Chapter 1: The Ricardo Model The main question of the Ricardo model is why should countries trade? There are some countries that are better in producing a lot of goods compared to other countries. Imagine a country that produce two goods: wine and cars. This country is more productive than anywhere else in the world. Should this country trade with the rest of the world? Apparently, the simplest answer would be the negative. Why a country should stop producing a good to import it from elsewhere if this country is more productive in producing itself the good? At first sight this answer seems correct, but let's take another example. Suppose that you want to prepare a breakfast to somebody and your little brother or sister is there to help you. You are better in doing everything. Cooking eggs, setting the table, making cakes. But do you really think that this means that your little brother or sister cannot do something? Even if he or she is worst in everything, maybe he can do a task relatively best compared to you. He might be relatively best in setting the table compared to cooking eggs compared to you. The same reasoning holds for countries. Some countries may be better in producing some goods because there might exist different technology and resources (more productive workers and new technology) and because there might exists economies of scale that gives a cost advantage to large firms. The main message of the Ricardo model is the following. If each country exports the good in which it has a comparative advantage then all countries can gain from trade. Even if the country has an absolute advantage 1 (he is better in doing everything), the country should trade because there always exists a comparative advantage. A country has a comparative advantage in a good if it can produce that good at a lower relative opportunity cost. Opportunity costs measure the number of good that a country has to forego to obtain one unit of the other good. 1- The principle of comparative advantage. The Ricardo model relies on four main assumptions. (i) labor is mobile within countries but immobile between countries. (ii) industries produce with constant return to scale. Doubling the quantity of inputs will exactly double the quantity of output. (iii) The model is under pure and perfect competition. Firms are price takers. (iv) There are no trade imbalances. Exports bay back for all imports. Let's go back to our first example. Assume two countries. The United-States () and (EU) that produce two goods. Wine and cars. Here is a an example of a typical Ricardian table. It reports the labor productivity in each countries. It reports the number of good produced by one worker in a given period of time. Labor productivity: units of output per worker Wine 6 1 Cars 4 2 1 Absolute advantage refers to the ability of a country to produce more number of goods compared to its competitor.
The question you need to ask when looking at this table is "which country should export wine and which country should export cars". To answer this question we need to analyze absolute and comparative advantage. It is easy to see that has an absolute advantage in the production of wine (one worker in can produce 6 gallons of wine against only 1 in the ). has also an absolute advantage in the production of cars (one worker in can produce 4 cars against 2 in the ). A lot of people would say that should produce both goods and export it to the. However, it is important to recall that trade is balanced in the Ricardo model. should export back to. In order to understand which good can be shipped back by the we need to analyze comparative advantage. The analysis of comparative advantage is based on the opportunity cost. We have defined earlier the concept of opportunity cost. It is now easy to calculate it for each country. Let's describe the opportunity cost of wine in. How many cars do needs to sacrifice to obtain one gallon of wine? If you move one worker out of the car sector to go in the wine sector. The output of car would go down by 4 and the output of wine would go up by 6. The opportunity cost of wine in is defined by =4/6=0.66. With corresponding to the output of cars. You can repeat this operation for every country and goods and you will obtain the following table of opportunity cost. Opportunity cost Wine 0.66 2 Cars 1.5 0.5 The wine sector has a lowest opportunity cost than the car sector in (0.662) and has a lowest opportunity cost in the car sector than in the wine sector (0.51.5). should specialize in cars and in wine. The comparative advantage of one country can also be determined by looking at relative productivity. Relative productivity compares the productivity in each sector. Here is the table of relative productivity. Relative productivity Wine (6/1=6) (1/6=0.17) Cars (2/1=2) (1/2=0.5) is relatively more productive in the production of cars (0.5>0.17) and EU is relatively more productive in the production of wine (6>2). should specialize in the production of cars. It is also possible to analyze comparative advantage by looking at unitary cost rather than labor productivity. It is very easy to derive unitary cost from the labor productivity table by doing a
cross product. Take the example of wine. One worker in can produce 6 gallons of wine, so you need 1/6 unit of labor to produce 1 gallon of wine in. Repeat this operation for every goods in each country and you will obtain the following table of unitary cost. Unitary Cost Wine 1/6=0.17 (= ) 1/1=1 Cars 1/4=0.25 1/2=0.5 The opportunity cost in that case are the relative costs. For example the opportunity cost of wine is the relative cost of wine in terms of cars. The opportunity cost of wine in is defined by =0.17/0.25=0.66. With the unit labor requirement of wine. Let's repeat this operation for each goods and we obtain the same table as previously for the different opportunity costs. Opportunity cost Wine 0.66 2 Cars 1.5 0.5 2- How does specialization work? Under pure and perfect competition there is only one wage rate in each country in both sectors. To see that assumption, suppose the opposite. Wage is higher in one industry compared to the other. All workers in the second industry would like quit their jobs in the low-paying industry, go to the high-paying industry and only one wage rate would prevail. This result is obtained because we assume full-employment and perfect mobility between sectors in the Ricardo model. When trade is allowed, firms in one industry will try to expand to reach other consumer and all the firms are going to think in the same way. Recall that we are at full-employment and the only way for firms to expand is by getting more resources out of one sector to go in the other. So what can firm do? Firms can raise wage to attract workers. Who is going to be in a better position to do it? The answer is firms that are best capable to bid up wages. Representative firms in the comparative advantage sector are better able to rise wage because firms in the disadvantage sector would lose their absolute advantage by increasing too much wage. According to the Ricardo model, this mechanism will transfer workers from one sector to another and would lead to full specialization. What does full specialization imply for output? will fully specialize in the production of wine and will fully specialize in the production of cars. The implications of this specialization on output is given in the following table.
