# International Economics: Theory and Policy, v. 1.0

by Steve Suranovic

## 2.10 Welfare Effects of Free Trade: Real Wage Effects

### Learning Objectives

1. Learn why real wages are an appropriate way to measure individual well-being.
2. Learn how the real wages formulae are derived from zero-profit conditions.

There are two ways to evaluate the welfare effects of trade in the Ricardian model. The first method evaluates the real wages of workers as two countries move from autarky to free trade. It is shown that the purchasing power of all workers’ wages in both countries would rise in moving to free trade.

The focus on real wages allows us to see the effect of free trade on individual consumers in the economy. Nominal wages are not sufficient to tell us if workers gain since, even if wages rise, the price of one of the goods also rises when moving to free trade. If the price rises by a greater percentage than the wage, the ability to purchase that good falls and the worker may be worse off.

For this reason, we must consider real wages. The real wageThe quantity of a good that can be purchased per unit of work. Real wage is a measure of the purchasing power of a wage and is an effective measure of well-being. represents the purchasing power of wages—that is, the quantity of goods the wages will purchase. Real wages are typically measured by dividing nominal wages by a price index. The price index measures the average level of prices relative to a base year. The nominal wage is the amount of dollars the worker receives.

In this model, we need not construct a price index since there are only two goods. Instead, we will look at the real wage of workers in terms of the purchasing power of each good. In other words, we will solve for a real wage in terms of purchases of both wine and cheese.

## Numerical Example: Calculating a Real Wage

Consider the real wage of a worker in terms of cheese. Suppose the worker earns $10 per hour and the price of cheese is$5 per pound. The real wage can be found by dividing the wage by the price to get

$wPC=10/hr5/lb=2 lbs/hr.$

This means the worker can buy two pounds of cheese with every hour of work.

## The Real Wage of Cheese Workers in Terms of Cheese

The real wage of cheese workers in terms of cheese is the quantity of cheese that a cheese worker can buy with a unit of work. It is calculated by dividing the worker’s wage by the price of cheese, written as $wCPC$. Since zero profit results in each producing industry, we can simply rewrite the relationship derived above to construct the following formula for the real wage:

$wCPC=1aLC.$

This means that the real wage of a worker in terms of how much cheese can be purchased is equal to labor productivity in cheese production. In other words, the amount of cheese that a worker can buy per period of work is exactly the same as the amount of cheese the worker can make in that same period.

## The Real Wage of Cheese Workers in Terms of Wine

The real wage of cheese workers in terms of wine is the quantity of wine that a cheese worker can buy with a unit of work. It is calculated by dividing the cheese worker’s wage by the price of wine and is written as $wCPW$. Using the relationship between wages and prices when zero profit results in the cheese industry implies that

$wCPW=( P C a LC )PW=1aLCPCPW.$

This means that the real wage of cheese workers in terms of wine is the product of labor productivity in the cheese industry and the price ratio. Labor productivity gives the quantity of cheese a cheese worker makes in an hour of work. The price ratio gives the quantity of wine that exchanges for each unit of cheese. The product gives the quantity of wine that a cheese worker can buy with a unit of work. To calculate the autarky real wage, simply plug in the autarky price ratio. To calculate the free trade real wage, plug in the free trade price ratio.

## The Real Wage of Wine Workers in Terms of Wine

The real wage of wine workers in terms of wine is the quantity of wine that a wine worker can buy with a unit of work. It is calculated by dividing the worker’s wage by the price of wine, written as wW/PW. Since zero profit results in each producing industry, we can rewrite the relationship to get

$wWPW=1aLW.$

As with cheese, the real wage of a worker in terms of how much wine can be purchased is equal to labor productivity in wine production. In other words, the amount of wine that a worker can buy per period of work is exactly the same as the amount of wine the worker can make in that same period.

## The Real Wage of Wine Workers in Terms of Cheese

The real wage of wine workers in terms of cheese is the quantity of cheese that a wine worker can buy with a unit of work. It is calculated by dividing the wine worker’s wage by the price of cheese, written as (wW/PC). Using the relationship between prices and wages when zero profit results in the wine industry implies that

$wWPC=( P W a LW )PC=1aLWPWPC.$

This means that the real wage of wine workers in terms of cheese is the product of labor productivity in the wine industry and the price ratio. Labor productivity gives the quantity of wine a wine worker makes in an hour of work. The price ratio gives the quantity of cheese that exchanges for each unit of wine. The product gives the quantity of cheese that a wine worker can buy with a unit of work. To solve for the autarky real wage, simply plug in the autarky price ratio. To find the free trade real wage, plug in the free trade price ratio.

## Real Wages in Autarky

To calculate autarky real wages, we simply plug the autarky price ratio into the real wage formulae.

Recall that the autarky price ratio is $( P C P W )Aut= aLCaLW$. Plugging this in and simplifying yields the results in Table 2.13 "Autarky Real Wages".

Table 2.13 Autarky Real Wages

In Terms of Cheese In Terms of Wine
Real Wage of Cheese Workers $wCPC=1aLC$ $wCPW=1aLCaLCaLW=1aLW$
Real Wage of Wine Workers $wWPC=1aLWaLWaLC=1aLC$ $wWPW=1aLW$

where

PC = price of cheese

PW = price of wine

wC = wage paid to cheese workers

wW = wage paid to wine workers

aLC = unit labor requirement in cheese production in the United States (hours of labor necessary to produce one unit of cheese)

aLW = unit labor requirement in wine production in the United States (hours of labor necessary to produce one unit of wine)

Notice that in autarky, the real wage of cheese workers is exactly the same as the real wage of wine workers with respect to purchases of both goods. This occurs because labor is assumed to be homogeneous—that is, all labor is the same—and because there is free mobility between industries. (If workers were paid different wages, the lower-wage workers would move to the higher-wage industry.)

