up many units of food. It follos that if a / is high, the opportunity cost of producing clothing in terms of food is high as ell. Part 4 The PP of the orld is the set of all combinations of output (, ) that make use of all of the orld s factors of production. Given that labor is not mobile, in order for an output bundle in the orld s PP (, ) to make use of both L US and L AN, it ill have to be the sum of an output bundle in the U.S. s PP, (, ) US and an output bundle in anada s PP, (, ) AN. It follos that the maximum amount of food that the orld can produce is the maximum amount of food that the U.S. can produce plus the maximum amount of food that anada can produce. Also, the maximum amount of clothing that the orld can produce is the maximum amount of clothing that the U.S. can produce plus the maximum amount of clothing that anada can produce. It follos that intercepts of the orld PP are: World s PP x intercept = 50; y intercept = 30 The P for the orld ill just be a sum of the U.S. s and anada s PP: ********* I still haven t learned ho to dra decent graphs, if you have questions about the PPs, please let me kno ****************** The interpretation of the slope is very similar to the interpretation of the slope of the PP of individual countries. The slope of the PP just measures the opportunity cost of producing clothing in terms of food. Hoever, hen e consider the orld economy, the opportunity cost is not constant and ill depend on the output that the orld is currently producing. If the U.S. is specialized in food, the opportunity cost of clothing in terms of food ill be anada s opportunity cost or /aan. On the other hand, then anada is fully specialized in clothing, the opportunity cost of clothing in terms of food ill be the U.S. s 6

7 opportunity cost or Part 5 /aus a World a World =. So the orld s opportunity cost is: /aan = 1/2 if Q lothing [0, 40) /aus = 1 if Qlothing (40, 50] With Leontief preferences, each consumer ill ant to buy the same number of units of food and clothing. No, if she has an income I and faces prices and P, her optimal consumption of clothing D ill be the same as her consumption of food D such that she uses up all of her income: It thus follos that the relative demand ill be 1: D + P D = I D = D I = + P RD (P / ) = D D = 1 No hat about the relative supply? As usual, there are five possibilities: ( ) ( ) P 1. < 1 = aus < 2 = aan l : If the relative price of food is less than the opportunity cost of food in the US, then, it is also less than the opportunity cost of food in anada and both countries specialize in the production of clothing and the relative supply of food ill be 0. ( ) ( ) 2. 1 = aus = P P < 2 = aan l : If the relative price of food is the same as the opportunity cost of food in the US, then, the US ill be indifferent beteen producing food or clothing and anada ill specialize in the production of clothing. The relative supply of food could be anything from 0 to L US / = 10 L AN / 40 = 1 4. ( ) ( ) : If the relative price of food falls beteen the opportunity cost of 1 = aus < P P < 2 = aan l food in the US and in anada, then both countries ill be fully specialized: the US in the production of food and anada in the production of clothing. Thus, the relative supply of food ill be exactly L US / = 1 L AN / 4. ( ) ( 2 = aan l ) : If the relative price of food is the same as the opportunity cost 1 = aus < P P = of food in anada, then anada ill be indifferent beteen producing food or clothing hereas the US ill specialize in the production of food. The relative supply of food ill be anything from L US / = 1 L AN / 4 to. ( ) ( ) 1 = aus < 2 = aan l < P P : If the relative price of food is greater than both the opportunity cost of food in the US and in anada, then both countries specialize in the production of food and thus the relative supply is infinite. 7

8 Given that /aus = 1 and aan / = 2, e can describe the relative supply as: RS (P / ) = Q Q = x here x = 0 [ ] x 0, 1 4 x = 1 4 x [ 1 4, ) x = if P < 1 if P = 1 if 1 P 2 if P = 2 if 2 < P To find the equilibrium in free trade, e need to look for the relative price at hich relative demand equals relative supply. Given that relative demand is alays 1, it must be the case that at the equilibrium prices, relative supply must also be one. Note that this is only possible if P / = 2 so that the US is fully specialized in the production of food and anada is producing both food and clothing. Ho much does each country produce? Note that because of Leontief preferences, the demand for clothing and food in each country ill be the same so that D US = DUS = D US and also D AN = D AN = D AN. It also follos that the orld s demand, and therefore the production, of of food and clothing ill be the same D W = DW = QW = QW. To find at the levels of production, it is enough to look at a production bundle (Q, Q ) on the production possibilities frontier such that Q = Q. One can find that point by draing a ray through the origin and seeing here it intercepts the PP. In this case the solution is Q = Q = No the pattern of trade is clear. The US manufactures 10 units of food hereas anada makes 10 units of food and 20 units of clothing. Given that the relative price of food is 2, and that the value of consumption in the US has to be the same as the value of production, e can rite: D US + P D US = 10P D US + P D US = 10 P D US = 20/3 Then, the US produces 10 units of food of hich it consumes 20/3. The US exports the other 10/3 units of food and buys 20/3 units of food from anada. Given that the relative price of food is 2, trade is balanced. anada on the other hand, produces 20 units of clothing and 10 units of food. Note that in addition to the 10 units of food it produces, it consumes the 10/3 units of food that it buys from the US. Thus, the consumption of food in anada is 40/3 units of food. Out of the 20 units of clothing, anada consumes 40/3 and exports 20/3 to the US to pay for its imports. 1 Another ay of finding the equilibrium levels ould be to note that the folloing equations must hold: D US + P D US = 10P D US + P D US = 10 P D US = 20 3 Q AN = 10 + Q AN QAN + Q AN = 40 Q AN = 10, Q AN = 20 and from there, it is easy to see that given that D US + D AN = 20, it must be that D AN = 40/3. 8

