A case of anti complementarities

Traffic: A case of “anticomplementarities”.

Now observe that history can have no effect on the equilibrium dispersion of traffic on these routes. For instance, suppose initially that route A existed and then route B was set up. Initially no one used route B, so the cost of travel on this route is only YM (see diagram). Route A has a cost of YN, which is larger. Hence, traffic will begin to switch to the new route, which drives up its cost and brings down the cost of the old route. Ultimately, XZ commuters will use A and the rest, ZY, will use B, and transportation costs will be equalized across routes. This solution ultimately occurs regardless of whether A or B was created first.

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What do we learn from this discussion? Three things: first, it is possible that, because of complementarities, there may be “multiple equilibria” in a system. After all, everybody using Dvorak would also be a stable state of affairs (provided we could somehow get there). Thus in this example, universal adoption of the QWERTY system and universal adoption of the Dvorak system represent two equilibria, which no individual can affect by some unilateral action. Second, the particular equilibrium in which society might find itself depends on the history of that society. For instance, QWERTY was initially popular and appropriate because of the jamming typewriters. The jamming typewriters went away, but QWERTY didn’t. History and externalities combined to lock QWERTY in. Finally, we saw that externalities create possible multiple equilibria, and historical lock-in occurs only when externalities take the form of complementarities.3

5.2.2. Coordination failure Pervasive complementarities might therefore lead to a situation where an economy is stuck in a “low-level

equilibrium trap,” while at the same time there is another, better equilibrium, if only all agents could appropriately coordinate their actions to reach it. This view of underdevelopment has gained some popularity.4 Its genesis lies in a classic paper by Rosenstein-Rodan [1943], which went unnoticed by mainstream economists for many decades.

According to this view, economic underdevelopment is the outcome of a massive coordination failure, in which several investments do not occur simply because other complementary investments are not made, and these latter investments are not forthcoming simply because the former are missing! The argument sounds circular. It is and it isn’t, as we will soon see. For now, observe that this concept provides a potential explanation of why similar economies behave very differently, depending on what has happened in their history.

From Rosenstein-Rodan comes the parable of the shoe factory. Imagine a region where there is potential for investment in a number of different enterprises. Suppose, moreover, that all the output of the enterprises must be sold within the region.5 Now suppose that a giant shoe factory is set up, which produces a million dollars worth of shoes and thus creates a million dollars of income in wages, rents, and profits. Can the enterprise survive? It can only if all the income is spent on shoes, which is absurd. The recipients of the new income will want to spend their money on a variety of objects, which includes but is certainly not limited to footwear! Thus the shoe factory on its own cannot be viable.

Now consider a different thought experiment. Imagine that enterprises are set up in the correct ratios in which people spend their money on different commodities. For instance, suppose that people spend 50% of their income on food, 30% of their income on clothing, and 20% of their income on shoes. In that case, setting up three enterprises in the ratio 50:30:20 would actually generate income that would come right back to these enterprises.

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The conjunction of the three enterprises would be jointly viable, in a way that each individual enterprise was not.6

Now here is where the issue of coordination makes an appearance. Suppose that no entrepreneur is large enough to invest in more than one enterprise. Then notice that each entrepreneur would invest if he were to believe that the others would invest as well, but in the absence of such optimistic beliefs, he would not do so, for the same reason that the shoe factory in isolation would not be set up. Thus we have two equilibria: one in which the region is devoid of any investment at all and another in which there is investment by all three entrepreneurs in the appropriate proportion.

Whether or not such a coordinated equilibrium would arise depends on the expectations that each entrepreneur holds about the others. To the extent that the formation of expectations is driven by past history, it may well be that a region that is historically stagnant continues to be so, whereas another region that has been historically active may continue to flourish. At the same time, there may be nothing that is intrinsically different between the two regions.7

Is this situation the same as the QWERTY example? It is. Think of “investing” and “not investing” as the two options analogous to adopting QWERTY or Dvorak. Note that the gain to investing depends positively on investments made by others. Therefore, we are in the standard framework of complementarities, and viewed from this angle, the possibility of multiple equilibrium outcomes should not be at all surprising.

Coordination failure emerges from complementarities, and the situation that generates it is often known as a coordination game.8 The “failure” manifests itself in the inability of a group of economic agents, whose actions are “complementary” in the sense described earlier, to achieve a “desirable” equilibrium, because of the presence of another “undesirable” equilibrium in which they are trapped. This notion of coordination is closely linked with the concept of linkages, to which we turn next.

5.2.3. Linkages and policy The parable of the shoe factory is particularly compelling if many different industries are involved in

coordination to a “desirable” equilibrium. Figure 5.3 provides an example of the interaction between various industries. Only a small number of industries are involved in this diagram, but you can see the point. The idea of the arrows is to suggest that one industry might facilitate the development of another by easing conditions of production in the latter industry.

Note that it is quite possible for these links to be simultaneously in two states: one in which all activity is depressed and another in which the links are active. The problem is that if all industries are simultaneously in a depressed state, it may be hard to “lift” the entire network of linkages to a more active state.

Of particular interest is the structure of the various linkages that connect different industries. Hirschman [1958] distinguished between backward and forward linkages. Thus, in Figure 5.3, the steel industry facilitates the development of other industries, such as railways, by increasing the availability of steel and/or lowering its price. This is an example of a forward linkage—one that works by affecting the ease of supply of another product. A forward linkage is captured in this diagram by the direction of the arrows. On the other hand, the steel industry possesses a backward linkage to the coal industry: the expansion of the former raises the demand for the latter. Likewise, the shipping industry links forward to exports and backward to railways: the former because it facilitates the transportation of exports; the latter because it creates a demand for freighting of products from the interior to the ports. Typically, a backward linkage is created by reversing the direction of the arrows in Figure 5.3. If industry A facilitates production in industry B, then an expansion of industry B (for some other reason) will generally create an increase in demand for the product of industry A. Thus backward linkages are like “pulls” and forward linkages are like “pushes.”

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