Ricardian Model. Recaps. The Concept of. Comparative Advantage. Production Possibilities Frontier

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1 month) Recaps The oilfish incident in HK and the prevalent fake products problem in the mainland show that Consumers do not necessarily know the quality of the good they buy (or they can t tell a fake product from a genuine one) It takes time for the market to improve There is greater demand for government service Ricardian Model A first look at the Ricardian model Relative demand-relative supply analysis Relative demand Homothetic preferences Cobb-Douglas Utility Function 1 Production Possibilities Frontier cheese (millions of pounds per 15 a b Unattainable c 10 d Attainable 5 e z f wine (millions of bottles per month) 3 The Concept of Opportunity Cost The opportunity cost of wine in terms of cheese is the amount of cheese that could be produced with the same resources as a given number of wine. A country has a comparative advantage in producing a good if the opportunity cost of producing that good in terms of other goods is lower in that country than it is in other countries. 4 1

2 China Imagine there are only two countries can produce 4,000 wine/hour or Can produce 1,333 cheese/hour o.c. of 1 cheese is 3 wine o.c. 1 unit of wine is cheese Montenegro can produce 1,333 wine/hour or can produce 4,000 cheese/hour o.c. of 1 cheese is wine oc. of 1 unit of wine is 3 cheese China Montenegro Opportunity cost of One wine 1/3 cheese 3 cheese one cheese 3 wine 1/3 wine 5 cheese (thousands per hour) China s PPF Montenegro s PPF wine (thousands per hour) 6 cheese (thousands per hour) 5 4 b' 3 1 China s opportunity cost: 1 wine costs 1/3 cheese, and 1 cheese costs 3 wine c Montenegro s PPF a China s PPF wine (thousands per hour) Montenegro s opportunity cost: 1 wine costs 3 cheese, and 1 cheese costs 1/3 wine b 7 Bottom Line Both countries can be made better off by engaging in international trade! China the country with absolute cost disadvantage can benefit from trade Montenegro the country with absolute cost advantage can benefit from trade too But how much exactly do they produce? At what prices? 8

3 Relative Demand-Relative Supply Analysis Relative Demand Relative Supply Analysis Pc Dc Sc Pw Dw Sw 9 Dc, Sc The two markets in the home country; there are two markets in the foreign country Dw, Sw 10 Relative Demand Relative Supply Analysis Pc/ Pw: relative price of cheese Dc/ Dw: relative demand for cheese S / S : relative supply of cheese c w Suppose income=expenditure Dc = Sc and Dw = Sw if and only if Dc S = D S w c w Hence, we don t need to two separate diagrams for the home country We just need to look at one relative demandrelative supply diagram Relative Demand-Relative Supply Analysis Suppose income=expenditure Dc + Dc* = Sc + Sc* and Dw + Dw* = Sw + Sw* if and only if Dc + Dc* Sc + Sc* = D + D * S + S * w w w w

4 Relative Demand Relative Supply Analysis To study the Ricardian Model, we need to clarify what the RD and RS are. The RS is determined by the technology The RD is determined by consumers preferences The preferences to be introduced are more general, apply to other models 13 Assume identical, homothetic preferences Each consumer s relative demand depends only on relative price, and not on her income level Given the relative price, each consumer s relative demand is determined, so is that of the whole population One example is Cobb- Douglas utility function Demand Q w I =P c Q c +P w W w I >I I=P c Q c +P w W w Q c 14 Cobb-Douglas Utility Function Relative Demand max UQ (, Q) = Q Q ( α) α 1 α Qc, Qw c w c w subject to I = PQ + PQ marginal utility of Cheese = αq ( α ) marginal utility of Wine = 1- At Optimum c c w w MUc MUw MUc Pc = or = P P MU P c w w w α 1 1 α c w αq Q P Q α P 1-1 Q Q Q α α c w α 1 1 α c w c c w = = α α Qc Qw Pw Qw α Pc 15 Pc/Pw Relative demand by a Qc 1 Q = α single consumer w 1 α ( Pc/ Pw) =Relative demand by the whole country High α =Relative demand by the whole world Low α Relative Demand, Qc/Qw, or (Qc+Qc*)/(Qw+Qw*) 16 4

