French Language in Canada.

A Network Externality.

Introduction Present Situation Theorization One country, two policies. Conclusion

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Introduction

North America is a 300 million English speaking country. In Canada, due to historical reasons 25% of the population speaks French: that represents 7.5 million people over a 30 million populated country. However, this population is not homogeneously distributed. Indeed, 87% of French speaking Canadians live in Quebec. Consequently, 82% of Quebec population speaks French, whereas only 5% of the population speak French in the other provinces. There is approximately the same amount of English speakers in Quebec than French speakers in the rest of Canada: 1 million. However English speakers are concentrated in Montreal whereas French speaking Canadians are more isolated outside Quebec. Overall, the French speaking population in Canada is decreasing. This is due to two main factors: the integration of French speaking people in English speaking provinces and the weight of immigration in Canadian population. Immigrants in a majority, if they do not already speak one language (French or English) tend to learn English more than French. This is due to the fact that they see more externalities in English than in French. It is obvious in all Canadian provinces where French is not the main language, but this is also true when French is dominant. Indeed, Montreal is the main immigration destination in Quebec. In this city where there is a strong English speaking community (40%), speaking French is not necessary. All public services are bilingual and English is the working language of most of the companies (because of historical reasons coming from Quebec industrialization). Thus new immigrants do not see any incentives to speak French. Furthermore, if in the future, these immigrants want to move outside Quebec (to other provinces or to the US), they would better learn English than French. We observe two externalities: the actual use of French in day to day life, and the use of French outside Quebec. The first externality is slightly in favor of English and the second is strongly in favor of English. Thus, even in Quebec, in the sixties, only 30% of the immigrants could speak French. Moreover, only 15% of their children went to French speaking schools. This would worsen the trend in the long run.

Now, we have to describe the revenue and cost curves of each language in this space:

1) Revenue curve:

a) Difference between the French and English revenue curve:

We see that English is more attractive for several reasons:

• Network externalities in a 75% English speaking country (possibility of work evolution, communication, travel, media, culture, convenience to study just one language etc.)
• Network externalities in a 300 million English speaking continent (foreign exchanges, career opportunities, media, culture, etc.)
• Possibility to use English in Montreal as the only spoken language.
• English is the main working language.
• The economy is dominated by the English speaking community: English is the economical language.

b) Shapes of the curves.

In order to trace the shape of the curve, we should set the value of the derivative at each extremities of the curve and the sign of the second derivative.

We consider that the marginal gain of having new members for one community is negligible if this community is already the majority: Thus the first derivative tends to 0 for each revenue curve when the proportion of people tends to 100%.

However, we consider that the marginal revenue of having a new member is high if the community is a minority. We do not consider that we have a classical suite: n*(n-1)/2, because people tend to group in communities. Once one community is big enough to offer positive externalities, people are happy with their language. But another growing community do not affect their own externalities as individuals (because external relationships < internal relationships).

Let say that one person comes in a community and that this person creates A amount of externality to each person he is in contact with. We assume that he cannot have more relationships than with n people. This community contains N people (N>n). His arrival creates to the community n*A amount of externalities; not N*A. n*A/(N+1) is higher if N is a small number. Thus, the externality curve has a higher slope in minorities. The second derivative is thus negative. Here is the curve for French and English:

English intrinsic value is positive, in a North American English speaking continent, whereas French intrinsic value is zero (if you are the only one to speak French in North America, it is not very helpful). We immediately observe that the situation is not symmetrical. The two curves equal at approximately 70% French / 30% English.

For English or French speakers, this revenue curve equals the benefits curve, because they had no particular effort to make in order to learn this language. However, for new immigrants who speak neither French nor English, we have to subtract a cost curve that represents their difficulties to learn a new language.

2) Cost curve.

We consider that English and French have the same degree of difficulty for an immigrant whose mother tongue is not French neither English. However, it is slightly more easy to learn English in a 100% French speaking community because of North American externalities (TV, Movies, tourists, businessmen) than learning French in a 100% English speaking community. We consider that the more people speak a language around you, the less difficult it is to learn it. We also consider, as we did for the revenue curve, that the difference to learn French (for example) in a 99% or in a 100% French speaking community is negligible. Which is obviously not the case if you have the choice to learn it in a 0% (you are the only one, alone with your books) French speaking community or in a 1% (you can train). Thus the curves are like these:

We observe on this graph that the situation of French in Canada equals the English, even if we consider that English is easier to learn because of the North American externalities. This graph is quasi symmetrical.

As a conclusion of those two graphs, we observe that the asymmetry between the two languages depends quasi exclusively on the revenue curve. The main asymmetry comes from the intrinsic value of English in North America (when French has no intrinsic value).

3) Learning benefits.

• English.

• French.

 






• Learning both languages.

 

Thus, the main issue is about French and English, not about bilinguals. We also could study the benefits for French or English speaking people to switch for the other language when they are strongly in minority. However, in most of the case we have an inertia phenomenon. This inertia is due to the fact that this French person will have to renounce to his French externalities. He saw as benefits what are now costs, when he decides to get rid of these externalities. Indeed, for example, to find the benefits for a French speaker to switch to English, we have this equation: Switching Benefits = English revenue curve –French revenue curve – English learning cost curve (if we consider that this person abandons his French speaking community). Thus we have the following curve:

We observe that there are more incentives to switch from French to English than from English to French. However in each case, there are few incentives to switch from one language to another. People can observe some benefits only if they are really isolated (Manitoba), but they do not see any advantage for bigger communities (New Brunswick).

