[Voision and Calculation] Chapter 6 Transactions and Cities / Sheng Hong

Abstract: The main objectives of this paper are to explain the origination, development, density, scale determination, and industry positioning of cities using the concept of transactions and to discuss the impacts of institutional changes and policy improvements on cities. Statistically, transactions can bring about transaction benefits. Pursuing transaction benefits leads people to congregate, which may yield congestion externalities and market-net externalities, and their differences form the congregation rent. Population density may reach the optimal equilibrium when the congregation rent corresponding to the population density is at its maximum, which determines the economic density and scale of the city. The time distribution of the city’s growth process is similar to the economic income change corresponding to the change in population density because the people’s incentive to swarm into cities is proportional to the benefits that they may receive from cities. A larger economic scale results in a stronger congregative effect. Different industries may position from the center of the city to the outside according to their congregative effects from higher to lower that depend on the different optimal economic scales of different industries. Finally, the decrease in nonmarket transaction costs brought about by institutional changes may affect the density and scale of cities through an impact on the volume of transactions; policy changes may also affect transaction costs and the density and scale of cities. However, such effects may not be as obvious and sustainable as institutional changes.

Key words: city, transaction, congregation, institutions
JEL Classification: C21, R12, R29

Vision and Calculation, published by Palgrave Macmillan, 2020.

The research on spatial economics led by Krugman primarily names economies of scale in production as the reason for spatial agglomeration (Fujita Masahisa, Paul Krugman and Venables, 2005). However, some gaps exist between this statement and the facts. In fact, most of today’s cities are mainly finance-, trade-, commerce-, education-, and entertainment-oriented, and they house government agencies. These functions can be summed up in one word, “transaction.” Industrial production is generally located in suburbs not far from the city. Explaining the origination of cities with economies of scale in production may apply to the industrial period of the 18th century but not to today.

The purpose of this article is simple: to explain the origination, development, and spatial layout of cities with “transactions.” The “transactions” to which this article refers is a broad term in institutional economics that means the interactions between people, including transactions in the market, management and collaboration within enterprises, and interactions between the government and citizens, the government and businesses, such as taxation and paying taxes, public goods provided by the government, and enjoyment by citizens and businesses.

In particular, transactions include remote transactions, often called “trade.” However, the “trade” referred to includes only local activities and impact; that is, regardless of where goods are bought and sold by a trader, we only count his results in local transactions—we only assume that all or part of the transaction benefits fall to local places. This understanding even includes offshore trading and online transactions; that is, both producers and consumers of that product are not local. This is similar to our understanding of the fact that trade creates wealth. The purpose is only to consider the impact of trade locally to simplify the problem.

We will find that once we make “transactions” the basic unit of the research on spatial economics, we associate this theory with institutional economics because “transactions” is also the basic unit of institutional analysis (Commons, 1983, p. 73). When we use “transactions” as the “common unit” for spatial and institutional economics, we can both spatialize the institutions and add institutional and policy variables into spatial economics, which significantly expands the dimensions of the analysis.

1. The spatial nature of transactions

Economists believe that transactions create value, which refers to not only the dynamic results—the transaction price may guide the effective allocation of resources and promote the deepening of the division of labor and specialization—but also to a static value—the increase in the present welfare attributable to different resource endowments and comparative advantages. In this article, we discuss only the static value of transactions and assume that each transaction has benefits, as indicated in Figure 1.

Figure 1 Transaction benefits

Note: The triangle represents transaction benefits and consists of two parts: consumer surplus (the white part) and producer surplus (the gray part). The benefit of consumer surplus is expressed as lower prices, and producer surplus can be expressed as money or, approximately, as value added or GDP.

Because achieving a deal creates a benefit of transaction, people have an incentive for more transactions. To achieve this goal, they must overcome the obstacles posed by transaction costs. In the broadest sense, transaction costs contain much content, one of which is distance costs. A significant change is traders moving their place of residence closer to other traders, which significantly reduces the distance costs, even approaching zero.

The phenomenon of traders coming close to each other can be described as “space congregation,” and its popular name is “city.” Compared with “fragmentation,” “congregation” creates a permanent asset. If the distance costs for A’s round trip from his residence to B’s residence is a, and the benefits that he gains from transactions with B is greater than a, this is equivalent to permanently reducing the cost of a if A moves to B’s residence, and the value of the assets is as follows:

V = A/r

where V is the value of congregation assets, A is the total distance costs for one year, and r is the discount rate.