Output after full specialization A Wine 6+6=12 1-1=0 Car 4-4=0 2+2=4 If takes one worker out of the car sector to put in the wine sector then the output of wine will go up by 6 and the output of cars will go down by 4. The same reasoning holds for A. To summarize, before free trade the world output of wine (output of wine in and in the ) =7, the world output of cars =6. After free trade the total output of wine is 12 and the total output of cars is 4. In reality, consumers may not be happy with having so many wine and few cars. In reality, a firm's competitive position is not only determined by comparative advantage. Some firms can have a brand name or a good market position so they can survive even in the disadvantage sector. In reality, world can end up with incomplete specialization. Let's assume that the world doesn't want so much wine and just want to increase the amount of wine by as much as the has decreased it. only needs to produce one more gallon of wine. How many car does has to stop produce by taking one worker out of the car sector to produce one more gallon of wine? The answer is given by the opportunity cost. We know that the opportunity cost of wine in terms of car is equal to 0.66. A country has to renounce to 0.66 units of car to produce one gallon of wine. So the total output with incomplete specialization is given by the following table. Output after incomplete specialization Wine 6+1=7 1-1=0 Car 4-0.66=3.44 2+2=4 The world has now 7.44 cars and 7 gallons of wine which is better than the situation under autarky. 3- The price of exchange in the Ricardo model In autarky, every products i are sell at the same price Pi in every country. The world ends up with 3 prices: in the wine sector in the, in the car sector in the, in the wine sector in and in the car sector in. Under pure and perfect competition, no firms can bargain over price, each firm choose the optimal level of quantity produced in order to maximize profit. The profit is maximized when price is equal to marginal cost: P=MC. The marginal cost is the cost of the last unit of output. We know from Table on unit input requirement that to produce one gallon of wine you need unit of labor in the. So the marginal cost of wine in the is =.. The price of wine in
the is thus equal to =.. It is now easy to know the price of each good in each country. In the the price of wine and cars is =. and =.. In the price of wine and cars is =. and =.. The relative price in the is then = and the relative price in is = With free trade there is only one price that holds. Simply put, the law of one price states that every product i sells at the price Pi in every country. All final products sell at the same price worldwide. What is the world price of each good after free trade. We know from the previous analysis that may specialize in the production of cars while should specialize in the production of wine. The relative price of wine in terms of cars should be higher than the relative cost of wine in terms of cars in if wants to specialize in wine while the relative price of cars in terms of wine should be lower than the relative cost of wine in terms of cars in the if wants to specialize in cars. The relative price must be in-between these two limits if the world has to end up with full specialization. It is the only way to create incentives for country to specialize. With the relative world price of wine in terms of cars. Suppose the world price ratio were either above the opportunity cost in the then everyone in the world would produce wine, leaving consumers without one of the two goods. That cannot be an equilibrium. 4- Wage under free trade There is only one wage rate in each economy. w is the wage rate of the and w* is the wage rate of the EU. Section 2 has shown that the wage rate in each country must change in order to attract workers in the comparative advantage sector. What will be the wage ratio after free trade? The relative wage has to be in-between the countries' relative productivity. If the country's relative wage is higher than what it does most productively compared to other countries, it would price itself out of the market and nobody would buy any product in that country. Reversely, if the relative wage were to be lower than what it does worst, everybody would want to buy any product in that country. In order to define the equilibrium wage after free trade, we need to define relative productivities. We know that the relative productivity of labor in the EU compared to the in the wine sector is higher than the relative productivity of labor in the EU compared to the in the car sector. If you look at the relative productivity Table. The relative productivity of labor in the EU compared to the in the wine sector is 6, while the relative productivity of labor in the EU compared to the in the car sector is 2. We have:!"# $ %& $& '& $ ()!"# $ %& $& '& $ )* >!"# $ %& " '& $ ()!"# $ %& " '& $ )*