5 Relative Supply Assume that we are dealing with an economy (which we call Home). In this economy: Labor is the only factor of production. Only two goods (say wine and cheese) are produced. The supply of labor is fixed in each country. The productivity of labor in each good is fixed (c.r.t.s. technology). Perfect competition prevails in all markets. 17 A One-Factor Economy The unit labor requirement is the number of hours of labor required to produce one unit of output. Denote with a LW the unit labor requirement for wine (e.g. if a LW =, then one needs hours of labor to produce one gallon of wine). Denote with a LC the unit labor requirement for cheese (e.g. if a LC = 1, then one needs 1 hour of labor to produce a pound of cheese). The economy s total resources are defined as L, the total labor supply (e.g. if L = 10, then this economy is endowed with 10 hours of labor or 10 workers). 18 Relative Price and Supply I have a unit of labor, should I produce cheese or wine? To produce cheese, I can make 1/ a LC units and get a revenue of P c / a LC. To produce wine, I make 1/aLw units and hence get a revenue of P w / a LW. Hence, If P c /P w > a LC / a LW, I should produce cheese If P c /P w < a LC / a LW, I should produce wine If P c /P w = a LC / a LW, I don t mind produce any combination 19 Relative Price and Supply The above relations imply that if the relative price of cheese (P C / P W ) exceeds its opportunity cost (a LC / a LW ), then the economy will specialize in the production of cheese. In the absence of international trade, both goods are produced, and therefore P C / P W = a LC /a LW. 0 5

6 Equilibrium under Autarky Trade in a One-Factor World Relative price of cheese, P C /P W a LC /a LW Q RD (low α) RS Relative quantity of cheese, Q C /Q W RD (high α) 1 Assumptions of the model: There are two countries in the world (Home and Foreign). Each of the two countries produces two goods (say wine and cheese). Labor is the only factor of production. The supply of labor is fixed in each country. The productivity of labor in each good is fixed. Labor is not mobile across the two countries. Perfect competition prevails in all markets. All variables with an asterisk refer to the Foreign country. Trade in a One-Factor World Absolute Advantage A country has an absolute advantage in a production of a good if it has a lower unit labor requirement than the foreign country in this good. Assume that a LC > a * LC and a LW > a * LW This assumption implies that Home has an absolute disadvantage in the production of both goods. Another way to see this is to notice that Home is less productive in the production of both goods than Foreign. Even if Home has an absolute disadvantage in both goods, beneficial trade is possible. The pattern of trade will be determined by the concept of comparative advantage. 3 Trade in a One-Factor World Assume that a LC /a LW < a * LC /a * LW (-) In other words, in the absence of trade, the relative price of cheese at Home is lower than the relative price of cheese at Foreign. Home has a comparative advantage in cheese and will export it to Foreign in exchange for wine. 4 6

7 Trade in a One-Factor World Determining the Relative Price After Trade What determines the relative price (e.g., P C / P W ) after trade? To answer this question we have to define the relative supply and relative demand for cheese in the world as a whole. The relative supply of cheese equals the total quantity of cheese supplied by both countries at each given relative price divided by the total quantity of wine supplied, (Q C + Q * C )/(Q W + Q* W ). The relative demand of cheese in the world is a similar concept. Relative Word Supply Recall a LC /a LW < a * LC /a * LW If P c /P w < a LC /a LW, no workers will produce cheese: RS=0 If P c /P w = a LC /a LW, workers in Foreign will produce wine only, workers in Home are indifferent. RS=S c /(S w +L*/a* Lw ) If a* LC /a* LW >P c /P w > a LC /a LW, all Home workers produces cheese, all Foreign workers produce wine. RS=(L/ a LW )/(L*/a* LW ). 5 6 Trade in a One-Factor World Relative price of cheese, P C /P W World Relative Supply Relative price of cheese, P C /P W Trade Equilibrium a * LC /a* LW RS a * LC /a* LW Autarky equil for Foreign RS Trade equil a LC /a LW a LC /a LW Autarky equil for Home RD L/a LC L * /a * LW Relative quantity of cheese, Q C + Q * C Q W + Q * W 7 L/a LC L * /a * LW Relative quantity of cheese, Q C + Q * C Q W + Q * W 8 7

