Transactions and Cities

Abstract

The main objectives of this chapter 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 non-market 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.

This chapter reflects the author when taking charge of an urban planning project under the auspices of the Unirule Institute.

Translated from Research of Institutional Economics (《制度经济学研究》), Volume 41, Issue 3, 2013

Appendices

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

$$ {\displaystyle \begin{array}{l}\mathrm{The}\ \mathrm{aggregate}\ \mathrm{demand}\ \mathrm{function}\ \mathrm{of}\ \mathrm{the}\ \mathrm{entire}\ \mathrm{society}\ \\ {}\mathrm{relative}\ \mathrm{to}\ \mathrm{the}\ \mathrm{population}\ \mathrm{density}:\mathrm{Marginal}\ \mathrm{Utility}=a-b\ast n\end{array}} $$

$$ {\displaystyle \begin{array}{l}\mathrm{The}\ \mathrm{aggregate}\ \mathrm{supply}\ \mathrm{function}\ \mathrm{of}\ \mathrm{the}\ \mathrm{entire}\ \mathrm{society}\ \\ {}\mathrm{relative}\ \mathrm{to}\ \mathrm{the}\ \mathrm{population}\ \mathrm{density}:\mathrm{Marginal}\ \mathrm{Costs}=c+d\ast n\end{array}} $$

$$ {\displaystyle \begin{array}{l}\mathrm{Marginal}\ \mathrm{Transaction}\ \mathrm{Dividends}=\mathrm{Marginal}\ \mathrm{Utility}\hbox{--} \mathrm{Marginal}\ \mathrm{Costs}\\ {}\kern19.75em =\left(a\hbox{--} b\ast n\right)\hbox{--} \left(c+d\ast n\right)=\left(a\hbox{--} c\right)\hbox{--} \left(b+d\right)\ast n\end{array}} $$

$$ {\displaystyle \begin{array}{l}\mathrm{Network}\ \mathrm{Externalities}\ \mathrm{of}\ \mathrm{Marginal}\ \mathrm{Transaction}\ \mathrm{Benefits}\ \left(\mathrm{CE}\right)\\ {}=\sum \mathrm{Marginal}\ \mathrm{Transaction}\ \mathrm{Benefits}\ast \left(\mathrm{ME}(n)\hbox{--} \mathrm{ME}\left(n\hbox{--} 1\right)\right)\\ {}=\sum \left(\left(a\hbox{--} c\right)\hbox{--} \left(b+d\right)\ast n\right)\ast \left[n\left(n\hbox{--} 1\right)/2\hbox{--} \left(n\hbox{--} 1\right)\left(n\hbox{--} 2\right)/2\right]\\ {}=\sum \left(\left(a\hbox{--} c\right)\hbox{--} \left(b+d\right)\ast n\right)\ast \left(n\hbox{--} 1\right)\approx \sum \left(\left(a\hbox{--} c\right)\hbox{--} \left(b+d\right)\ast n\right)\ast n\\ {}=\sum \left(\left(a\hbox{--} c\right)\ n\hbox{--} \left(b+d\right)\ast {n}^2\right)n=1,2,3,\dots \end{array}} $$

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 N_in (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 (N_t); then, the number of commuting people entering the city is as follows:

$$ {\mathrm{N}}_{\mathrm{in}}={\mathrm{N}}_t\ast \mathrm{N}\ \left(\mathrm{per}\ \mathrm{square}\ \mathrm{kilometer}\right) $$

$$ {\displaystyle \begin{array}{l}\mathrm{Unit}\ \mathrm{Transport}\ \mathrm{Resources}\ \mathrm{Capacity}\\ {}={\mathrm{N}}_{\mathrm{in}}/\left[2\pi\ {\left(\mathrm{N}/\pi n\right)}^{0.5}\right]={\mathrm{N}}_{\mathrm{in}}/\left[2{\left( N\pi /n\right)}^{0.5}\right]\end{array}} $$

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 non-linear 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:

$$ \mathrm{Congestion}\ \mathrm{Externalities}={\mathrm{N}}_{\mathrm{in}}/\left[2{\left( N\pi /n\right)}^{0.5}\right]\ast {\mathrm{n}}^h $$

Appendix 3: Formula for Congregation Rent

$$ {\displaystyle \begin{array}{l}\mathrm{Congregation}\ \mathrm{Rent}\ \left(\mathrm{CR}\right)=\mathrm{CE}\hbox{--} \mathrm{JE}\\ {}=\left[\left(a\hbox{--} c\right)\hbox{--} \left(b+d\right)\ast n/2\right]\left(n\ast \left(n\hbox{--} 1\right)/2\right)\hbox{--} {\mathrm{N}}_{\mathrm{in}}/\left[2{\left( N\pi /n\right)}^{0.5}\right]\ast {n}^h\end{array}} $$

Appendix 4: Analyses of Policy Effects

6.1.1 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 6.4 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 (Fig. 6.22).

Table 6.4 Policy effects by the government’s initial promotion (unit: 100 million yuan)

Fig. 6.22

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 ten years. Additionally, in this model, we do not count the cost of government promotion in industrial congregation policy.

6.1.2 Housing Rent Subsidy Policy

To facilitate the industrial congregation planned, the government can adopt policies to subsidize housing rents or prices. Beijing Financial Street subsidizes 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 6.5 and Fig. 6.23 represent the effect of the housing rent subsidy policy.

Table 6.5 Effects of housing rent subsidy policy (unit: 100 million yuan)

Fig. 6.23

Effects of housing rent subsidy policy (unit: 100 million yuan)

Figure 6.23 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.

6.1.3 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 ten 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 6.6).

Table 6.6 Effects of policy subsidizing transaction costs (unit: 100 million yuan)

Figure 6.24 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.

Fig. 6.24

Effects of policy subsidizing transaction costs (unit: 100 million yuan)

6.1.4 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 ten 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 6.7).

Table 6.7 Effects of policies promoting industrial alliances (unit: 100 million yuan)

Figure 6.25 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.

Fig. 6.25

Effects of policies promoting industrial alliances (unit: 100 million)