Question

1. (Specific Factor Model, Chapter 3) In the "simple" version of the specific factor model, there are two sectors (goods), one factor (labor) that is perfectly mobile between the two sectors, and one fixed - or specific - factor in each sector. To be concrete, suppose the two goods are food and clothing, the specific factor in food is "land" - represented by "T", and the specific factor in clothing is "capital", represented by "K'. The production functions for each sector are given by:

$$ C=\lambda(K)^{\sqrt{2}}\left(L_{c}\right)^{\gamma / 2} ; \quad F=\theta(T)^{1 / 2}\left(L_{j}\right)^{1 / 2} ; \quad \theta>0 ; \text { resource constraint: } L_{c}+L_{j}=L $$

where \(C, F\) are the outputs of clothing and food, \(L_{e}, L_{f}\) are labor employed in clothing and food, respectively, and " \(L^{\prime \prime}\) is the total available labor available in the economy, " \(\theta "\) and " \(\lambda\) "are productivity factors, so an increase in \(\theta\) (in \(\lambda\) ) represents an increase in productivity in food (clothing) production.

b) Consider a market economy with labor mobility so that wages are equalized across the two sectors. Let \(P_{c}, P_{f}\) represent output prices and \(W\) the wage rate. Labor demand in each sector comes from profit maximiziation - which entails equating the marginal value product of labor to the wage:

i Given output prices, show graphically how the equilibrium wage rate and the allocation of labor between the two sectors is determined.

ii Using the production functions, show mathematically how the equilibrium wage rate and the supply curve for each good \((C, F)\) is determined (as a function of output prices). Also, discuss how the returns to land and capital are determined.

iii Using your result in part ii, given output prices, show how an increase in the amount of capital (K) available for production affects: (1)the quantity supplied of each good; (2)the real return to capital; \((3)\) the real return to land; and \((4)\) the real wage rate.

iv Given output prices, show how an increase in food productivity \(\left({ }^{*} \theta^{\prime \prime}\right)\) affects the supply (output) of each good and the real return to each input.

v Given output prices, what happens to the supply of each good, and the real return to each factor, if productivity in both sectors (i.e., \(\lambda\) and \(\theta\) ) doubles?

Answer 1

1)   

The specific factor (SF) model was originally discussed by Jacob Viner and it is a variant of the Ricardian model. Hence the model is sometimes referred to as the Ricardo-Viner model. The model was later developed and formalized mathematically by Ronald Jones (1971) and Michael Mussa (1974). Jones referred to it as the 2 good-3 factor model. Mussa developed a simple graphical depiction of the equilibrium which can be used to portray some of the model results. It is this view that is presented in most textbooks.

The model's name refers to its distinguishing feature; that one factor of production is assumed to be "specific" to a particular industry. A specific factor is one which is stuck in an industry or is immobile between industries in response to changes in market conditions. A factor may be immobile between industries for a number of reasons. Some factors may be specifically designed (in the case of capital) or specifically trained (in the case of labor) for use in a particular production process. In these cases it may be impossible, or at least difficult or costly, to move these factors across industries. See Sections 70-1 and 70-2 for more detailed reasons for factor immobility.

The specific factor model is designed to demonstrate the effects of trade in an economy in which one factor of production is specific to an industry. The most interesting results pertain to the changes in the distribution of income that would arise as a country moves to free trade.

Basic Assumptions

The specific factor model assumes that an economy produces two goods using two factors of production, capital and labor, in a perfectly competitive market. One of the two factors of production, typically capital, is assumed to be specific to a particular industry. That is, it is completely immobile. The second factor, labor, is assumed to be freely and costlessly mobile between the two industries. Because capital is immobile, one could assume that the capital in the two industries are different, or differentiated, and thus are not substitutable in production. Under this interpretation, it makes sense to imagine that there are really three factors of production: labor, specific capital in industry one, and specific capital in industry two.

These assumptions place the specific factor model squarely between an immobile factor model and the Heckscher-Ohlin model. In an immobile factor model, all of the factors of production are specific to an industry and cannot be moved. In a Heckscher-Ohlin model, both factors are assumed to be freely mobile; that is, neither factor is specific to an industry. Since the mobility of factors in response to any economic change is likely to rise over time, we can interpret the immobile factor model results as short-run effects, the specific factor model results as medium-run effects and the Heckscher-Ohlin model results as long-run effects.

