Labor Productivity and Comparative Advantage - Ricardian Model PDF

LABOR PRODUCTIVITY AND COMPARATIVE ADVANTAGE: THE RICARDIAN MODEL CH3 By professor Cristina Vinyes Pinto Cristina Vinyes  Preview A. Comparative advantage and opportunity costs B. A one-factor Ricardian model 1. Production possibilities 2. Relative prices, wages and supply C. Trade...

LABOR PRODUCTIVITY AND COMPARATIVE ADVANTAGE: THE RICARDIAN MODEL CH3 By professor Cristina Vinyes Pinto Cristina Vinyes  Preview A. Comparative advantage and opportunity costs B. A one-factor Ricardian model 1. Production possibilities 2. Relative prices, wages and supply C. Trade in a One-Factor World - Gains from trade D. Misconceptions about comparative advantage Cristina Vinyes Introduction Theories of why trade occurs: – Differences across countries in labor, labor skills, physical capital, natural resources, and technology – Economies of scale (larger scale of production is more efficient) Cristina Vinyes A. Comparative Advantage and Opportunity Cost The Ricardian model uses the concepts of opportunity cost and comparative advantage. The opportunity cost of producing something measures the cost of not being able to produce something else with the resources used. Cristina Vinyes A. Comparative Advantage and Opportunity Cost For example, a limited number of workers could produce either roses or computers. – The opportunity cost of producing computers is the amount of roses not produced. – The opportunity cost of producing roses is the amount of computers not produced. Cristina Vinyes  A. Comparative Advantage and Opportunity Cost Suppose that in the U.S. 1 million roses could be produced in 5 hours while a computer would require 10 hours. Suppose that in Colombia 1 million roses could be produced also in 5 hours but a computer requires 20 hours. Workers in Columbia would be less productive than those in the U.S. in manufacturing computers. Cristina Vinyes  A. Comparative Advantage and Opportunity Cost Opportunity Cost Mill Roses Computer USA 5/10= ½ comp 10/5= 2 roses Colombia 5/20= ¼ comp 20/5= 4 roses Colombia has a lower opportunity cost of producing roses. – Colombia gives up a smaller amount of computers than US to produce roses (¼ vs ½). US has a lower opportunity cost of producing computers. – US gives up a smaller amount of roses than Colombia to produce computers (2 vs 4). Cristina Vinyes A. Comparative Advantage and Opportunity Cost A country has a comparative advantage in producing a good if the opportunity cost of producing that good is lower in this country than in other countries. – The U.S. has a comparative advantage in computer production. – Colombia has a comparative advantage in rose production. Cristina Vinyes A. Comparative Advantage and Opportunity Cost Suppose Colombia produces rose and the U.S. produces computers, and that both countries want to consume computers and roses. Can both countries be made better off? Cristina Vinyes Hypothetical Changes in Production Mill Roses Computer USA -5h +10h Colombia +5h -20h Total 0h -10h When countries specialize in production in which they have a comparative advantage, more goods and services can be produced and consumed. – They could still consume the same 1million roses and 1 computer, but could consume some extra as now 10 hours are freed up. Cristina Vinyes A. Comparative Advantage and Opportunity Cost Unit labor Mill Computer requirements Roses USA 5h 10h Colombia 5h 20h ABSOLUTE ADVANTAGE USA has an absolute advantage on computer production since it takes less time to produce than computers than Colombia. No country has an absolute advantage on rose production as they take the same amount of time to produce roses. A country may have no Absolut advantage on any good, or have it on both goods, but a country can only and will always have a comparative advantage in producing one good. Cristina Vinyes Example Unit labor Wheat (lb) Beef (lb) requirement USA 20h 30h Argentina 100h 50h (a) Does either country have an absolute advantage in the production of wheat or beef? Explain. (b) What is the opportunity cost of wheat in each country? (c) What is the opportunity cost of beef in each country? (d) Analyze comparative advantage using the concept of opportunity cost for trade between the U.S. and Argentina. Cristina Vinyes B. A One-Factor Ricardian Model The simple example with roses and computers explains the intuition behind the Ricardian model. We formalize these ideas by constructing a one-factor Ricardian model using the following assumptions: Cristina Vinyes  B. A One-Factor Ricardian Model 1. Labor is the only factor of production. 