In addition to significantly reducing traders’ distance costs, congregation also brings about the unexpected benefit that the transactions achieved are disproportionately higher than the number of traders gathered. This benefit is also referred to as the “network externalities of the market.” This term borrows from the concept of “network externality”: as the number of nodes increases, the number of relationships between the nodes increases at a faster rate. The reason for “externality” is because the benefits from the increase in the number of transactions brought by congregation is not the result of traders’ efforts but of other traders’ congregation, whereas the latter is the external factor for this trader. If we use ME to represent the network externality of the market, it can be expressed as follows:

ME = n (n–1) / 2

where n is the population density or the number of people per unit area. This formula represents in certain areas the combinations of the one-to-one relationships among n people and represents the potential market transaction volume. In practice, within a certain period, not every person can engage in one-to-one transactions, but a certain percentage of people will. Therefore, the formula can be multiplied by a coefficient of less than 1 (such as 1/100), but the trend that the formula represents remains unchanged. See Figure 2.

Figure 2 Population Density and Market Network Externality

Note: The horizontal axis is population density (100 persons per square kilometer), and the vertical axis is market network externalities (number of transactions).

If congregation only has such features, then a higher population density and larger city are preferred. However, congregation also bring opposing forces that prevent cities from expanding indefinitely. For example, as more people congregate in a city, the economy becomes similar to a large economy from which the marginal utility of a product or service decreases and its marginal costs increase as the population density increases. That is, the marginal transaction benefits decrease with an increase in population density, as shown in Figure 3.

Figure 3 Marginal Transaction Benefit

Considering this factor as within the network externalities of the market, the formula can be revised as follows:

CE ≈ ∑(a – c) n – (b + d) * n2) (for a detailed derivative process, please see Annex 1)

where CE is the network externalities of marginal transaction benefits; a and b are the intercept and slope of the marginal utility function, respectively; and c and d are the intercept and slope of the marginal cost function, respectively. We draw the following trend, as illustrated in Figure 4.

Figure 4 Population Density and Network Externality of Marginal Transaction Benefit

Note: The horizontal axis is population density (100 persons per square kilometer), and the vertical axis is the network externalities of marginal transaction benefits (100 yuan per square kilometer).

In contrast, an increase in the population density also leads to pure cost increases, such as an increase in the costs of congestion externalities. Assume that the city is in the shape of a circle and that the commuting population lives outside the city and only enters the city when going to work or shopping. If we calculate according to the city’s highest population density within one square kilometer and consider the proportion of people living inside and outside the city, we can assume that there are Nin people (100 people) entering the city center. If the transport resource is the land that is covered by roads, we assume that the circumference of any radius of the circle from the center of the city is transport resources. When people move toward the city center, the radius distance from the city center decreases, and the circumference—the transport resources—also lessens, but the number of people has not decreased, which leads to congestion. The costs of congestion cannot be attributed to a single person but, rather, to the congregation of all traders who gather. Therefore, negative “externalities” exist that can be expressed as follows:

JE = Nin / [2(Nπ / n)0.5]*nh (for a detailed derivative process, please see Annex 2)

where JE is congestion externality, Nin is the number of people entering the city center daily (per square kilometer) and includes not only the employed but also external consumers; and H is the congestion coefficient, a number greater than 1. Congestion externalities change as the population density changes, as shown in Figure 5.

Figure 5 Population Density and Congestion Externality

Note: The horizontal axis is population density (100 persons per square kilometer), and the vertical axis is congestion externalities (100 yuan per square kilometer).

2. Equilibrium Scale and Population Density Distribution of Cities

Clearly, the equilibrium level of the population density brought by congregation, or the equilibrium level of a city’s population density, is determined by both market-network externalities of marginal transaction benefits and the costs of congestion externalities. That is, at different population density levels, market-network externalities (congregation benefits) minus congestion externalities (congregation costs) are what we call “congregation rent” (see Appendix 3 for the formulas), as shown in Figure 6.

Figure 6 Relationship between Population Density and Economic Benefits, as well as Optimal Population Density

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Note: The horizontal axis is population density (100 persons per square kilometer), and the vertical axis unit is 100 Yuan/square kilometers. The light blue line is the congestion rent curve.

Figure 6 shows that congestion rent increases with an increase in population density and begins to decline when reaching the maximum point. This relationship indicates that this maximum point is the optimum scale of urban population density.

“Optimal population density” is emphasized as not referring to the overall size of the city or the population density in all areas of the city. Instead, optimal population density refers to the population density of the city center. This model can provide both the population density in the city center but also the urban population density in any area of the city. In reality, the population density varies in different parts of the city. Generally, in a single-centered city, the population density is higher in areas closer to the city center and lower in areas closer to the edge of the city. Transforming these coordinates, with the horizontal axis as distance to the city center and the vertical axis as population density, the specific circumstance is shown in Figure 7.

Figure 7 Population Density and Distance to City Center

Note: The horizontal axis is the distance to the city center, and the vertical axis is population density. Figures in brackets are negative values.

The three-dimensional figure is shown in Figure 8.

Figure 8 Population Density and Distance to City Center (three-dimensional)

Practically, we use a city’s geographic data and our model to simulate a population density map. See Figure 9.