Production of good one requires the input of labor and industry-one specific capital. Production of good two requires labor and industry-two specific capital. There is a fixed endowment of sector-specific capital in each industry as well as a fixed endowment of labor. Full employment of labor is assumed, which implies that the sum of the labor used in each industry equals the labor endowment. Full employment of sector-specific capital is also assumed, however, in this case the sum of the capital used in all of the firms within the industry must equal the endowment of sector-specific capital.

The model assumes that firms choose an output level to maximize profit, taking prices and wages as given. The equilibrium condition will have firms choosing an output level, and hence labor usage level, such that the market determined wage is equal to the value of the marginal product of the last unit of labor. The value of the marginal product is the increment to revenue that a firm will obtain by adding another unit of labor to its production process. It is found as the product of the price of the good in the market and the marginal product of labor. Production is assumed to display diminishing returns because the fixed stock of capital means that each additional worker has less capital to work with in production. This means that each additional unit of labor will add a smaller increment to output, and since the output price is fixed, the value of the marginal product declines as labor usage rises. When all firms behave in this way, the allocation of labor between the two industries is uniquely determined.

The production possibilities frontier will exhibit increasing opportunity costs. This is because expansion of one industry is possible by transferring labor out of the other industry, which must therefore contract. Due to the diminishing returns to labor, each additional unit of labor switched will have a smaller effect on the expanding industry and a larger effect on the contracting industry. This means that the graph of the PPF in the specific factor model will look similar to the PPF in the variable proportion Heckscher-Ohlin model. However, in relation to a model in which both factors were freely mobile, the specific factor model PPF will lie on the interior. This is because the lack of mobility by one factor, inhibits firms from taking full advantage of efficiency improvements that can arise when both factors can be freely reallocated.

Specific Factor Model Results

The specific factor model is used to demonstrate the effects of economic changes on labor allocation, output levels and factor returns. Many types of economic changes can be considered including a movement to free trade, the implementation of a tariff or quota, growth of the labor or capital endowment, or technological changes. This section will focus on effects that result from a change in prices. In an international trade context, prices might change when a country liberalizes trade or when it puts into place additional barriers to trade.

When the model is placed into an international trade context, differences between countries, of some sort, are needed to induce trade. The standard approach is to assume that countries differ in the amounts of the specific factors used in each industry relative to the total amount of labor. This would be sufficient to cause the PPFs in the two countries to differ and could potentially generate trade. Under this assumption the specific factor model is a simple variant of the Heckscher-Ohlin model. However, the results of the model are not sensitive to this assumption. Trade may arise due to differences in endowments, differences in technology, differences in demands or some combination. The results derive as long as there is a price change, for whatever reason.

So suppose, in a two-good specific factor model, that the price of one good rises. If the price change is the result of trade liberalization, then the industry whose price rises is the export sector. The price increase would set off the following series of adjustments. First, higher export prices would initially raise profits in the export sector since wages and rents may take time to adjust. The value of the marginal product in exports would rise above the current wage and that will induce the firms to hire more workers and expand output. However, to induce the movement of labor, the export firms will have to raise the wage that they pay. Since all labor is alike (the model assumes labor is homogeneous) the import-competing sector will have to raise their wages in step so as not to lose all of its workers. The higher wages will induce the expansion of output in the export sector (the sector whose price rises) and a reduction in output in the import-competing sector. The adjustment will continue until the wage rises to a level that equalizes the value of marginal product in both industries.

The return to capital, in response to the price change, will vary across industries. In the import-competing industry, lower revenues and higher wages will combine to reduce the return to capital in that sector. However, in the export sector, greater output and higher prices will combine to raise the return to capital in that sector.

The real effects of the price change on wages and rents is somewhat more difficult to explain but is decidedly more important. Remember that absolute increases in the wage, or the rental rate on capital, does not guarantee that the recipient of that income is better-off, since the price of one of the goods is also rising. Thus, the more relevant variables to consider are the real returns to capital (real rents) in each industry and the real return to labor (real wages).