2. Labor productivity varies across countries due to differences in technology, but labor productivity in each country is constant. 3. The supply of labor in each country is constant. Cristina Vinyes B. A One-Factor Ricardian Model 4. Two goods: wine and cheese. 5. All workers are skilled to produce either good and there is free movement of workers between sectors. 6. Competition allows workers to be paid a “competitive” wage equal to the value of what they produce, and allows them to work in the industry that pays the highest wage. 7. Two countries: home and foreign. Cristina Vinyes  B. A One-Factor Ricardian Model A unit labor requirement indicates the constant number of hours of labor required to produce one unit of output. – aLC is the unit labor requirement for cheese in the home country. For example, aLC = 1 means that 1 hour of labor produces one pound of cheese in the home country. – aLW is the unit labor requirement for wine in the home country. For example, aLW = 2 means that 2 hours of labor produces one gallon of wine in the home country. Unit labor Cheese Wine requirement (lb) (gal) Home 1h 2h A high unit labor requirement means low labor productivity. Cristina Vinyes  B. A One-Factor Ricardian Model Labor supply L indicates the total number of hours worked in the home country (a constant number). Cheese production QC indicates how many pounds of cheese are produced. Wine production QW indicates how many gallons of wine are produced. Cristina Vinyes  Production Possibilities The production possibility frontier (PPF) of an economy shows the maximum amount of a goods that can be produced for a fixed amount of resources. The production possibility frontier of the home economy is: aLCQC + aLWQW ≤ L Total amount of labor resources Total Labor required for Labor required for Total gallons pounds of each gallon of each pound of of wine cheese wine produced cheese produced produced produced Cristina Vinyes  B.1 Production Possibilities aLCQC + aLWQW ≤ L For example, suppose that the economy’s labor supply is 1,000 hours. The PPF equation aLCQC + aLWQW ≤ L becomes QC + 2QW ≤ 1,000. Maximum home cheese production is QC = L/aLC =1000/1= 1000 when QW = 0. Maximum home wine production is QW = L/aLW = 1000/2= 500 when QC = 0. Cristina Vinyes Fig. 3-1: Home’s Production Possibility Frontier Cristina Vinyes  B.1 Production Possibilities The opportunity cost of cheese is how many gallons of wine Home must stop producing in order to make one more pound of cheese: aLC /aLW =½ in our example. This cost is constant because the unit labor requirements are both constant. The opportunity cost of cheese appears as the absolute value of the slope of the PPF: │–(aLC /aLW )│=1/2. The PPF can be rearranged as an equation for a straight line (y=b+mx): QW = L/aLW – (aLC /aLW )QC Cristina Vinyes  B.1 Production Possibilities Producing an additional pound of cheese requires aLC hours of labor. Each hour devoted to cheese production could have been used instead to produce an amount of wine equal to 1 hour/(aLW hours/gallon of wine) = (1/aLW) gallons of wine This is the opportunity cost of cheese. Cristina Vinyes  B.1 Production Possibilities For example, if 1 hour of labor is moved to cheese production, that additional hour could have produced 1 hour/(2 hours/gallon of wine) = ½ gallon of wine. Unit labor requirement Cheese (lb) Wine (gal) Opportunity cost of Home 1h 2h producing one pound of Opp Cost cheese is ½ gallon of wine. Home ½ gal wine 2 Lb cheese Similarly, opportunity cost of producing 1 gal of wine is 2 lb of cheese. Cristina Vinyes B.2 Relative Prices, Wages, and Supply Let PC be the price of cheese and PW be the price of wine. Let wC be the wage paid to workers who make cheese and wW is the wage paid to workers who make wine. Due to competition & no profit assumption: – hourly wages of cheese makers equal the value of the cheese produced in an hour: PC WC = aLC – hourly wages of wine makers equal the value of the wine produced in an hour: PW WW = aLW Workers will choose to work in the industry that pays the higher wage. Cristina Vinyes B.2 Relative Prices, Wages, and Supply Here let’s show that it makes sense that the hourly wage of cheese makers is defined as PC WC = aLC Recall aLC = h/lb. & PC = $/lb. Then, when we do PC /aLC = $/lb.