The association between productivity and size in the New Economic Geography angle and the standard agglomeration literature

When people and firms live side by side in cities and industrial areas, some benefits come to exist out of this coexistence. These benefits are studied under the title of agglomeration economies. In this writing, I will try to figure out the difference between New Economic Geography angle and standard agglomeration literature in suggesting that productivity and size may be directly associated. Also, I will try to interpret rank size rule when applied to city size distribution in a country. 

The agglomeration literature built on the studies of Henderson (1974) and Sveikauskas (1975) posits that firms in large cities are more productive. This increased productivity comes from the indivisibilities in investment, huge infrastructure base, large market size, lower labour turn-over cost, and easy information-sharing that exist in large cities. Combes et al. (2012) furthers the literature by offering two main explanations for the average increased productivity of firms in larger cities. The first explanation involves firm selection that means competition among firms are tough in larger cities and this allows only the most productive to survive. The second explanation involves agglomeration economies which is possibly reinforced by localized natural primacy. The New Economic Geography (NEG) literature, too, discusses the impact of agglomeration on economic growth. According to this strand of literature, migration and population expansion in cities are motivated by the trade-off between increasing returns and mobility costs. According to Krugman (1991), employees and companies become more productive due to the existence of external-scale economies. What makes the New Economic Geography angle different from standard literature produced by urban economists is the level of their analysis: NEG literature analyses the impact of city size or agglomeration on economic growth at the national level while standard agglomeration looks into the impact of city size on the productivity of urban workers at the city level.

Now, let's see the interpretation of the rank size rule when applied to city size distribution in a country. Zipf’s rank size rule suggests that the largest city is roughly twice the size of the second largest city, about three times the size of the third largest city, and so on. This relationship can also be understood and explained as inverted u-shaped relationship between city size and productivity/growth, meaning that initially as city increases in size, productivity of the firms in that city increase. This continues up to a certain point beyond which growth decreases as city increases. The decrease in productivity beyond the threshold limit in the city size would mean that firms will need to look for fresh urban setting in other places in order to make new investment. In the same way, new migrants may not find it worthwhile to migrate to the cities which have already reached an optimum size. 

To sum up, the New Economic Geography angle analyses the impact of city size or agglomeration on economic growth at the national level while the standard agglomeration looks into the impact of city size on the productivity of urban workers at the city level. And, Zipf’s rank size rule can be understood and explained as inverted u-shaped relationship between city size and productivity/growth, meaning that initially as city increases in size, productivity of the firms in that city increase. This continues up to a certain point beyond which growth decreases as city increases. The decrease in productivity beyond the threshold limit in the city size would mean that firms will need to look for fresh urban setting in other places in order to make new investment.

References: 

Henderson, J. (1974). The Sizes and Types of Cities. The American Economic Review, 64(4), 640-656. Retrieved March 27, 2021, from http://www.jstor.org/stable/1813316 

Leo Sveikauskas, 1975. "The Productivity of Cities," The Quarterly Journal of Economics, Oxford University Press, vol. 89(3), pages 393-413. 

Combes, P., Duranton, G., Gobillon, L., Puga, D., & Roux, S. (2012). The Productivity Advantages of Large Cities: Distinguishing Agglomeration From Firm Selection. Econometrica, 80 (6), 2543-2594. http://dx.doi.org/10.3982/ECTA8442 

Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.

The role of complementarities, increasing returns to scale and multiple equilibria in the process of economic development

In 1970’s the world of economic thought experienced a re-emergence of neoclassical economics that has traditionally been pre-occupied with laissez-faire. Given such obsession, neoclassicals posited that the application of standard microeconomic principles in the third world context would tackle the issue of underdevelopment as it (i.e. underdevelopment) is born out of lack of markets due to weak or non-existent property rights.  In this essay, with the help of QWERTY example, I want to argue that even if one comes from a neoclassical perspective, still there will exist market failure that may require some form of state intervention; and in the LDCs underdevelopment will be the result of such massive coordination failures. In particular, under neoclassical assumptions, issues of complementarities and increasing returns to scale will lead to existence of multiple equilibria where only one is pareto-efficient; in the presence of multiple equilibria, issues such as path dependency and history will force the economy to get stuck with pareto-suboptimal equilibrium.    