Figure 9 Single Center City Area Diagram

Note: This diagram is generated using ARCGIS software with data from EXCEL. Each small square represents a space of 100 meters x 100 meters. Different colors represent different population densities, with darker colors indicating higher population densities.

Given that the distribution of the population density is related to the economic variables, such as transaction benefits or congregation rent, the density distribution of these economic variables is quite similar. See Figure 10.

Figure 10 Economic Density and Distance to City Center

Note: The horizontal axis is the distance from the city center (km), and the vertical axis is economic densities (100 persons per square kilometer, yuan per square kilometer). Among them, producers’ network externalities and congregation rent and congestion externalities are set according to the left axis, whereas population density is set according to the right axis. Figures in brackets are negative values.

The distribution of population density and other economic densities presents the equilibrium density of various parts of the city and provides a possible forecast for urban planning. Meanwhile, by integrating the population density or other economic densities in various parts of the city, we obtain the aggregate data, that is, total population, total congregation rent, or total GDP. We also obtain the per capita or per area economic magnitude by dividing these total data.

In the previous analysis, we assume that a sufficient number of people exists around the city, and the supply of resources such as water is also abundant. However, in reality, this is not always the case, and we have found that some cities are large and some are very small, implying that different needs and resource constraints exist on premises with the same theoretical scale.

The so-called “demand constraint” for urban development refers to the demand of the population congregation for urban space. This constraint depends on the amount of peri-urban population as well as the city’s geographical location. In a sparsely populated area, even if urban space can be formed theoretically, it is impossible to form large cities. The scale of the city simulated by the previous analysis can be compared to a bottle, and the demand for urban space is water. The real scale of the city is determined by the water inside the bottle. Of course, if the water is beyond the space of the bottle, it will flow out to another bottle—another city.

Similarly, the resource constraint compares the city’s maximum scale at which resources around the city would be able to sustain with its theoretical scale, and selects the smaller of the two as the real “space supply.”

Therefore, if we want to determine the scale of a city in reality, we need to compare its theoretical scale subject to resource constraints, that is, the actual “space supply,” and its actual “space demand” and choose the smaller one as the actual scale.

3. Formation of the City

The power of the formation of urban congregation comes from the agents of the market economy, that is, individuals and institutions as economic agents. Figure 11 illustrates that the maximum value of per capita congregation rent is to the left of the maximum value of congregation rent as a whole. This comparison indicates that economic individuals have more motivation to gather in urban areas and, thus, become the main driving force for the development of a city congregation. In turn, the population density increases, especially before the maximum point, further encouraging people to gather in urban centers. This process is said to be of congregation and density increase as reciprocal causation.

Figure 11 Diagram of Congregation Rent and Per Capita Congregation Rent

Note: The horizontal axis is population density, and the vertical axis is congregation rent. The congregation rent is set according to the left axis, and the per capita congregation rent is set according to the right axis.

This diagram also shows that (1) when the per capita congregation rent passes the maximum value point, people still have the incentive to enter the city center because it is more competitive than other places despite the diminishing returns; and (2) when the per capita congregation rent is reduced to a certain level that is not enough to compete with other places, people lack the motivation to enter the city center and stop entering. At this time, the population density reached its maximum equilibrium levels.

From the derivative of congregation rent, we see more clearly that the increasing “speed” of the economic benefits is different as the population density increases. It starts slowly, then speeds up, and finally slows down. See Figure 12.

Figure 12 Congregation Rent and Derivative of Congregation Rent

Note: The horizontal axis represents population density, and the vertical axis represents congregation rent and its derivative. The congregation rent for producers is set according to the left axis, and the derivative of the congregation rent for producers is set according to the right axis.

If the amount of revenue directly corresponds to the intensity of the motives, this derivative curve for congregation rent is the time distribution of motives.

In general, the greater benefit an economic activity, the greater motives people have and the faster they move. We use this relationship to derive the speed of urban congregation—the development speed—to estimate the time distribution of urban development.

Assume that di/dn is the differential of economic benefits to population density and dn/dt is the differential of population density relative to time. Generally, the growth speed of population density and the change in economic benefits relative to population density is similar in terms of direction and speed. Therefore:

dn/dt = f(di/dn)

Simply put:

dn/dt = di/dn

We directly switch the coordinates of population density (n) with coordinates of time (t) as follows:

dn/dt = di/dt

The derivative of the congregation rent reflects changes in the population density relative to the changes in the congregation rent. Therefore, this derivative directly describes the density changes per unit time.

Figure 13 is the distribution of the population density in a new urban area of a city at different distances from the city center (including downtown) according to the time frame of 10 years.

