Chapter 4: Specific Factors Model

Slope of the PPF - Specific Factors Model

-MPLf / MPLc = -Pc /Pf The left side of this equation is the slope of the PPF at the actual production point. The right side is minus the relative price of cloth. The result tells us that at a production point, the PPF must be tangent to a line whose slope is minus the price of cloth divided by that of food. As we will see in following chapters, this is a very general result that characterized production responses to changes in relative prices along a PPF.

Three reasons why economists are in favor of free, or international trade despite negative income distribution effects?

1. Income distribution effects are not specific to international trade --> Every change in a nation's economy - including technological progress, shifting consumer preferences, exhaustion of old resources and discovery of new ones, and so on - affects income distribution. 2. It is always better to allow trade and compensate those are hurt by it than to prohibit the trade --> All modern industrial countries provide some sort of "safety net" of income support programs that can cushion the losses of groups hurt by trade. 3. Those who stand to lose from increased trade are typically better organized than those who stand to gain (bc the former are more concentrated within regions and industries) --> This imbalance created a bias in the political process that requires a counterweight, especially given the aggregate gains from trade.

Three points to note about the redistribution of the world's labor force?

1. It leads to a convergence of real wage rates --> Real wages rise in Home and fall in Foreign. 2. It increases the world's output as a whole --> Need to see changes to output by taking area under the MPL curve, even if one country's output increases, while the others decreases - the gain is larger than the loss. 3. Despite this gain, some people are hurt by the change --> Those who would have originally worked in Home receive higher real wages, but those who would have originally worked in Foreign receive lower real wages. Landowners in Foreign benefit from the larger labor supply, but landowners in Home are made worse off.

Do the gains from trade outweigh the losses?

A better way to assess the overall gains from trade is to ask a different question: Could those who gain from trade compensate those who lose and still be better off themselves? If so, then trade is potentially a source of gain to everyone. In order to show aggregate gains from trade, we need to state some basic relationship among prices, production, and consumption. In a country that cannot trade, the output of a good must equal its consumption. If Dc is consumption of cloth and Df is consumption of food, then in a closed economy Dc = Qc and Df = Qf. International trade makes it possible for the mix of cloth and food to differ from the mix produced --> While the amounts of each good that a country consumes and produced may differ, however, a country cannot spend more than it earns. The value of consumption must be equal to the value of production --> That is, Pc x Dc + Pf x Df = Pc x Qc + Pf x Qf.

Specific Factors Model

A realistic analysis of trade must go beyond the Ricardian model to models in which trade can affect income distribution. In this chapter, we focus on the short-run consequences of trade on the income distribution when factors cannot move without cost between sectors. To keep our model simple, we assume that the sector-switching cost for some factors is high enough that such a switch is impossible in the short run. Those factors are SPECIFIC to a particular sector.

General Principle on Specific Factors Model

Changes in the overall price level have no real effects, that is, do not change any physical quantities in the economy. Only changes in relative prices - which in this case means the price of cloth relative to the price of food, Pc/Pf - affect welfare or the allocation of resources.

A Change in Relative Price

Consider the effect of a price change that does affect relative prices. A 7% increase in the price of Pc --> The increase in Pc shifts the cloth labor demand curve in the same proportion as the price increase and shifts the equilibrium from point 1 to point 2. Two important facts: 1. First, although the wage rate rises, it rises by less than the increase in the price of cloth. If wages had risen in he same proportion as the price of cloth (7%), then wages would have risen from w1 to w2. Instead, wages rises by a smaller proportion. Second, when only Pc rises, in contrast to a simultaneous rise in Pc and Pf, labor shifts from the food sector to the cloth sector and the output of cloth rises while that of food falls. (This is why w does not rise as much as Pc, bc cloth employment rises, the marginal product of labor in that sector falls).

Pc x Dc + Pf x Df = Pc x Qc + Pf x Qf. This equation can be rearranged to yield the following: Df - Qf = (Pc/Pf) x (Qc - Dc)

Df - Qf is the economy's food imports, the amount by which its consumption of food exceeds its production. The right-hand side of the equation is the produce the relative price of cloth and the amount by which production of cloth exceeds consumption, that is the economy's exports of cloth. The equation, then, states that imports of food equal exports of cloth times the relative price of cloth. ***While it does not tell us how much the economy will import or export, the equation does show that the amount the economy can afford to import is limited, or constrained, by the amount it exports --> Therefore, it known as the budget constraint.***

What are the reasons why international trade has strong effects on the distribution of income?