Let's right, the productivity of labor (units of output per worker). EU has an asterisk while the has no asterisk. The relative wage of the EU compared to the cannot be higher than what it does most productively, otherwise nobody would buy wine and cars in the EU.,, > () )* Conversely, the relative wage of the compared to the EU cannot be higher than what it does most productively, otherwise nobody would buy wine and cars in the.,, > )* () The relative wage -. /- has to be in-between these two limits in order to have trade between the two economic partners.,, )* (),, Let's measure the relative wage and the relative price with the Ricardian Table of this lecture. We have already measured the relative productivity. Relative productivity Wine Cars 0 0 =6/1=6 0 0 2/1=2 0 0 =1/6=0.17 0 0 =1/2=0.5 The relative wage after free trade has to be in-between these two limits. 0.17 )* () 0.5 From section 3 and 4, we are now able to determine the equilibrium in autarky and with freetrade. a- Equilibrium wage and price in autarky Let's start with the equilibrium in autarky. Recall that there is one wage rate in and one wage rate in the United-States. We have seen in section 3 that the price is equal to the marginal cost. In the price of cars is =. () and the price of wine is =. (). We can use these two equations to determine the wage in. () =. Similarly we can measure the hourly wage in the. )* = = =. We can use the values in the Table of
unitary cost to derive the autarkic equilibrium wage in the and in EU. () = 4.56 =1.5 and )* = 4.6 7 =0.5. Now let's measure the prices in autarky. Recall that there are four different prices when trade is not allowed. Consumers cannot buy any product from abroad so they have to face the equilibrium price of each good in their country. The equilibrium price in autarky has been measured in section 3. We already know that the price of wine in is equal to the marginal cost =. (), the marginal price of cars in that is equal to =. (), the price of wine in the that is equal to =. )* and the marginal price of cars in the that is equal to =. )*. We can easily measure the four equilibrium prices in autarky by replacing the unit labor requirement by their value and the equilibrium wage by the values we calculated. The prices of each good in are =1.5 0.17=0.255 and =1.5 0.25=0.375. The prices of each good in the are =0.5 1=0.5 and =0.5 0.5=0.25 Price under autarky A Wine 0.255 0.5 Cars 0.375 0.25 4.78 b- Equilibrium wage and price under free-trade Under free trade, two conditions must hold to have full specialization:,, )* (),, 0.17 )* () 0.5 0.17 0.25 1 0.5 0.66 2 Let's assume that the equilibrium wage established at -. /- =0.35. We can assume that )* = 0.35 and () =1. What are the equilibrium prices under free trade? The following table reports the different prices with a relative wage of 0.35. Price after free trade Wine =. () =0.17 1=0.17 1*0.35=0.35 Cars 0.25*1=0.25 0.5*0.35=0.175 The law of one price implies that every product i sells at the same world price Pi in every country. Consumers will buy wine in because the price of wine is lower than in the (0.170.35) and buy cars in the because the price is lower than in the EU (0.1750.25). After free trade, specializes in the production of wine and the in the production of cars.
5- Which country specializes? Another way to analyze specialization is graphically. An economy's production possibilities plays a crucial role in determining its comparative advantage. The production possibility frontier (PPF) determines all the combination of production that are technically possible in an economy given the economy's total resources. In other word, the production possibility frontier shows the maximum amount of one good that an economy can produce for any given amount of the other good produced. can produce cars or wine or a mix of the two. Similarly, can produce cars or wine, or a mix of the two. How do we arrive at the economy's production possibility frontier? The PPF is delimited by the maximum amount of labor available in an economy such as. +. =>? @A BC DhF GH) + =>? @A BC DhF IG) where is the unit labor requirement in the. Qc is the amount of cars produced in the and is the total employment needed to produce Qc units of cars in the. We need to rewrite these equations so they can fit in a graph with Qc on the vertical axis and Qw in the horizontal axis. In the the PPF can be written as follows = J?. You can do the same for. corresponds to the slope of the PPF and J? the intercept. Does the slope remind you of something? It corresponds to the opportunity cost of wine. How many cars do I need to sacrifice to obtain one more gallon of wine. The slope of the PPF is then extremely important to analyze comparative advantage. The slope of the PPF will always corresponds to the opportunity cost of the product in the horizontal axis in terms of the product in the vertical axis. How can we draw the PPF? We need to define the maximum amount of cars produced (when the quantity of wine is set to zero) and the maximum amount of wine produced (when the quantity of cars is set to zero). The maximum amount of cars produced when Qw=0 is J? and the maximum amount of wine produced when Qc=0 is J?. The PPF joins the these two points such as illustrated in the following Figure. As you move along the PPF you can map out all the possible combinations of cars output and wine output. Of course, the economy can also make any combination of cars and wine below the PPF, but that would not be efficient. Any combination above the PPF is impossible because the economy hasn't enough resources of labor > to produce more than the PPF constraint.