Figure 13 Changes in Population Density in Different Locations over Time (unit: 100 persons per square kilometer)

Population Density

Note: The vertical axis represents economic density, and the horizontal axis represents time. Curves of different colors represent different locations from the city center in kilometers.

Figure 14 Annual Population Density across Center Point Unit: 100 persons per square kilometer

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Note: The horizontal axis is distance from the city center (kilometer), and the vertical axis is population density.

4. Industrial Distribution of the City

The layout of industries in the city includes the location of a certain industry and the relative position between one industry and another industry.

Factors determining the location of industries in the city include economies of scale, frequency of transactions, the nature of the face-to-face transactions, distance to the enterprises directly served, and demand for special resources (such as water, green space, and cultural resources). Among them, one of the important factors is the industry’s economies of scale. Masahisa Fujita and Krugman pointed out that people are less sensitive to economies with increasing returns of scale because its advantages mainly manifest as congregation (2005, p. 70); they also indicated that when the industry’s “fixed cost increases, the distance between cities will also increase; this indirectly reflects the amount of the fixed costs, which can be used to roughly measure the importance of economies of scale.”(2005, p. 150) In other words, higher industry economies of scale result in a higher the degree of congregation and the closer the industry should be to the city center. It should be pointed out that Masahisa Fujita and Krugman and others mainly refer to economies of scale of industrial establishments, whereas we discuss economies of scale of the transaction industry.

Specifically, the larger the average size of the enterprises in an industry, the more people it will provide services for—theoretically—and the closer it should be to the center of town. This theory is generally reflected in the bidding of the rent; that is, enterprises with greater economies of scale generate higher revenue in the city center (given the high population density); however, with the increasing distance from the city center, their revenues decline rapidly.

Economic descriptions of different industries mainly reflect the differences in the scales of their economies, demand and supply functions, market structure, and market scale.

Because demand and supply functions are difficult to obtain, this paper only does a rough estimate of these functions mainly to describe different industries with different scales of economies. The market structure is used to adjust the transaction costs; that is, the monopoly market structure has higher transaction costs than the competitive market structure. Scale is used to estimate the total size of the market.

Because the object of our study is the service industry, the supply function mainly reflects transaction costs.

The cost function for a general industry is as follows:

C(q) = F + vq

where F is fixed costs, v is variable expenses, and q is output. We can also use n to replace p, which is the number of people being served. That is:

C(n) = F + vn

More simply, we only consider the fixed costs as follows:

C(n) ≈ F

Large-scale industries have a greater F value, and the corresponding maximum number (n) of people served is also greater. Conversely, smaller-scale industries have smaller F values, and the maximum number (n) of people served that corresponds is also smaller. Specifically:

C(n) ≈ n / ñ * F

That is, when the amount of people in need of services exceeds the technical limits that a fixed asset is able to offer regarding those services, we need to invest in more of the same fixed asset.

According to Krugman and Masahisa Fujita, industries with greater economies of scale will be much more congregated. Thus, we obtain the spatial locations of different industries.

Assume that three industries exist, and their costs functions are as follows:

C1(n) ≈ n / ñ1 * F1
C2(n) ≈ n / ñ2 * F2
C3(n) ≈ n / ñ3 * F3

F1 > F2 > F3, ñ1 > ñ2 > ñ3

The congregation rent (CR) corresponding to each population density or spatial location (in this case, we assume that congregation rent and fixed costs are measured with the same time unit) separately divides the fixed costs of the three industries representing the asset scale (depreciation plus the return on the opportunity assets). We can obtain the unit asset’s return per unit area, which we refer to as return on assets or, in short:

Return on Industrial Assets (Ii) = CR / (n / ñi * Fi)

where i = 1, 2, 3,… represents industries. The unit is unit currency per unit asset per kilosquare meter.

This determines their degree of congregation and location in the city, that is, at any point where the industry with the highest return on assets should be distributed. At a certain place:

MAX(I1, I2, I3, …, Ii, …) = Ij, then Industry J should be located at this place.

See Figure 15.

Figure 15 Economies of Scale, Degree of Congregation, and Positioning of Three Industries

Note: The horizontal axis is the distance from the city center (kilometer), and the vertical axis is the return on assets of the industries. Different colors represent three different industries. At any point, industries with a higher yield (monetary unit/per unit asset/per square kilometer) should be distributed at this place.

In contrast, the relative position between industries is determined by the supply and demand relationship and the degree between them. We use the logistics, information, finance, trade, and technology services industries as examples. These industries are both suppliers and markets to each other; they are mutual penetrating, complementing, and reinforcing. According to the 2007 Chinese input-output table (National Accounts Division of the National Statistics Bureau, 2009), adjusting with the added value of 1 results in the input-output relations of five industries (the “Direct Consumption Coefficient”), as shown in Table 1.

Table 1 Direct Consumption Coefficient between Five Industries (with added value of 1)

The input-output relation in Table 1 is better reflected using the diagram in Figure 16.