First, resources cannot move immediately or without cost from industry to another - short-run consequence of trade. Second, industries differ in the factors of production they demand. A shift in the mix of goods a country produces will ordinarily reduce the demand for some factors of production, while raising the demand for others - a long-run consequence of trade. While trade may benefit a nation as a whole, it often hurts significant groups within the country in the short run, and potentially, but to a lesser extent, in the long run.

Labor Force Function

For the economy as a whole, the labor employed must be equal to the total labor supply, L. Lc + Lf = L.

International Trade in the Specific Factors Model

For trade to take place, a country must face a world relative price that differs from the relative price that would prevail in the absence of trade.

Prices, Wages, and Labor Allocation

How much labor is employed in each sector? To answer this, we need to look at supply and demand in the labor market. The demand for labor in each sector depends on the price of output and the wage rate. In turn, the wage rate depends on the combined demand for labor by food and cloth producers. Given the prices of cloth and food together with the wage rate, we can determine each sector's employment and output.

Equal Proportional Change in Prices - Specific Factors Model

If the prices of both good increase by 10 percent, the labor demand curves will also shift up by 10 percent. As you can see from the diagram, these shifts lead to a 10 percent increase in the wage rate from w1 to w2. However, the allocation of labor between the sectors and the outputs of the two goods does not change.

Labor Demand Curve - Specific Factors Model

If w is the wage rate of labor, employers will therefore hire workers up to the point where: MPLc x Pc = w.

Specific Factors Model - Assumptions

Imagine an economy that can produce TWO goods: 1. Cloth and 2. Food. The country has THREE factors of production: 1. Labor 2. Capital and 3. Land. Cloth is produced using capital and labor. Food is produced using land and labor. Labor is therefore a MOBILE factor that can be used in either sector, while land and capital are both SPECIFIC factors that can be used only in the production of one good.

Demand for Labor

In each sector, profit-maximizing employers will demand labor up to the point where the value produced by an additional person-hour equals the cost of employing that hour. In the cloth sector, for example, the value of an additional person-hour equals the cost of employing that hour. In the cloth sector, fore example, the value of an additional person hour is the marginal product of labor in cloth multiplied by the price of unit of cloth: MPLc x Pc.

Impact of Equal Proportional Change in Prices - Specific Factors Model

In fact, when Pc and Pf change in the same proportion, no real changes occur. The wage rate rises in the same proportion as the prices, so real wage rates, the ratios of the wage rate to the prices of goods, are unaffected. With the same amount of labor employed in each sector, receiving the same real wage rate, the real incomes of capital owners and landowners also remain the same. So everyone is in exactly the same position as before.

PPF - Difference between Ricardo and SFM

In the Ricardian model, where labor is the only factor of production, the PPF is a straight line bc the opportunity cost of cloth in terms of food is constant. In the specific factors model, however, the addition of other factors of production changes the shape of the PPF to a curve. The curvature of the PPF reflects diminishing returns to labor in each sector; these diminishing returns are the crucial difference between the specific factors and the Ricardian models.

International Labor Mobility

In the previous sections, we saw how workers move between the cloth and food sectors within one country until the wages in the two sectors are equalized. Whenever international migration is possible, workers will also want move from the low-wage to the high-wage country --> To keep things simple and to focus on international migration, let us assume that two countries produce a single good with labor and an immobile factor, land. Since there is only a single good, there is no reason to trade i; however, there will be "trade" in labor services when workers move in search of higher wages. In the absence of migration, wage difference across countries can be driven by technology differences, or alternatively, by difference in the availability of land relative to labor.

Wages - Specific Factors Model

In this model, wages in both sectors must be equal because labor is completely mobile - aka free to move between sectors. That is, because labor is a mobile factor, it will move from the low wage sector to the high wage sector until wages are equalized. The wage rate, in turn, is determined by the requirement that total labor demand equals total labor supply.

Ricardian Trade Model - Summary

International trade can be mutually beneficial to the nations engaged in it. The Ricardian model of international trade illustrates the potential benefits from trade. In that model, trade leads to international specialization, with each country shifting its labor force from industries in which that labor is relatively inefficient to industries in which it is relatively more efficient. Labor is the only factor of production, and it is assumed that labor can move freely from one industry to another, there is no possibility that individuals will be hurt by trade. The Ricardian model thus suggests not only that all countries gain from trade, but also that every individual is made better off as a result of trade, because trade does not affect the distribution of income. Issues with Ricardo: In the real world; however, trade has substantial effects on the income distribution within each trading nation, so that in practice the benefits of trade are often distributed very unevenly.