8 Gains from Trade If countries specialize according to their comparative advantage, they all gain from this specialization and trade. Gains from Trade L=L*=10 a LC =4, a LW =8, hence a LC /a LW =1/ a* LC =, a* LW =1, hence a* LC /a* LW = If free trade relative price is in between ½ and Home specializes in Cheese production. Foreign specializes in Wine production Gains from Trade Gains from Trade Quantity of wine, Q W T P Slope =-a LC /a LW =-1/ Slope=Pc/Pw Quantity of wine, Q * W F * Slope=-a* LC /a* LW =- Slope=Pc/Pw Quantity of wine, Q W A B Trade moves Home country s consumption bundle from A to B, surely an improvement! (a) Home F Quantity of cheese, Q C P * (b) Foreign T * Quantity of cheese, Q * C (a) Home Quantity of cheese, Q C A similar conclusion for Foreign country

9 When is complete specialization? When is complete specialization? Relative price of cheese, P C /P W Autarky equil for Foreign RS -1/ -1/4 Trade equil Autarky equil for Home RD Relative quantity of cheese, Q C + Q * C Q W + Q * W 33 Complete specialization if and only if RD=1/4 and 1/ P / P α 1 Using RD = 1 α P / P α PC or = RD 1 α P W C C W W 1 α α Hence, complete specialization if and only if 1/9 α 1/ 3 34 Incomplete specialization Incomplete Specialization If α 1/9, then Home has incomplete specialization, it is neither better off nor worse off under trade. But Foreign still has complete specialization and is still strictly better off If α 1/3, then Foreign has incomplete specialization, it is neither better off nor worse off under trade. But Home is still better off 35 Relative price of cheese, P C /P W RS -1/ RD for lower α -1/4 If α is low enough, there will be incomplete specialization by Home. RD for higher α Relative quantity of cheese, Q C + Q * C Q W + Q * W 36 9

10 Wages Relative Wages Because there are technological differences between the two countries, trade in goods does not make the wages equal across the two countries. A country with absolute advantage in both goods will enjoy a higher wage after trade. Wages This can be illustrated with the help of a numerical example: Assume that P C = $1 and that P W = $1. Therefore, we have P C / P W = 1. Since Home specializes in cheese after trade, its wage will be (1/a LC )P C = ( 1/4)$1 = $3. Since Foreign specializes in wine after trade, its wage will be (1/a * LW) P W = (1/1)$1 = $1. Therefore the relative wage of Home will be $3/$1 = 1/4. Thus, the country with the higher absolute advantage will enjoy a higher wage after trade with Many Goods Setting Up the Model Both countries consume and are able to produce a large number, N, of different goods. with Many Goods Table -4: Home and Foreign Unit Labor Requirements Relative Wages and Specialization The pattern of trade will depend on the ratio of Home to Foreign wages. Goods will always be produced where it is cheapest to make them. For example, it will be cheaper to produce good i in Home if wa Li < w * a * Li, or by rearranging if a * Li/a Li > w/w *

11 with Many Goods Which country produces which goods? A country has a cost advantage in any good for which its relative productivity is higher than its relative wage. If, for example, w/w * = 3, Home will produce apples, bananas, and caviar, while Foreign will produce only dates and enchiladas. Both countries will gain from this specialization. with Many Goods Determining the Relative Wage in the Multigood Model To determine relative wages in a multigood economy we must look behind the relative demand for goods (i.e., the relative derived demand). The relative demand for Home labor depends negatively on the ratio of Home to Foreign wages with Many Goods Figure -5: Determination of Relative Wages Relative wage Rate, w/w * 10 Apples Bananas Caviar RS Dates Enchiladas RD Summary Countries engage in international trade for two basic reasons: They are different from each other in terms of climate, land, capital, labor, and technology. They try to achieve scale economies in production. The Ricardian model is based on technological differences across countries. These technological differences are reflected in differences in the productivity of labor. Relative quantity of labor, L/L *

12 Summary (contd.) A person or nation has a comparative advantage in an activity if he/it can perform an activity at a lower opportunity cost than others. (David Ricardo) Caveats of Ricardian model Only one factor, no income distribution issue Switching production from one sector to the other often involves costs but is ignored here End