÷ h/lb = $/h which is the unit of a wage. Cristina Vinyes  B.2 Relative Prices, Wages, and Supply CASE 2: suppose PC = $3/lb. and PW = $7/gal – Wage paid producing 1 lb. of cheese is PC /aLC = ($3/lb.)(1 lb./hour) = $3/h = WC – Wage paid producing I gal. wine is PW /aLW = ($7/gal)(1/2 gal/h) = $3.50/h = WW Since WC < WW workers would be willing to make only wine since it pays a higher wage. The country would specialize in wine. Cristina Vinyes  B.2 Relative Prices, Wages, and Supply CASE 3: suppose PC = $3.5/lb. and PW = $7/gal – Wage paid producing 1 lb. of cheese is PC /aLC = ($3.5/lb.)(1 lb./hour) = $3.5/h = WC – Wage paid producing I gal. wine is PW /aLW = ($7/gal)(1/2 gal/h) = $3.50/h = WW Since WC = WW workers would be indifferent between producing wine or cheese. The country will produce both. Cristina Vinyes  B.2 Relative Prices, Wages, and Supply Having both wages be the same means WC = WW or what is the same: PC PW = , aLC aLW Rearranging the terms, we get: PC aLC = PW aLW This is saying that the relative price of cheese is equal to the relative unit labor requirement of cheese (or the opportunity cost of cheese). Cristina Vinyes  B.2 Relative Prices, Wages, and Supply Now, suppose the country does not trade internationally. This means: 1. Everything you want to consume you need to produce it yourself. 2. The country produces the good that pays the highest wage, so to produce both goods the country needs to pay the same on both sectors In the absence of international trade, WC = WW or alternatively PC PW = , aLC aLW So one can say that relative prices must adjust so that wages are equal in the wine and cheese industries (as a is constant). Cristina Vinyes  B.2 Relative Prices, Wages, and Supply In the absence of international trade: Relative prices of goods = Relative unit labor requirements PC aLC = PW aLW In our example then we can find the relative equilibrium price of cheese by setting it equal to the opportunity cost of cheese PC 1 = PW 2 Cristina Vinyes  C. Trade in a One-Factor World Now we add the foreign country. Their unit labor requirements are as follows: Unit labor Cheese Wine requirement (lb) (gal) Home 1h 2h Foreign 6h 3h Home then has an absolute advantage in the production of both goods as it takes less time to produce both than Foreign: its unit labor requirements for wine and cheese production are lower than those in the foreign country: ½ = aLC < a*LC and aLW < a*LW = 2 Still, only one country will have a comparative advantage in one good. Hence, it still can benefit from trade. where “*” notates foreign country variables. Cristina Vinyes  C. Trade in a One-Factor World Opportunity Cost Cheese Wine HOME ½ gal wine 2 lb cheese FOREIGN 6/3= 2 gal wine 3/6=½ lb cheese The home country has a comparative advantage in cheese production as its opportunity cost of producing cheese is lower than in the foreign country. aLC /aLW < a*LC /a*LW or ½ aLC /aLW Cristina Vinyes  C. Trade in a One-Factor World If countries open to trade, it will be profitable to ship cheese from Home to Foreign as moving from no trade to trade we start with cheese being relatively cheaper at home: P*C /P*W > PC /PW and will be profitable to ship wine from Foreign to Home, as it is relatively cheaper in the foreign country. Eventually, home will export enough cheese and foreign enough wine to make P*C /P*W = PC /PW Where does the relative price of cheese to wine settle? That is, what is the world equilibrium relative price of cheese with trade? Cristina Vinyes  C. Trade in a One-Factor World To understand how the world equilibrium relative prices are determined we would need to find the world relative supply and relative demand. The world relative supply of cheese: the quantity of cheese supplied by all countries relative to the quantity of wine supplied by all countries Q C + Q∗C RS = Q W + Q∗W Cristina Vinyes C.1 Relative price after trade Relative demand of cheese is the quantity of cheese demanded in all countries relative to the quantity of wine demanded in all countries. ∗ QC + QC R𝐷 = Q W + Q∗W In this case, RD has the same shape as a partial equilibrium demand function. This is because we assume that consumers in both countries have the same preferences. Cristina Vinyes C.2 Gains From Trade How can a country that has an absolute advantage in all production benefit from trade? Gains from trade come from specializing in the type of production which uses resources most