Figure 16 Supply and Demand Relationship between Five Industries

In the diagram, the larger the ring with colored lines, the higher degree of interdependence this industry has with other industries. The diagram also indicates the following points:

1. Each industry has a high input-output relation with itself; for example, the input-output ratio of the finance industry with itself is up to 12.3%, that of the information industry is 10.2%, and that of the logistics industry is 6.6%. These percents describe the high input-output relationships with segments within industries. For example, in the finance sector, the securities industry and the banking industry have a close relationship, and information providers have more business relationships with the software industry.
2. Relative to other industries, the finance industry has a higher input-output relationship with the other industries category. In addition to its high input-output ratio with itself, the input-output ratio of the finance industry to the trade industry is 8.4%, to the information industry is 4.2%; and to logistics industry is 4.1%. Although the technology services industry does not need many financial services, its major clients—science and technology enterprises—have a very high demand for finance industry services, such as venture capital, bank loans, and issuing stocks and bonds in the securities market. Therefore, the finance industry should be in the central position according to either the economic logic or the space.
3. In second place is the information industry.
4. In contrast, the trade industry’s output has a relatively lower dependence on other industries, indicating that it has the characteristics of initial incentives and sources.

These analyses further strengthen the previous judgments made on economies of scale. We can use the actual data of a certain place as an example and draw up the spatial distribution of these industries, as indicated in Figure 17.

Figure 17 Industrial Distribution of an Urban Area

Given the diversification of the economic and technological characteristics of enterprises within an industry, that we can only use the average date to estimate the reasonable layout of the industry should be stressed. This statement precisely proves that this layout structure has no rigid boundaries. In practice, the business space in which most enterprises engage is in the form of an office building, which is universal and interchangeable. Therefore, overemphasizing borders between industries is not needed. Instead, enterprises should be encouraged to find their own locations based on market signals, which is more efficient.

5. Institutions and Policies that Promote Urban Development

Because cities form and develop through transactions, and the transaction is the basic unit of institutions (Commons, 1983, p. 73), institutions themselves determine the efficiency of transactions and, thus, affect the density and scale of a city. A combination point of institutional economics and spatial economics exists. In general, we can use transaction costs—strictly, unit transaction costs—to evaluate institutions. Under the same transaction utility, institutions with lower unit transaction costs have higher efficiency and vice versa (Sheng Hong, 1992, p. 152). Conversely, institutional innovation and technological innovation will, in turn, reduce transaction costs, which will also promote transactions and contribute to the formation and development of the city.

In this paper, we discuss institutional innovation. Institutional change or innovation includes many aspects, the most important of which is the protection of property rights, the safeguarding market order, and fair adjudication of disputes. Normal market order includes the freedom to access the market, fair competition, and the elimination of monopolies. Here, the market includes both the product market and the factor market.

From a market perspective, we can divide transaction costs into two types. One is transaction costs that are market-oriented, can be measured and traded by currency and are managed by professionals or businesses; these are expressed as the incomes of those professionals and enterprises’ revenues, including also government taxes. The other type of transaction costs is the nonmarket costs that, at least for the time being, cannot be measured in monetary terms, and no professionals or businesses exist to manage these costs. The main reflection is the time and trouble of dealing, which reduces transaction volume and, thereby, reduces the economic density and scale of the city. See Figure 18.

Figure 18 Two Types of Transaction Costs

Note: In the diagram, S is the supply curve excluding transaction costs, and TC2 is the supply curve of nonmarket transaction costs added to the supply curve. When counting nonmarket transaction costs, the price increases from P0 to P0+TC2, and transaction volumes are reduced from Q0 to Q (TC2). The TC1 curve is the curve of market transaction costs, which decrease as producer surplus decreases and, eventually, confluences with supply curve S at the equilibrium point. No negative impact occurs on the price and trading volumes. When nonmarket transaction costs (TC2) are replaced by market transaction costs, transaction volumes increase from Q (TC2) to Q0.

Market-oriented transaction services can replace the time loss and trouble of nonmarket services, the unit transaction costs of which are significantly lower than those of nonmarket transaction services. Moreover, only completed transactions are charged, such as commissions. If not completed, fees are not charged. In addition, ad valorem taxes or fees are only charged after the transaction is completed in proportion to their income, such as sales tax and income tax, and the income of services personnel can also form market demand without reducing average transaction volumes. Nonmarket transaction activities have the characteristics of time and trouble, which potentially affect the realization of the transaction, thereby reducing transaction volumes. An increase in aggregate market-oriented transaction costs indicates that market-oriented transaction services replace nonmarket transactions, increasing efficiency and transaction volumes. See Figure 18.