4) Analysis:

If we want to compare the advantages of one language over another, we have to compare the benefits on the x = X% line.

With this graph, we easily can report the different benefits in a precise situation:

Canada: 25% of French speakers.
 

If we consider Canada as a homogeneous society, the best benefits goes to bilingual people. But the benefits of speaking just English are very close. Then people should have incentives to speak both French and English. This is not really the case because in all the provinces of Canada except Quebec, French is marginal and thus, as we will see, being Bilingual gives less benefits than simply speaking English.

Canada without Quebec: 5% of French speakers.
 

Now, if we consider Canada without Quebec, we see that the benefits of speaking French are negative. The benefits of being bilingual are positive but small compared to the benefits of speaking English. Thus, for 75% of the population, speaking French or even being bilingual is not the issue. They have to speak English to maximize their profit (the externalities with Quebec are less important than the externalities with the English speaking North American).

New Brunswick: 30% of French speakers.
 

This study would not be complete without mentioning Acadie. 30% of New Brunswick inhabitants are French speakers. They had a particular history, distinct from the Quebecois. In this case, we see that French is not the most interesting language, but being bilingual is obviously the most interesting position. However it may be more profitable for a French speakers to be bilingual than for an English speaker. This repartition may explain why French language in Acadie is altered and mixed with English words and grammar. However we understand why New Brunswick is one of the two official bilingual provinces (with Ontario).

Quebec: 82% of French speakers.
 

If we consider Quebec as a whole, French is the most profitable language, but being bilingual is still more beneficial. However as for Canada, Quebec is not a homogeneous society. Most of the English speakers are living in Montreal. Outside Montreal, the French speakers represent 95% of the population.

Montreal: 60% of French speakers.
 

In Montreal, being bilingual is the most profitable situation. However, speaking only English is also quite beneficial. Indeed, Montreal is probably the most bilingual city in Canada. But this would not recognize the fact that Montreal is more or less separated in two areas: one is French speaking, the other English speaking. Bilingual people are also often more fluent in one or another language. True bilingual people are rare and are generally children of mixed couples.

Quebec without Montreal: 95% of French speakers.
 

In the ‘deep Quebec’ French is the most profitable language. It is even more profitable than being bilingual. In these parts of Quebec, English speaking minorities are threatened, as well as French speaking minorities in the rest of Canada.

5) Conclusion:

In this model, we observe that in Canada, the situation is obviously asymmetrical. For immigrants, the benefits of speaking English are far more important than the benefits of speaking English. If the federal government wants to protect the right of its French speaking citizens, an intervention is necessary to give the same benefits to French speakers and to English speakers. Those interventions could be:

• Bilingual institutions (public services, hospitals, tribunals, etc) all around the country
• French speaking schools for any French speaking community.
• French speaking media all around the country.

We have to distinct several parts of Canada:

• In Canada without Quebec, French is not a profitable language. In those regions, French speaking communities will slowly disappear. Protecting the use of French is a lost battle. Money has to be spent in specific communities: in Ontario and in New Brunswick, where French speaking communities are significant.

• In Quebec, French is the most profitable language. French language is not threatened by English language.

• In Montreal, English is still the most profitable language. This is a real threat, considering that Montreal is a key city for Quebec. Without its cultural and economical capital, Quebec is not a viable province. In our model, we see that the use of French has to be protected, even if Montreal is a 60% French speaking city. This situation is due to network externalities of English language with North America that creates an asymmetry in the revenue curves. Indeed, as long as those curves are asymmetrical, immigrants will have a tendency to learn English, and French speaking people to speak English (however in a few proportion, considering the inertia of switching from a language to another). Actually, people whose mother tongue is neither French nor English represent 8% of the population in Montreal. These people will decide the trend. If they adopt English, French speaking population will decrease in Montreal (resulting in more benefits for learning English…). If they adopt French, the benefits of learning French will rise in Montreal and maybe will equal the benefits of learning English.

In order to keep an equilibrium in the proportion of every speaking communities, some incentives have to be created.

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One Country, two policies.

In Quebec, the language protection legislation is based on three strong points:

• All public writings (advertisements, shops writings etc.) have to be predominantly in French. This first point is aimed to move up the revenue curve of French (but this is just available for Quebec and Montreal, so the curve moves up significantly when the proportion of French speakers > 50%. In parallel, the revenue curve for English speakers moves down in the same region.

• French has to become the main teaching language for immigrant children. People whose language was not English before immigrating in Quebec will have to send them in French speaking schools. Doing so, the cost for learning French will be less important for immigrants. The cost curve will go down. In parallel, the cost for learning English will be more important. The cost curve will go up. Indeed, in 1995, 79% of the new immigrants went to French speaking schools when they were just 15% in 1971. But the effects on the cost curve are not significant. The benefits of such a policy is more long term: it shifts directly the proportion of French speaking people left, giving then less importance to the English revenue curve.

• French has to become the main working language. The use of French is now regulated at work. These actions should also shift the revenue curve of French up and move down the revenue curve of English. In 1992, only 42% of Quebecois spoke French at work. In 1989, they were 56%.

The second equilibrium reduces the asymmetry of the system. For Quebec in general, the situation of French is clearly improved. This graphs shows that if these laws are effective and well balanced, we can obtain an equilibrium in Montreal in the near future.

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Conclusion

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