9 Part 6 Relative demand ill not change as preferences don t change. It follos that the orld s relative demand ill still be 1. Relative supply ill change. Note that hen both countries are fully specialized, the US ill no produce 20 times more than it did before hereas the production in anada ill stay the same. Thus, relative supply if relative prices are 1 P / 2 ill no be 5. Note that no the relative demand curve intersects the relative supply curve hen the relative price is 1 and anada is fully specialized in the production of clothing hereas the US is producing both clothing and food. This implies that the US ill sell food to anada and anada ill sell some clothing to the US. Note that even though the pattern of specialization is different, both countries still export and import the same products. This is because in the Ricardian model the only determinant of comparative advantage is relative productivity hich doesn t change hen the labor force in the US increases. Exercise 4 We assume to countries Home and oreign hich produce clothing and food. The unit labor costs are a,, a, a such that Home has a comparative advantage in clothing: a < a a Workers have the same preferences everyhere. urthermore, they are obb-douglas preferences that can be represented by the folloing utility function: U (D, D ) = (D ) β (D ) 1 β Part 1 The equilibrium relative price of clothing under free trade is: P T = PT P T A orker in Home can produce either 1/a units of clothing or 1/ units of food. This means that, given P T, a orker can make P T /a dollars selling the unit of clothing or P T / dollars selling the unit of food. It follos that orkers at Home ill: Specialize in food if : Not specialize in either food or clothing if : Specialize in clothing : P T a < PT P T < a P T a = PT P T = a P T a > PT P T > a 9

10 Similarly, in oreign orkers ill: Specialize in food if: Not specialize in either food or clothing if: Specialize in clothing: P T a P T a P T a < PT a P T < a a = PT a P T = a > PT a P T > a a No, given that e kno that a 1. If P T < a < a a e can predict the patterns of specialization: < a a : orkers in both Home and oreign produce food. 2. If a = P T < a : orkers in Home are indifferent beteen producing clothing or food and a orkers in oreign specialize in the production of food. 3. If a food. 4. If a < P T < a a : orkers in Home specialize in clothing and orkers in oreign specialize in < P T = a a : orkers in Home specialize in clothing and orkers in oreign are indifferent beteen producing clothing or food. 5. If a < a a It follos that only if: < P T : orkers in both Home and oreign produce clothing. a < P T < a a ill there be complete specialization in both countries. Part 2 We assume that countries are fully specialized: Home produces clothing and oreign produces food. irst, let s compute the relative supply of clothing. irst recall that Home is endoed ith L units of labor and oreign is endoed ith L units of labor. Given that Home is fully specialized in clothing and oreign is fully specialized in food, the total supplies of both food and clothing are: and the relative supply of clothing is then: Q = L a Q = L a RS = Q = Q Q = L L a a 10

11 On the demand side, obb-douglas preferences are homothetic so that the share of income spent in clothing and food that orkers spend in food and clothing ill be the same across countries. Also, given that orkers in both countries face the same relative prices hen there is trade, relative demand in both countries ill be the same. Given that orkers have obb-douglas preferences e kno that her demand for each good ill be given by: and thus the relative demand for clothing is: D = β I and D = (1 β) I P RD = D D = β 1 β P T P T = β 1 1 β P T No, in order for the market for good to clear, e have to find a relative price for hich relative supply equals relative demand: Part 3 RS = RD L L a a = P T = β 1 1 β P T β L a 1 β L a To figure out ho an increase in the endoment at Home changes the relative price e can take the derivative of P T ith respect to L: dp T dl = β L a 1 β L 2 a < 0 hich is negative. Thus, an increase in the labor force in Home decreases the relative price of clothing. The intuition for the previous result is that, assuming that both countries are fully specialized, after the increase in its labor force Home can produce more clothing than before. It follos that the relative supply of clothing ill increase. Then, given that demand doesn t change, the relative price of clothing ill decrease. A proportional increase in the productivity of Home in both the clothing and food sector can be interpreted as a proportional fall in the amount of labor required to produce a unit of clothing and that required to produce a unit of food: both a and go don leaving a unchanged. To assess the effect on relative prices, again assuming that both countries remain fully specialized, e can compute the derivative of P T ith respect to a : dp T = β L da 1 β L 1 a > 0 and again, an increase in the productivity of Home (or a decrease in a ) reduces the relative price of clothing. 11