Overall, with the development of the market system, the ratio of aggregate market-oriented transaction costs to GDP probably increases and nonmarket transaction costs decline. See Figure 19. According to the estimate from North et al., total transaction costs in the United States are increasing in the long run (Wallis and North, 1986, pp. 95–162). This increase is occurring probably because, first, institutional and technological changes in modern times reduce unit transaction costs and increase the transaction volumes. Second, more nonmarket transaction activities are improved into services provided by the market and, thus, can be incorporated into the currency calculation. The estimate of North et al. in fact refers to market-oriented transaction costs. This estimate also indicates that the market system can promote the monetization and professionalization of transactions and, meanwhile, save time and reduce problems in transactions.

Figure 19 Aggregate Transaction Costs of China, Nonmarket Transaction Costs, and Transaction Costs of Transaction Sector

Source: Jin Yuguo, Dec 2006; Da Fengyuan, Zhang Weidong, 2009.

Note: TC is the aggregate amount of transaction costs, and NTC is nonmarket transaction costs.

Conversely, we can determine whether institutional efficiency has been improved simply by examining nonmarket transaction costs, which should decline if institutional reform was conducted. This relationship has been proven by numerous facts. Since the reform and opening up of China, the ratio of nonmarket transaction costs to GDP has been declining (Da Fengyuan and Zhang Weidong, 2009). Intuitively, large nonmarket transaction costs affect the amount of transaction benefits and further exert a stronger impact on transaction volume similar to a lever, which will ultimately hinder the increase in urban economic density and equilibrium scale. Therefore, the decline in nonmarket transaction costs indicates that market-oriented services and transaction volumes increase. As a result, urban density and scale will be increased.

In particular, when calculating the balanced urban economic density and scale, the congregation rent per unit of time minus the nonmarket transaction costs are used. Changes in the latter lead to changes in the urban equilibrium economic density and scale and eventually lead to changes in the aggregate economy. In our model, we could simply simulate the results of changes to the aggregate GDP by adjusting nonmarket transaction costs.

In 2007, China’s nonmarket (nonmonetary) transaction costs accounted for 24.8% of the GDP (Da Fengyuan, Zhang Weidong, 2009), or approximately 22% of the GDP after deducting the transaction costs associated with transportation. Taking these data into account, we use the estimated development of a specific urban area as an example. Assume that under the existing system, noncommercial transaction costs are approximately 22% of the GDP. If we continue to promote market-oriented reforms and reduce the institutional barriers for factors flow, the nonmonetary transaction costs are reduced by 8% in 15 years, reaching 14% (of the GDP). In addition, the speed of institutional change in 15 years has been even. The impact on GDP simulated by our model is shown in Table 2.

Table 2 Impact of Institutional Change on GDP
GDP under Current Institution GDP under Institutional Change Institutional Impact (%)

Figure 20 Impact of Institutional Change on GDP

Figure 20 illustrates that institutional changes can result in irreversible and sustained economic growth. Compared with policies, the impact of institutional change is longer term and more stable, and accumulates. The longer it takes, the more significant the impact of institutional change will be.

Under the premise that the market system is the basic system for urban development, market failures occur in urbanization and industrial development, including the following:

1. Lack of forecast for the vision of urban development and the final equilibrium scale;
2. Difficulty bearing the advanced financial costs of large-scale urban infrastructure investments;
3. Unable to generate valid intellectual property rights and protect and enforce them effectively;
4. The investments in science and technology innovation are smaller than the investments made when the government intervenes;
5. The congregation speed is slow when it has not reached the tipping point; and,
6. Lack of motivation and means of implementation for collaboration between enterprises within an industry.

For some of the market failures, governments can use corresponding policies as remedies, including the following:

1. The favored policy at start-up;
2. The house rent allowance policy;
3. Policies on transaction cost allowances; and,
4. Policies promoting industrial alliances and association development.

For the content and analysis of the impact of these policies, please see Annex 4.

These policies can be implemented simultaneously and have cumulative or even integrated effects. Table 7 presents our summary and cumulative effects of various policies.

Table 7 Summary and Cumulative Effects of Policies Unit: 100 million yuan
Original GDP Initial Promoting Polices GDP Transaction Costs Allowance GDP Housing Rent GDP Transaction Costs Saved by Coalition GDP Aggregate Effects of All Policies GDP Policy Impact (%)

Figure 21 Overall Effects of Policies Unit: 100 million yuan

Overall, compared with the urban development mechanism and institutional change, the role of policy is smaller. Policy has a larger role only in the early stage of development, which has gradually declined over time. Therefore, prudent and appropriate implementation of policies and putting more effort into improving the market system and promoting businesses and residents to participate in the market is the best way for the government to promote urbanization.

6. Conclusion

Transactions can form cities, and an analysis of transactions can help improve urban economics and spatial economics theory. On the basis of the transaction analysis, we found that constructing a theory of cities is not difficult and can better explain their formation and development.

