1. D IFFERENTIATION IN P OLICE S ERVICES I N C ITY N EIGHBORHOODS Tchai Tavor, Uriel Spiegel, Simon Hakim, Erwin A. Blackstone

2. Background Tiebout explained variations in the mix of local public services by households moving to or within an area choosing the community that best meets their preferences. This creates within a metropolitan area communities with various combinations of public services which yields higher social welfare than uniformity throughout the area. However, variation in preferences towards any specific service will still exist. What can households do to improve their own position given what their local government already provides?

3. Our Conceptual Model Our model considers welfare gained by additional private supply of public goods when preferences differ among households already located in a given community. The analysis is applied to police services supplemented by various types of private provision.

4. The Theoretical Model The question is whether we consider public security like police patrol as a pure local public good that should be financed by government through tax revenues, or should public security be privatized and financed by payments of private individuals.

5. Assumption: Let us assume that in the market we have N identical consumers whose identical demand to the public security, G, is as follows: (1) for all i = 1,……,N. The aggregate demand of the market for G can be derived by vertical summarization: (2) Case 1

6. Assuming a linear cost function of G with marginal cost per unit, C, the cost function is: (3) According to the simple Lindhal solution for pure public good we can find the optimal value of G as follows: (4)

7. From (3) – (4) we get: (5) Or, we can find the optimal value of G: (6) From (6) and (5) we can measure the total consumer’s surplus, TCS, as follows: (7) For simplicity of presentation we assume further that α = 1.

8. Case 2 Assumptions In the following case we assume heterogeneous customers that on average the representative consumer I, has the same demand for G as at case 1. The demand curves of all N consumers are rectangular (uniformly) distributed.

9. The demand of any consumer i is defined as (8) below: (8) Since we face some consumers with very low reservation price that is equal to, for specific consumer I, it is possible to gain disutility from certain level of G demonstrating negative consumers’ surplus.

10. Therefore we can introduce the demand curves for different value of G as follows: (9)

11. In more general terms we can write the equations of (9) in reduced forms as: (9’) We assume that government ignores the differences in preferences, and treats identically all constituents, like in case 1,.

12. and charges all customers the equal cost sharing burden as follows: (10) For any customer we can define his consumer surplus as: (11)

13. Therefore the total consumers’ surplus in case 2 is: (12)

14. Comparing TCS1 to TCS2 We conclude that since

15. Case 3 We now extend case 2 assuming the same demand distribution. N/2 customers are satisfied with the public supplied quantity of G0. Other customers, N/2, are willing to add additional units of private security that might be supplied as supplement in order to increase their consumer surplus.

16. In this case we allow more flexibility in consuming security either by consuming pure public goods shared by all customers or by extra/additional private security, PS, provided individually/privately by part of the population with high reservation prices. We use several assumptions for the extension of case 3. a. A public good and a private good are full substitutes b. C, per unit cost, for the private and public good are the same c. The burden of a public good is shared equally, but private security is totally paid as a private and individual burden

17. Consumer Surplus: Case 1

18. Consumer Surplus: Case 2

19. Consumer Surplus: Case 2, 3 demands

20. Consumer Surplus Cases 2, and 3

21. At equilibrium we can measure the quantity demanded for private security of the highest demand customer that is as follows: (13) Since P=C we find the highest PS of this customer as follows:

22. For each customer i, the "leftover" demand for the private security, PS, is obtained as follows: (14) From (14) we find that PS, the demand for extra private security for each customer i, is: (15)

23. The extra welfare resulting from the purchase of private security as supplement to the optimal public security, G0 as follows: (16) Therefore the extra welfare obtained by private security supplement is: (17)

24. The PS of the highest demand customer for private security is The next is customer The last customer who prefers only the pure public security without any extra private supplement is customer i=

25. Thus, the total private security supplement units TPS, are: (18) The ratio "mixture" between the two kinds of security units is: (19)

26. Comparative static analysis: Case 3

27. Implications for Supplementing Public Police In reality there is significant supplementation in the forms of: 1. Private police 2. Volunteer efforts 3. Self protection 4. Property insurance 5. Protection design

28. Private Police In the US private police number more than 3 times the combined federal, state, and local law enforcement agents. In order for households and/or businesses in a neighborhood to feasibly supplement public police, and prevent “free ridership”, residents vote by majority rule to tax themselves for private patrol. Examples include Philadelphia, Chicago and New Orleans. Gated communities include households of similar and usually higher income & security preferences than others in the locality. Examples include the US, Mexico, Brazil, and South Africa in places of high income and wealth disparity.

29. Volunteer Efforts This category includes neighborhood watch, safety control committees in apartment complexes, auxiliary volunteer police officers, and safe haven homes. Volunteer efforts are significant in the US and the UK. In the UK in the early 2000, 27 percent of total population lived in areas covered by Neighborhood watch; In the US 41 percent.

30. Self Protection This category includes deterring, prevention, and detection measures held by individual households as supplement to public police. Burglar alarms appear in the US appear to be a more effective measure for property security than all others combined. Burglar alarms are shown empirically to involve high income elasticity.

31. Property Insurance This is a supplement private measure to recover the monetary losses resulting from crime. Interestingly, the extent of private versus public security used, and the relative use of each private security measure depends upon the relative prices. We could expect that households choose rationally the quantities of the private measures. However, the implicit price of public police may distort the socially optimization process.

32. Environmental Design Oscar Newman in his two seminal books discusses how the physical layout of the community can reduce crime and hence becomes a supplement to public police. His premise is that by creating observable inner hallways and common areas, and external access paths, security is enhance security.

33. Conclusions This paper extends the Tiebout model by supplementing private security services to existing public police and thereby raise social welfare. The model allows for different preferences of individuals and groups in the community. Allowing private choices in augmenting public police is shown to enhance social welfare.