The types of externalities can broadly be categorized into technological and pecuniary ones. While market can capture technological externalities (i.e. due to such externalities market might be in disequilibrium), pecuniary externalities are not captured in the General Equilibrium framework. Pecuniary externality occur when the profit of one producer is affected by the actions of other producers through market prices; in other words, pecuniary externality arises when the price of one good in an economy depends on the prices of other goods in the economy: 

, 

where P is the price at which the first firm sales its products. 

Pecuniary externality leads to market imperfection and complementarities that will in turn, along with the assumption of increasing returns to scale (IRS), will lead to the existence of multiple equilibrium. Let’s consider To-Become-Tea-Lovers country. Suppose that two firms, T and S exist in this economy: while T produces tea, S produces sugar; suppose that due to some changes in the taste of people living in this economy, the demand for tea increases and as a result T expands. This will result in increase in the demand for S’ product; so, S will expand. This in turn will have a positive impact on the demand for T’s products because now with more income available from the expansion of S, demand for tea further increase. These two firms will keep reinforcing each other’s profit. Thus, a monopolistic economy will be shaped: imperfect market. This way, pecuniary externality leads to imperfection in the market. Let’s note that in such a scenario, the First Fundamental Theorem of Welfare Economics stands in the way because it rules out Pareto-ranked equilibria in the absence of technological externalities.

Now, to show that complementarities and IRS lead to the existence of multiple equilibria, let’s consider QWERTY example. Dvorak Simplified Keyboard (DSK), according to experiments, is more efficient arrangement compared to QWERTY, and it is said that typing with DSK is 20 to 40% faster compared to QWERTY. However, we are still stuck with the later due to 3 issues, namely (1) technical interrelatedness, (2) economies of scale, and (3) quasi-irreversibility of investment.

Technical inter-relatedness refers to the interdependence that exists between typewriters and typing skill. In the past, when typewriters were invented, it was purchased by businesses for business use. The purchaser wouldn’t himself/herself use the machine, rather it was used by typists who were trained in typing schools. This gives rise to some form of inter-relatedness; the business will buy those types of machines for which typist (soft skill) can be found; on the other hand, the typist would try to learn typing with those types of machine that are available with businesses. Thus, a form of complementarity is formed.

In this situation, when a firm buys a QWERTY-keyboard typewriter, this signals a positive pecuniary externality to those typists who are skilled in typing with QWERTY-keyboard. Also, the demand for QWERTY-keyboard learning will go up which will result in the reduction of average cost of learning QWERTY-keyboard due to economies of scale (IRS). Thus, complementarity and economies of scale create QWERTY path-dependency, meaning the purchase of a QWERTY-keyboard by a firm and subsequence choice of learning this QWERTY-keyboard skill by potential learners will finally lead to dominance of QWERTY-keyboard. However, if the issue of quasi-irreversibility of investment did not exist, it would have been possible, even now, to go to DSK.

Quasi-irreversibility of investment refers to rise of asymmetry that rose between the cost of hardware and software conversion in mid-1890s. In mid-1890’s, the possibility to move back and forth between QWERTY-keyboards and DSKs without any extra cost was made possible but the cost of learning DSK was going up because the demand for QWERTY-keyboard learning was rising. This is called Quasi-irreversibility of investment.

In this example, we see that pecuniary externalities, complementarities, increasing returns to scale, history and path dependency and quasi-irreversibility of investment have led to multiple equilibria, being caught up in low level equilibrium and market failure. In other words, if someone, say government coordinated the actions of business owners and labor force at the initial stage, pareto-optimal equilibrium would have been achieved. Based on this example, we can argue that even coming from a pure neoclassical perspective, market failure can happen and there is a need for coordinated action to help the economy achieve a pareto-efficient equilibrium. In the LDCs, underdevelopment can be a result of massive coordination failures do to the issues of complementarities and increasing returns to scale.  We can also show the existence of multiple equilibria, coordination failure and the need for some form of intervention to coordinate actions by considering an economy where left to themselves, firms may not invest because they might expect that other firms will not invest.