This finding is because the economic variables and their characteristics involved in transactions, such as market-net externalities, have a more congregation nature than economies of scale in production. Put another way, these variables lead to more pronounced congregating results.

The analyses of transactions (omitting the analysis of production costs) focus only on transaction costs. The basic methods of analysis compare transaction costs and transaction utility (or transaction benefits) and identify the dynamic characteristics of which transaction utility is higher than transaction costs, thus further identifying the dynamic characteristics of urban spatial congregation.

Analyzing only transaction costs is within the field of institutional economics because institutional economics believes that the transaction is the basic unit of an institution, and transaction costs and transaction utility are important concepts in the analysis of institutions. Here, spatial economics and institutional economics overlap and generate organic links.

The conclusions of this paper are as follows:

1. The underlying cause of urban congregation is the growth in market network externality benefits, which is caused by the growth in population density but is faster than the latter.
2. Two main factors counteract congregation. One is the diminishing marginal utility and increasing marginal costs resulting from the increase in the scale of the market, and the other is the increase in congestion externalities costs.
3. Congregation rent is the difference in (by diminishing marginal transaction benefits) the market’s corrected network externalities and congestion externalities costs. When the congregation rent reaches the maximum point given an increase in population density, in theory, the city’s population density reaches its maximum balance.
4. Other constraints on the scale of the city are the demand for urban space and resources.
5. The subjects of urban congregation are individuals or enterprises; because the per capita congregation rent has a variation feature that it arrives sooner than the aggregate congregation rent to the maximum points, first, economic individuals have at least an early motivation to promote congregation, namely, to promote urbanization; second, the congregation rent of individuals declines after the maximum point, indicating that economic subjects represent the major force that brings the city automatically to the stable equilibrium points.
6. Because the individual’s motivation is proportional to how much he earns, the speed of action is also proportional to the motivation. We can simply use a derivative of congregation rent to approximately estimate the congregation process and the economic density distribution.
7. Industries with larger economies of scale have higher degrees of congregation; therefore, by comparing the return on assets of different industries at the same place, we will be able to identify the most suitable industry for the location.
8. Urban development has a close relationship with transactions and transaction costs and a very close relationship with institutional innovation. Therefore, to promote institutional change, particularly centrally planned economies promoting market-oriented reform, market-oriented reform should be further promoted. Institutional change has an increasingly significant impact on urban development.
9. Because market failures occur during the process of urbanization, policies implemented by the government to address these market failures will also promote urbanization. However, on the one hand, the influence is notable in the early stages but decrease later. On the other hand, compared with institutional change, the impact of policy is not very significant.

Appendix 1 Derivation of Market-Network Externalities Considering Diminishing Marginal Transaction Benefits

The aggregate demand function of the entire society relative to the population density: Marginal Utility = a – b * n

The aggregate supply function of the entire society relative to the population density: Marginal Costs = c + d * n

Marginal Transaction Dividends = Marginal Utility – Marginal Costs = (a – b *n) – (c + d * n) = (a – c) – (b + d) * n

Network Externalities of Marginal Transaction Benefits (CE) = ∑Marginal Transaction Benefits * (ME(n) – ME(n – 1))
= ∑((a – c) – (b + d) * n) * [n(n – 1) / 2 – (n – 1)(n – 2)/2]
=∑((a – c) – (b + d) * n) * (n – 1)
≈∑((a – c) – (b + d) * n) * n
=∑((a – c) n – (b + d) * n2)

n = 1, 2, 3, …

Appendix 2 Derivation of Congestion Externalities Formula

Assume that the city is a circle, and the commuting population lives outside the city and enters the city when going to work or shopping. According to the city’s highest population density per square kilometer and considering the proportion of people living in and outside the city, we assume that Nin (100 people) enter the city center from outside. The transport resources are the areas covered by roads, and transport resources are assumed to be the circumference of the circle of any radius from the center of the city. When people move from outside to the city center, the radius to the center is smaller, and the circumference (transport resources) is decreasing, but the number of people is not reduced, which leads to congestion. See the following figure.

Assume that the number of people entering the city to the total number of people in a square kilometer of the city center is a ratio (Nt); then, the number of commuting people entering the city is as follows:

Nin = Nt * N (per square kilometer)

Unit Transport Resources Capacity = Nin / [2π (N / πn)0.5] = Nin / [2(Nπ/n)0.5]

In fact, obtaining the population per square meter in a downtown area is very difficult because, in the absence of data for congestion externalities, we cannot determine the city center at equilibrium and its population density. Nonetheless, in the end, multiple iterations can achieve this information.