12 The intuition is exactly the same as before. When the number of orkers needed to produce a unit of a certain good decreases and both countries remain fully specialized, the output of clothing at Home ill increase hich in turn increases the relative supply of clothing and reduces its relative price. Also, as e sa in class, given that the price of the good that Home exports relative to the price of the good that Home imports decreases, elfare in Home is reduced. rom the equation of P T is easy to see that if L increases by 1% or a decreases by 1%, P T decreases by 1%. More formally, note that given the equation for P T e can take logs and get the folloing equation: log P T = log β log (1 β) + log L log L + log a log a and no e can totally differentiate and get: dp T P T = dβ β d (1 β) (1 β) + dl L dl L + da da a a No it is easy to see that if, for example, L increases by 1% and everything else stays the same (hich is equivalent to dl/l = 1/100) e get: hich means that P T decreases by 1%. dp T P T = Part 4 Given that countries are fully specialized, the age in Home is equal to the revenue per orker in cloth: = a and the age rate in oreign is equal to the revenue per orker in food: = P a It follos that the relative age of orkers is therefore: and given our anser in part 2, e can rite: = a P a = P T a a = = β L a a 1 β L a a β L 1 β L 12

13 Part 5 rom the equation derived in part 4 e can observe that an increase in the labor force in Home ill decrease the relative ages in that country. The intuition for this is that ith both countries fully specialized, an increase in L ill increase the production of clothing and thus the relative supply of clothing in the orld. And, as the relative supply of clothing increases, the relative price of clothing ill decrease. We can take the derivative to find that: d (/ ) dl = β L 1 β L 2 < 0 Also from the equation for relative ages e see that an increase in the productivity of the labor force at home does not change relative ages. The key observation here is that before and after the change in productivity both countries are still fully specialized. An increase in productivity ill have to effects: 1. As a decreases, the amount of clothing that each orker in Home can produce 1/a increases and thus his relative age (/ = a P a ) should tend to increase. 2. Hoever, as the amount of clothing that each orker at Home can produce increases, the supply of clothing in the economy increases as ell. Without an increase in the production of food, the relative supply of food of clothing in the economy increases as ell hich, given the fixed relative demand, pushes the relative price of clothing don. Then, the relative ages of orkers, hich also depend on the relative price, ill tend to go don. In this example, effects 1 and 2 exactly cancel each other out and an increase in the productivity in Home does not affect relative ages as long as countries remain fully specialized. Part 6 irst, note that given that countries are fully specialized, e can rite ages in each country in the folloing ay: = = 1 P T a 1 a P T We are interested in the purchasing poer of ages of both countries: = PT 1 a P T = 1 a = PT 1 P a P T 1 = PT a 1 P = a P T = 1 a P T = = L L 1 β β β L 1 β L 1 a 1 a 13

14 An increase in the labor force in Home ill not change the amount of clothing that Home orkers ill be able to buy. The intuition here is that the amount that each Home orker can buy is exactly the amount that she produces, 1/a, regardless of the relative prices in the economy. On the other hand, Home orkers ill see a decrease in the amount of food they can buy hen the labor force increases. An increases in the labor force ill increase the relative supply of clothing in the orld pushing its relative price don and therefore reducing the purchasing poer of ages. It follos that an increase in L makes Home orkers unambiguously orse off. An increase in the labor force in Home increases the purchasing poer of oreign orkers in terms of clothing. As e mentioned above, the increase in the labor force in Home increases the relative supply of clothing and pushes its relative price don increasing the purchasing poer of oreign orkers. An increase in the labor force in oreign has no effect on the purchasing poer of foreign ages in terms of food as each orker s consumption of food in oreign is independent of prices and limited to the amount that she can produce: 1/a. Thus, foreign orkers are unambiguously better off hen L increases. An increase in the productivity of Home orkers allos them to produce, and therefore consume, more clothing. As e sa in part 5, an increase in the productivity of home orkers tends to increase their ages by alloing them to produce more clothing but tends to decrease their ages by reducing the relative price of their production. In this case, both effects cancel out and the purchasing poer of Home ages ith respect to food does not change. An decrease in a makes Home orkers unambiguously better off. inally, given that the decrease in a increases the relative supply of clothing and thus reduces its relative price, orkers in oreign can buy more clothing ith their ages. On the other hand, the purchasing poer of their ages in terms of food is unchanged. Thus, an increase in the productivity at Home makes oreign orkers better off. Note that the key assumption for this results is that countries remain fully specialized. 14