>? PPF EU 1 PPF >? We can easily observe that the opportunity cost of wine is lower in the EU because the slope is flatter. The resulting trade pattern is clear: EU completely specializes in wine and the in the production of cars. How can we graphically determine the specialization of each country after free-trade? We need to know the slope of the international trade line, which corresponds to the slope of the demand curve with the new prices after free-trade. The demand curve is determined by the following relation: L = + with and the new prices after free-trade. We can rewrite this equation in order to draw in a plan with Qc on the vertical axis and Qw on the horizontal axis. = L The slope of the international trade line is. Once there is a tangency with the PPF and the international trade line, the use of factors of production is maximized. All consumers can afford to buy the production. 6- How much will be traded? The quantity of exports and imports depends on consumer preferences. So we need to specify some types of global consumer preferences. As consumers grow richer and richer, it is rational for them to chose combinations of the two products that lie further on the right. To make matters simple, let's assume that consumers purchase fixed proportions of the goods. If they consume 20 gallons of wine per car initially, they will consume 40 gallons of wine per two cars if their budget doubles. These preferences means that the product combinations that consumers choose all sit on a ray emanating from the origin of the graph.
It is easy to see that there are differences between what is produced and consumed (Please refer to explanations given in class). How can consumer in each country continue to consume both cars and wine? The answer is simple by exporting the good that is not produced in their country. The patterns of trade are given as follows. We can easily see from theses two graphs that consumer can consume more of the two goods, so there is a trade surplus that is measured by the green area as illustrated in the previous graph. The gains from trade for each economy are represented by all of the product combinations that are better than the closed-economy combination. The newly affordable combinations are represented by any point on or below the country's international trade line and above the country's PPF. Note that the green triangles are conservative measures of the gains from trade. For microeconomists, with realistic preferences that have smooth instead of kinked indifference curves, the gains from
trade areas are larger than the triangles. But recall that we have made the hypothesis that goods are complementary goods (consumers want to double the quantity of gallons of wine if they double the quantity of cars). For now we won't concern ourselves with precise measures of the actual gains from trade. We just note that they are positive measure for both economies. The following section will give a detailed analysis of the gain from trade. II- Detailed Analysis of Surplus. Under autarky, we have seen that the price of wine is higher in the than in and the price of cars is lower in the than in. The supply and demand functions in the wine sector for both country under autarky are illustrated as follows. You can do the same graphs in the car sector. Once we have free trade what will be the export supply and the import demand in each country. First, assume that the price in autarky is the same than the price with free trade. What will be the amount of goods exported? There is nothing available. The demand at home will not change so there won't be any excess supply to export.
Second, assume that now the price in autarky is lower than the price with free trade ( ). What will be the amount of goods exported? The demand at home will go down because consumers are not willing to pay a higher price after free trade. Producer are willing to export goods in order to sell them at a higher price on the world market. There will be an excess supply at home and the country can start exporting. This story is illustrated by the following figure. Export supply M Domestic market in the Exports in the World market On the world market, the export supply curve goes up as the world market price goes up. In other words, the quantity of exports come from two sources. An increase in the supply of good in the domestic market and a decrease in the demand of good in the domestic market. You can do the same graph for the other market in the and for. Third, assume that now the price in autarky is higher than the world price with free trade ( ). Firms supply less and consumers demand more in the domestic country and we now have an excess demand that will raise the import demand from the other country. S M D Domestic market in the Imports in the World market We can combine these two graphs to obtain the quantity exported and imported in both countries in the wine market after free trade with the Ricardian Table of this lecture.
Imports/Exports A The quantity traded is exported by and imported by the in the wine sector. You can do exactly the same analysis in the car sector. From this graph, you must be able to analyze change in consumer and producers surplus in and in the United States as detailed during the lecture.