General Rule for Trade

When opening up to trade, and economy exports the good whose relative price has increased and imports the goods whose relative price has decreased.

Diminishing Returns

Labor is subject to diminishing returns: Adding a worker means that each worker has less capital to work with, each successive increment of labor will add less to production than the last. Diminishing returns are reflected in the shape of the production function - Qc(K, Lc) gets flatter as we move to the right, indicating that the marginal product of labor declines as more labor is used.

Specific Factors Model - Summary

Like the simple Ricardian model, it assumes an economy that produces two goods and that can allocate its labor supply between the two sectors. Unlike the Ricardian model, however, the speficic factors model allows for the existence of factors of production besides labor. Whereas labor is a mobile factor that can move between sectors, these other factors are assumed to be specific --> That is, they can be used only in the production of particular goods.

Labor Demand Curve - Specific Factors Model

MPLc x Pc = W MPLf x Pf = W Since the marginal product of labor slopes downward bc of diminishing returns, for any given price, the value of the marginal product of labor - MPL x P will also slope down. If the wage rate falls, other things equal, employers in the cloth sector will want to hire more workers.

Effect of the Changes in Relative Prices on the Distribution of Income

Need to look at the incomes of three groups: workers, owners of capital, and owners of land. Workers find that their wage rate in terms of cloth (the amount of cloth they can buy with their wage income), w/Pc falls. Meanwhile, their real wage in terms of food, w/Pf rises. Given this information, we cannot say whether workers are better or worse off; this depends on the relative importance of cloth and food in workers' consumption (determined by workers' preferences). Owners of capital, however, are definitely better off --> The real wage rate in terms of cloth has fallen, so the profits of capital owners in terms of what they produce (cloth) rises. That is, he income of capital owners will rise more than proportionately with the rise in Pc. Since Pc in turn rises relative to Pf, the income of capitalists clearly goes up in terms of both goods. Conversely, landowners are definitely worse off. They lose for two reasons: 1. The real wage in terms of food (the good they produce) rises, squeezing their income, and the rise in the cloth price reduces the purchasing power of any given income. If the relative price had moved in the opposite direction and the relative price of cloth had decreased, then the predictions would be reversed: Capital owners would be worse off, and landowners would be better off. The change in welfare of workers would again be ambiguous because their real wage in terms of cloth would rise, but their real wage in terms of food would fall.

Real Wage Rates

Ratios of the wage rate to the prices of goods.

Marginal Product of Labor

Slope of the production function, also the addition to output generated by adding one more person-hour. However, if labor input is increased without increasing capital, there will normally be diminishing returns. When you plot labor input (x axis) and MPL (y axis), get a downward sloping curve to showcase MPL. Area under the MPL showcases the output of a particular good.

PPF

The PPF shows what the economy is capable of producing; in this case, it shows how much food it can produce for any given output of cloth and vice versa.

Production Possibilities

The SFM model assumes that each of the specific factors, capital and land, can be used in only one sector, cloth and food. Only labor can be used in either sector. Thus, to analyze the economy's production possibilities, we need only to ask how the economy;s mix of output changes as labor is shifted from one sector to the other.

Production Function

The economy's output of cloth depends on how much capital and labor are used in that sector - this is summarized by a production function that tells us the quantity of cloth that can be produced given any input of capital and labor. Qc = Qc(K, Lc). Similarly, for food we can write the production function. Qf = Qf(T, Lf).

A Change in Relative Price - Effect on PPF

The effect of a rise in the relative price of cloth can also be seen directly by looking at the production possibility curve. The production point, which is always located where the slope of PP equals minus the relative price, shifts from 1 to 2. Food output falls and cloth output rises as a result of the rise in the relative price of cloth.

General Rules for Relative Price Change on Income Distribution - Specific Factors Model

The factor specific to the sector whose relative price increases is definitely better off. The factor specific to the sector whose relative price decreases is definitely worse off. The change in welfare for the mobile factor is ambiguous.

Why might the relative supply curve for the world be different from that for our specific factors economy?

The other countries in the world could have different technologies, as in the Ricardian model. Now that our model has more than one factor of production, however, the other countries could also differ in their resources: the total amounts of land, capital, and labor available. What is important here is that the economy faces a different relative price when it is open to international trade.