efficiently, and using the income generated from that production to buy the goods and services that countries desire. where “using resources most efficiently” means producing a good in which a country has a comparative advantage. Cristina Vinyes C.2 Gains From Trade Domestic workers earn a higher income from cheese production because the relative price of cheese increases with trade. Foreign workers earn a higher income from wine production because the relative price of cheese decreases with trade (making cheese cheaper) and the relative price of wine increases with trade. Think of trade as an indirect method of production that converts cheese into wine or vice versa. Cristina Vinyes  C.2 Gains From Trade Without trade, a country has to allocate resources to produce all of the goods that it wants to consume. With trade, a country can specialize its production and exchange for the mix of goods that it wants to consume. With trade, consumption possibilities expand beyond the PPF. With trade, consumption in each country is expanded because world production is expanded when each country specializes in producing the good in which it has a comparative advantage. Cristina Vinyes Fig. 3-4: Trade Expands Consumption Possibilities Where PPFT,NT is the production possibility frontier when there is trade and no trade. The PPF does not change with trade as this is defined by the country’s resources, which have not changed with trade. CPFNT Is the consumption possibility frontier when there is no trade. In the absence of trade, this CPF is limited by how much the country can produce. CPFT Is the consumption possibility frontier with trade. When there is trade, the possibilities to consume expand by specialization. Cristina Vinyes Fig. 3-4: Trade Expands Consumption Possibilities Where PPF*T,NT is the production possibility frontier in the foreign country when there is trade and no trade. The PPF* also does not change with trade. CPF*NT Is the consumption possibility frontier in the foreign country when there is no trade. Again, in the absence of trade, this CPF* is limited by how much the country can produce. CPF*T Is the consumption possibility frontier with trade in the foreign country. When there is trade, the possibilities to consume also expand by specialization. Cristina Vinyes Fig. 3-4: Trade Expands Consumption Possibilities 1000 1000 CPFT CPF*T 500 PPF*T,NT PPFT,NT = CPF*NT = CPFNT 1000 500 1000 Cristina Vinyes Fig. 3-4: Trade Expands Consumption Possibilities Once they trade, they can specialize in the good they produce more efficiently. Home, can reserve all its resources to produce cheese, so the max it can produce is 1000lb. At the extreme, he could trade all the 1000lb for the maximum production of foreign’s wine, which is 1000gal. Thanks to trade, now home can consume 1000 gal of wine, which could have not produced by itself. Hence, the consumption possibilities have expanded (blue line). Cristina Vinyes  Fig. 3-4: Trade Expands Consumption Possibilities Similarly, once they trade. Foreign, can reserve all its resources to produce wine, so the max it can produce is 1000gal. At the extreme, he could trade all the 1000gal for the maximum production of home cheese, which is 1000lb. Thanks to trade, now foreign can consume 1000 lb. of cheese, which could have not produced by itself. Hence, the consumption possibilities have expanded too (blue line). Cristina Vinyes  D. Misconceptions About Comparative Advantage 1. Free trade is beneficial only if a country is more productive than foreign countries. – But even an unproductive country benefits from free trade by avoiding the high costs for goods that it would otherwise have to produce domestically. – High costs derive from inefficient use of resources. – The benefits of free trade do not depend on absolute advantage, rather they depend on comparative advantage: specializing in industries that use resources most efficiently. Cristina Vinyes  D. Misconceptions About Comparative Advantage 2. Free trade with countries that pay low wages hurts high wage countries. – While trade may reduce wages for some workers, thereby affecting the distribution of income within a country, trade benefits consumers and other workers. – Consumers benefit because they can purchase goods more cheaply. – Producers/workers benefit by earning a higher income in the industries that use resources more efficiently, allowing them to earn higher prices and wages. Cristina Vinyes