## Comparison of Autarky Real Wages between Countries

Suppose the United States has an absolute advantage in the production of both goods. In this case, $1aLC>1aLC∗$ and $1aLW>1aLW∗$. This implies that the real wages of workers in both industries in the United States are higher than the real wages in France. Put another way, workers in France earn lower wages in both industries.

Sometimes cross-country wage comparisons are made and it is suggested that firms in a high-wage country cannot compete with firms in low-wage countries. However, wage comparisons of this kind are not sufficient in this model to determine who will produce what or whether trade can be advantageous. Instead, what matters is relative wage comparisons. In this model, a country will tend to specialize in the good in which it has the greatest real wage advantage. Thus if

$1aLC1aLC∗ > 1aLW1aLW∗,$

then the United States has relatively higher real wages with respect to cheese purchases than it does in wine purchases. When trade opens, the United States will specialize in its comparative advantage good, which, by rearranging the above inequality, can easily be shown to be cheese.

## Effects of Free Trade on Real Wages

Suppose two countries, the United States and France, move from autarky to free trade. If the United States has the comparative advantage in cheese production, then $aLCaLW, which implies $( P C P W )Aut< ( P C ∗ P W ∗ )Aut$. When the two countries move to free trade, the free trade price ratio will lie somewhere between the autarky price ratios. This means that (PC/PW) rises in the United States when moving from autarky to free trade, while PC∗/PW∗ falls when moving to free trade.

The other major change that occurs is that the United States specializes in cheese production, while France specializes in wine production. This means that real wages in free trade for wine workers in the United States need not be calculated since the United States will no longer have any wine workers. Similarly, real wages for cheese workers in France need not be calculated.

Thus we can calculate the changes in real wages shown in Table 2.14 "Changes in Real Wages (Autarky to Free Trade)".

Table 2.14 Changes in Real Wages (Autarky to Free Trade)

In Terms of Cheese In Terms of Wine
Real Wage of U.S. Cheese Workers $wCPC=1aLC$ (no change) $wCPW=1aLCPCPW$ (rises)
Real Wage of French Wine Workers $wWPC=1aLWPWPC$ (rises) $wWPW=1aLW$ (no change)

First, consider the fate of U.S. cheese workers. Since the unit labor requirement for cheese does not change in moving to free trade, there is also no change in the real wage in terms of cheese. However, since the price of cheese in terms of wine rises, U.S. cheese workers can get more wine for each unit of cheese in exchange. Thus the real wage of cheese workers in terms of wine rises. This means cheese workers are at least as well off in free trade as they were in autarky.

The worst outcome occurs if a cheese worker has no demand for wine. Perhaps an individual abstains from alcohol consumption. In this case, the worker would be able to buy just as much cheese in free trade as in autarky, but no more. Such a person would receive no benefit from free trade. However, every worker who demands both wine and cheese will be able to buy more of both goods.

As for the workers who worked in the wine industry in the United States in autarky, they are now cheesemakers earning cheesemaker wages. Since real wages for wine workers were the same as wages for cheese workers in autarky, and since cheese workers are no worse off with free trade, then wine workers must also be no worse off in free trade. Of course, the model assumes that the movement of workers from one industry to another is costless. In the immobile factor model, we address the implications of adjustment costs across industries.

In France, the real wage of winemakers in terms of how much wine they can buy remains constant, while the real wage in terms of cheese must go up. French cheesemakers have all become winemakers because of specialization, which means all French workers are no worse off and most likely better off as a result of free trade.

The likely welfare effect of free trade, then, is that everyone in both trading countries benefits. At the very worst, some individuals will be just as well off as in autarky. This result occurs for any free trade price ratio that lies between the autarky price ratios.

In David Ricardo’s original numerical example, he demonstrated that when both countries specialize in their comparative advantage goods and engage in free trade, both countries can experience gains from trade. However, his demonstration was only true for particular numerical values. By calculating real wage changes, it is shown that it doesn’t matter which price ratio emerges in free trade as long as it is between the autarky prices. Also, because all workers receive the same wage in each country, the real wage calculations tell us that everyone benefits equally in each country.

### Key Takeaways

• Real wages are an appropriate measure of worker well-being because they represent the purchasing power of the wage.
• Real wages are positively related to labor productivity in the Ricardian model.
• When countries move to free trade, the real wage with respect to the exported good remains constant, but the real wage with respect to the imported good rises in both countries.
• If workers prefer to consume a positive amount of both goods, then when a country moves to free trade, every worker will be able to buy more of both goods. In other words, everyone in both countries will benefit from trade.

### Exercise

1. Consider a Ricardian model. Suppose the U.S. unit labor requirement for timber is three, its unit labor requirement for videocassette recorders (VCRs) is eight, and it has forty-eight million workers. Suppose Taiwan’s unit labor requirement for timber is six, its unit labor requirement for VCRs is two, and it has forty-eight million workers.

1. Which country has the absolute advantage in each good? Which country has the comparative advantage? Explain.
2. Calculate each country’s autarky price ratio. Then make up a plausible free trade price ratio. What are the levels of production and the pattern of trade when free trade occurs?
3. Calculate real wages for workers in both countries in autarky and free trade. Explain why everyone benefits from trade.
4. Suppose the United States implements a costless technology improvement program that lowers the U.S. unit labor requirement for timber to two. What effect would this have on the world supply of timber? What effect would this have on the free trade price ratio? Explain how real wages would change in both the United States and Taiwan.