Ronald Jones (1971) derived a magnification effect for prices in the specific factor model which demonstrated the effects on the real returns to capital and labor in response to changes in output prices. In the case of an increase in the price of an export good, and the decrease in the price of an import good, as when a country moves to free trade, the magnification effect predicts the following impacts,

1) the real return to capital in the export industry will rise with respect to purchases of both exports and imports,

2) the real return to capital in the import-competing industry will fall with respect to purchases of both exports and imports,

3) the real wage to workers in both industries will rise with respect to purchases of the import good and will fall with respect to purchases of the export good.

This result means that when a factor of production, like capital, is immobile between industries, a movement to free trade will cause a redistribution of income. Some individuals, owners of capital in the export industry, will benefit from free trade. Other individuals, owners of capital in the import-competing industries, will lose from free trade. Workers, who are freely mobile between industries may gain or may lose since the real wage in terms of exports rises while the real wage in terms of imports falls. If workers preferences vary, then those individuals who have a relatively high demand for the export good will suffer a welfare loss, while those individuals who have a relatively strong demand for imports will experience a welfare gain.

Notice that the clear winners and losers in this model are distinguishable by industry. As in the immobile factor model, the factor specific to the export industry benefits while the factor specific to the import-competing industry loses.

B) Labor mobility refers to the ease with which laborers are able to move around within an economy and between different economies. It is an important factor in the study of economics because it looks at how labor, one of the major factors of production, affects growth and production.

There are two primary types of labor mobility: geographic and occupational. Geographic mobility refers to a worker's ability to work in a particular physical location, while occupational mobility refers to a worker's ability to change job types. For example, a worker moving from the United States to France illustrates the concept of geographic mobility. An automobile mechanic who changes jobs to become an airline pilot reflects the concept of occupational mobility.

From a policymaker's perspective, geographic mobility can have important implications on the economy of a particular country. This is because easing immigration requirements can do several things:

• Increase the supply of labor. As more workers enter the economy, the general labor supply increases. An increase in labor supply accompanied by a static labor demand can decrease wage rates.
• Increase unemployment. Unless employers demand more workers, an increase in labor supply could lead to a glut in labor. This means more workers are available than jobs.
• Increase productivity. Not all laborers added to the labor supply will be unskilled. An influx in laborers can increase productivity if they bring specialized skills to the workplace, and they might push out existing employees who are less productive.

ECONOMICS  MACROECONOMICS

The Economics of Labor Mobility

• FACEBOOK
• TWITTER
• LINKEDIN

By BRENT RADCLIFFE

Updated Jun 25, 2019

Have you ever imagined what life would be like in another job or working in another country? It wasn't that long ago such a daydream would have to remain just that. However, as governments the world over continue to loosen restrictions on who can take what job, opportunities have popped up across the globe for qualified workers. Read on to find out how this change took place and how labor mobility really works.

What Is Labor Mobility?

Labor mobility refers to the ease with which laborers are able to move around within an economy and between different economies. It is an important factor in the study of economics because it looks at how labor, one of the major factors of production, affects growth and production.

There are two primary types of labor mobility: geographic and occupational. Geographic mobility refers to a worker's ability to work in a particular physical location, while occupational mobility refers to a worker's ability to change job types. For example, a worker moving from the United States to France illustrates the concept of geographic mobility. An automobile mechanic who changes jobs to become an airline pilot reflects the concept of occupational mobility. (For related reading, see: Get a Finance Job Overseas.)

Why Does Geographic Mobility Matter?

From a policymaker's perspective, geographic mobility can have important implications on the economy of a particular country. This is because easing immigration requirements can do several things:

• Increase the supply of labor. As more workers enter the economy, the general labor supply increases. An increase in labor supply accompanied by a static labor demand can decrease wage rates.
• Increase unemployment. Unless employers demand more workers, an increase in labor supply could lead to a glut in labor. This means more workers are available than jobs. (For more on this, see: Surveying The Employment Report.)
• Increase productivity. Not all laborers added to the labor supply will be unskilled. An influx in laborers can increase productivity if they bring specialized skills to the workplace, and they might push out existing employees who are less productive. (For related reading, see: Economic Indicators: Employee Cost Index (ECI))

Obtaining geographic mobility is not a purely economic matter. It can also be an issue of state sovereignty and government control. After all, governments are also concerned with security, and completely open borders mean governments are not sure who or what is coming into their countries. While increased geographic mobility generally has a positive impact on the economy, it is also one of the first targets to incur the wrath of both citizens and their representatives. Immigration is already a hot-button topic, both in the United States and abroad.