Relationship Between Labor Input and Output of Cloth

The production function is an upward sloping curve. The larger the input of labor for a given capital supply, the larger the output. The slope of the production is the MARGINAL PRODUCT OF LABOR.

Slope of PPF - Specific Factors Model

The slope of the PPF, which measures the opportunity cost of cloth in terms of food - that is, the number of units of food output that must be sacrificed to increase cloth output by one unit - is therefore: Slope of Production Possibilities Curve = =MPLf/MPLc. As more and more labor is moved to the cloth sector, each additional unit of labor becomes less valuable in the cloth sector and more valuable in the food sector: The opportunity cost (foregone food production) of each additional cloth unit rises, and PP thus gets steeper as we move down it to the right.

Production Possibilities - Two Graphs

This can be done graphically, first by representing the production functions and then by putting them together to derive the PPF.

Income Distribution and Gains From Trade - Who wins and loses?

To assess the effects of trade on particular goods, the key point is that international trade shifts the relative price of the goods traded. In the example given, we saw that opening to trade will increase the relative price of the good in the new export sector. More specifically, we saw that the specific factor in the sector whose relative price increases will gain and that the specific factor in the other sector (whose relative price decreases) will lose. We also saw that the welfare changes for the mobile factor are ambiguous. Trade benefits the factor specific to the export sector of each country but hurts the factor specific to the import-competing sectors, with ambiguous effects on mobile factors.

Why is trade a potential source of gain for everyone?

Trade allows for consumption to be different from production. A trading economy is able to consume more of both goods than it would have in the absence of trade. ***The fundamental reason why trade potentially benefits a country is that it expands the economy's choices --> This expansion of choice means that is always possible to redistribute income in such a way that everyone gains from trade.*** That everyone could gain from trade unfortunately does not mean that everyone actually does. In the real world, the presence of losers as well as winners from trade is one of the most important reasons why trade is not free.

The Political Economy of Trade: A Preliminary View

Trade often produces losers as well as winners --> This insight is crucial to understanding the considerations that actually determine trade policy in the modern world economy. Our specific factors model informs us that those who stand to lose the most from trade (at least in the short run) are the immobile factors in the import-competing sector. In the real world, this includes not only the owners of capital but also a portion of the labor force in those import-competing sectors --> Some of these workers (especially lower-skilled workers) have a hard time transitioning from the import-competing sectors (where trade induces reductions in employment) to export sectors (where trade induces increases in employment). In the US, workers in the import-competing sectors earn wages substantially lower than the average wage.

Budget Constraint for Trade

Two important features of the budget constraint for a trading economy: 1. First, the slope of the budget constraint is minus Pc/Pf, the relative price of cloth. The reason is that consuming one less unit of cloth saves the economy Pc/Pf, this is enough to purchase Pc/Pf extra units of food. In other words, one unit of cloth can be exchanged on world markers for Pc/Pf units of food. 2. The budget constraint is tangent to the PPF at the chosen production point --> Thus, the economy can always afford to consume what it produces.

Effect of the Changes in Relative Prices on the Distribution of Income

We have already noted that the demand curve for labor in the cloth sector will shift upward in proportion to the rise in Pc, so that if Pc rises by 7 percent, the curve defined by Pc x MPLc also rises by 7 percent. We have also seen that unless the price of food also rises by 7%, w will rise by less than Pc --> Thus, if only cloth prices rise by 7 percent, we would expect the wage rate to rise by only, say, 3%.

International Trade in the Specific Factors Model - Continued

When the economy is open to trade, the relative price of cloth is determined by the relative supply and demand for the world; this corresponds to the relative price (Pc/Pf)^2. If the economy could not trade, then the relative price would be lower, at (Pc/Pf)^1. The increase in the relative price of cloth induced the economy to produce relatively more cloth. At the same time, consumers respond to the higher relative price of cloth by demanding relatively more food. At the higher relative price of food, the economy thus exports cloth and imports food. If the opening up to trade had been associated with a decrease in the relative price of cloth, then the changes in relative supply and demand would be reversed, and the economy would become a food exporter and a cloth importer.

PPF - Specific Factors Model

With food (y) and cloth (x), if we shift one=person hour of labor from food to cloth, however, this extra input will increase output in that sector by the MPL of cloth. To increase cloth output by one unit then, we mist increase labor input by 1/MPLc. Meanwhile, each unit of labor input shifted out of food production will lower output in that sector by MPL of food. To increase output of cloth by one unit, then, the economy must reduce the ourpur of food by MPLf/ MPLc.