However, the congestion has not only linear proportional relations to the reduction in the number of transport resources per capita but also nonlinear reduction relations. Therefore, we need to add an index associated with population density, which we call the congestion coefficient, and it is represented by h:

Congestion Externalities = Nin / [2(Nπ / n)0.5] * nh

Appendix 3 Formula for Congregation Rent

Congregation Rent(CR) = CE – JE = [(a – c) – (b + d) * n / 2](n * (n – 1)/2) – Nin / [2(Nπ / n)0.5] * nh

Appendix 4 Analyses of Policy Effects

1. Policy Promotion at Startup

As previously mentioned, when the economic density is low, the market-led congregation speed is slow; only when the density reaches a certain point will the effects of the market increase. Therefore, if during the startup stage the government promotes urban districts to cross the tipping point earlier through policy and other operations, such as utilizing its influence to attract direct investments and to move in public institutions, doing so would also develop the city. However, this governmental role should not be overestimated. Table 1 assumes that, through government policies and operations, an urban district reaches 3000 people per square kilometer at the outset of economic development, and the contrast situation is one without these promotional procedures.

Table 1 Policy Effects by the Government’s Initial Promotion Unit: 100 million yuan
Original GDP Initial Promoting Policies GDP Policy Impact (%)

Figure 1 Policy Effects by the Government’s Initial Promotion Unit: 100 million yuan

This chart shows that the government’s initial push has an obvious impact in the first years, reaching up to a maximum of 55% of the GDP (2013). However, it decreases later and has almost no effect after 10 years. Additionally, in this model, we do not count the cost of government promotion in industrial congregation policy.

2. Housing Rent Subsidy Policy

To facilitate the industrial congregation planned, the government can adopt policies to subsidize housing rents or prices. Beijing Financial Street subsidies 1000 Yuan/square meter to attract financial firms.

We will consider a 10% subsidy of the housing rates, which is also equivalent to a permanent 10% rental subsidy. Table 2 and Figure 2 represent the effect of the housing rent subsidy policy.

Table 2 Effects of Housing Rent Subsidy Policy Unit: 100 million yuan
Original GDP Housing Rent Subsidy GDP Policy Impact (%)

Figure 2 Effects of Housing Rent Subsidy Policy Unit: 100 million yuan

Figure 2 shows that, although the impact of subsidizing rent is not very significant—usually at approximately 4%~5%—its effects last long and eventually bring a certain increase in total GDP.

3. Policies Subsidizing Transaction Costs

Administrative departments may establish related funds to subsidize transaction costs, namely, by providing subsidies to each transaction procedures, including the following:
Applications for intellectual property rights;
Technical standards;
Venture capital investment;
Open of the laboratory;
Incubation;
Credit rating;
Loan;
Mediation services;
Public offerings;
Purchasing information products;
Bringing up intellectual property litigation;
Establishment of information system; and
Others.

We assume that the policy on subsidizing transaction costs is implemented for 10 years. The government stops the policy’s implementation after the incubation of mature intermediary service institutions and intermediary service markets have grown up. The effect of the policy is as follows.

Table 3 Effects of Policy Subsidizing Transaction Costs Unit: 100 million yuan
Original GDP Subsidizing Transaction Costs GDP Policy Impact (%)

Figure 3 Effects of Policy Subsidizing Transaction Costs Unit: 100 million yuan

Figure 3 shows that, during the first few years, the effect of policies subsidizing transaction costs is significant, at up to 57% in 2013 and 30% in 2014. It then gradually decreases but still maintains a relatively significant influence. The effect is significantly higher than the government inputs of subsidies for transaction costs (2% of the GDP). Until 2021, the effect undergoes minor fluctuations after the subsidy policy is stopped.

4. Policies Promoting Industrial Alliance and Association Development

The administrative departments may lead or support enterprises or civil organizations to establish industrial alliances or associations or to support these industries by purchasing their products. The supporting policy can be implemented for 10 years. After that, industry alliances and associations develop and operate by themselves. The assumption is that the results of this policy reduce transaction costs (1% of total value added).

The effects of policies are as follows.

Table 4 Effects of Policies Promoting Industrial Alliances Unit: 100 million yuan
Original GDP Transaction Costs Saved by Industrial Alliances GDP Policy Impact (%)

Figure 4 Effects of Policies Promoting Industrial Alliances Unit: 100 million

Figure 4 shows that this policy has played a role; however, relative to other policies, the effect is not significant but is very efficient compared with the input. Furthermore, this result is only a static analysis. From a dynamic perspective, if this policy develops relatively mature industry associations and industry alliances, it will bring long-term benefits.

References

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藤田昌久，克鲁格曼和维纳布尔斯，《空间经济学——城市、区域与国际贸易》，中国人民大学出版社，2005。(Translated from: Masahisa Fujita, Krugman, Paul and Venables, Anthony J., The Spatial Economy–Cities, Regions and International Trade, The MIT Press, 1999)

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Author: flourishflood

Economist, Confucianist View all posts by flourishflood