A reduction in geographic restrictions can be reached in several different ways. Between countries, it is accomplished through treaties or economic agreements. Countries can also increase the number of worker visas available, or reduce the requirements of receiving one. For example, countries that are part of the European Union have fewer restrictions on the movement of labor between members, but can still place tight restrictions on labor movement from non-member countries.

The effectiveness of improved geographic mobility will ultimately depend on individual workers. If economic opportunities are not available in a different country or in a different part of one's current country, the likelihood of an employee wanting to make a change will be diminished.

Why Does Occupational Mobility Matter?

The ease with which employees can move from a job in one particular industry to a job in a different industry determines how quickly an economy can develop. For example, if there was zero occupational mobility, we would still be hunter-gatherers, because no one would have been able to become farmers or specialists.

An easing of occupational mobility restrictions can do several things:

• Increase the supply of labor in particular industries. Lower restrictions cause laborers to have an easier time entering a different industry, which can mean the demand for labor is more readily met.
• Lower wage rates. If it is easier for laborers to enter a particular industry, the supply of labor will increase for a given demand, which lowers the wage rate until equilibrium is reached. (For more insight, see: Exploring the Minimum Wage.)
• Allow nascent industries to grow. If an economy is shifting toward new industries, employees must be available to run that industry's businesses. A shortage of employees means overall productivity can be negatively impacted because there aren't enough employees to provide the service or work the machines used to make the product. (For related reading, see: Employability, the Labor Force and the Economy.)

Occupational mobility can be restricted through regulations. Licensing, training or education requirements prevent the free flow of labor from one industry to another. For example, restrictions limit the supply of physicians, since specialized training and licensing is required to work in that particular profession. This is why physicians can command higher wages because the demand for physicians coupled with a restricted supply increases the equilibrium wage. This funnels unqualified members of the labor force into industries with fewer restrictions, keeping the wage rate lower through a higher labor supply compared to the amount of labor demanded.

Labor Mobility: Two Perspectives

Labor mobility affects workers on two levels: the aggregate level and the personal level.

On a personal level, increased labor mobility gives workers an opportunity to improve their financial situations. If workers are permitted to train for new jobs, move locations or seek higher wages, they are more likely to be happy working, which can have a positive impact on productivity. Workers who do not feel indefinitely relegated to low wages or jobs with few benefits will consistently seek better positions, which also makes it easier for new industries to attract the most qualified applicants by offering better perks.

The aggregate level refers to the economy as a whole. The extent to which labor forces are mobile can impact how quickly an economy can adapt to technological changes, how quickly competitive advantages can be exploited and how innovative industries develop. Restrictions placed on how workers move around, either geographically or occupationally, can slow growth by making it more difficult for businesses to hire productive workers. At the same time, unrestricted labor can depress wages in certain industries and create unemployment.

The Bottom Line

As labor mobility improves, so do the lives of workers around the globe. As a general rule, workers are able to find better-paying jobs and improve their living situations when less control is placed on where they can move and what occupations they can apply for. At the same time, businesses improve because workers receive better training and the right employee can be hired. Economies improve as productivity improves.

Migration figures of the United Kingdom (UK) from 2004 to 2014 (in 1,000) 750 624 589 562 596 574 590 567 591 566 526 498 298 268267 265 273 229 229 256 205 177 209 Migration in thousands -250 -344 -341 -317 321 -361 359 351 -327 -368 -398 -427 -500 YE YE YE YE YE YE YE YE YE YEYE December December December December December December December December December December September 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Inflow Outflow Net migration Additional Information United Kingdom; Office for National Statistics (UK): January 1, 2004 to September 30, 2014 Source: Office for National Statistics (UK) Statista 2015

Figure 1. Share of migrant population within the European Union Population that are citizens of another EU28 country, as a percentage of total population 2007 2008 2009 2010 2011 2012 2013 2014 2015 Source: Eurostat (2015), "Population on 1 January by fve year age group, sex and citizenship, Eurostat Database