Substitution Between Public and Private Goods: an Overview of the Market Meeting Consumer Preferences

Charles L. Vehorn, U.S. General Accounting Office and Georgetown University
ABSTRACT - It has often been suggested that a consumer may substitute private goods for public goods that are not provided at the consumer's desired level, but until recently research had not been undertaken on the degree of substitution. This paper presents an overview of the public-private substitution question, dealing with how researchers conceptualize the issues and how they attempt to observe consumers registering preferences.
[ to cite ]:
Charles L. Vehorn (1981) ,"Substitution Between Public and Private Goods: an Overview of the Market Meeting Consumer Preferences", in NA - Advances in Consumer Research Volume 08, eds. Kent B. Monroe, Ann Abor, MI : Association for Consumer Research, Pages: 523-526.

Advances in Consumer Research Volume 8, 1981      Pages 523-526


Charles L. Vehorn, U.S. General Accounting Office and Georgetown University

[The author wishes to thank Gary C. Anders for his helpful comments and suggestions. Views expressed in this paper are solely the author's and not necessarily the GAO's.]


It has often been suggested that a consumer may substitute private goods for public goods that are not provided at the consumer's desired level, but until recently research had not been undertaken on the degree of substitution. This paper presents an overview of the public-private substitution question, dealing with how researchers conceptualize the issues and how they attempt to observe consumers registering preferences.


Many local officials make budgetary decisions based on the implicit assumption that the government has a monopoly on the provision of standard public services. However, this assumption that the government alone possesses the means to meet the preferences of citizen-consumers is often inaccurate. Instead, a number of private substitutes for public goods exist, although they may not be perfect substitutes. Thus, local decisions based on the monopoly assumption can lead to an inefficient allocation of public resources.

One fundamental difference between public and private provision is the way in which goods and services are rationed. When goods and services are provided in the private sector consumers and producers signal each other through the market process. If consumers, for example, desire more of a particular good, they bid up the price letting suppliers know it is advantageous to increase production. Consumers register changes in their preferences through this market mechanism and resources are allocated more efficiently to meet those new preferences.

In the public sector, on the other hand. middlemen drive a wedge between consumers and producers. These middlemen, whether elected or appointed public officials, have the authority to control the production process through their budgetary decisions. Thus the amount provided may vary from the amount that would have been supplied under market rationing. Because of non-market rationing and the collective nature of public goods many citizens are left dissatisfied, especially in communities where voters have heterogeneous preferences. This dissatisfaction creates incentives for a private market to spring up and fill the void. The mere existence of private substitutes for public goods indicates the market is working to meet consumer preferences.

The primary purpose of this paper is to present an overview of the public-private substitution process. First, a Lancasterian perspective is employed to provide an underlying conceptual framework for discussing the potential range of substitution (1966). Than a brief review of collective goods and their demand is given to introduce a more detailed treatment of recent attempts to observe consumers registering their preferences between public and private goods in the markets for police protection, fire protection, and education. The paper concludes by pointing out how further research in this area could provide information to aid public policy makers, who must decide how to allocate the public's scarce resources efficiently.


In a narrow sense of the word, substitution is simply the process of purchasing one commodity in place of another. This definition, however, fails to account for all those commodities that are not perfectly substitutable. Many commodities are closely related, yet in the eyes of the consumer not perfect substitutes, or for that matter perfect complements. It is perhaps useful to view pairs of goods as lying on a continuum according to how closely they are related. At one extreme are perfect substitutes, at the other perfect complements. In the middle are independent commodity pairs. In between either extreme and the middle is a wide range of closely related goods with some degree of substitutability or complementarity. Consumers do not make an either-or choice with these closely related goods, but select a commodity bundle with a desired mix, depending on prices, income, and tastes.

A key and sometimes neglected issue in discussing substitutability is the definition of a commodity. The traditional approach is to define a commodity as simply the physical item or service purchased -- a hamburger, a shirt, a glass of beer. If consumers desire commodities defined in this general way, it becomes difficult to explain why some consumers will drink only one particular brand of beer. If a beer is a beer, then there should be perfect substitution between brands. However, each brand of beer has its own particular taste, so consumers who are loyal to only one brand of beer are saying no other taste can substitute for the taste of my brand of beer. Thus the traditional approach to consumption overlooks the relationship between the purchase of goods and the purchase of attributes that are inherent in the goods.

A new approach to consumption, formally developed by Lancaster, specifically recognized that goods purchased in the market usually yield more than one well defined service. So it is reasonable to argue that consumers desire the satisfaction of a commodity's services or attributes when they make a market purchase. When consumers purchase housing they desire attributes like space, in the number and size of rooms, and location, with easy access to schools, transportation routes, and recreational facilities. Another example of a good with multiple attributes is the running shoe. When runners purchase shoes they are buying a series of attributes, some of which have only become available in the last few years through technological innovation. The attributes include flexibility, sole wear, rearfoot impact, forefoot impact, weight, rearfoot control, and traction.

Thus the new approach to consumer theory made attributes the object of choice by simply placing desired attributes instead of commodities into the utility function, and assuming an additive linear relationship between the two,

zi = Ej bijqj   (1)


zi = the attributes desired by consumers (i = 1, Y., m)

qj = the quantities of public and private goods (j = 1, Y., n)

bij = the amount of attribute i possessed by a unit of commodity j.

It can be shown that the new approach includes the traditional approach by writing equation (1) in matrix form

Z = BQ   (2)

where Z and Q are (m x 1) and (n x 1) column vectors respectively, and B is the (m x n) consumption technology matrix. Now if m = n and the B matrix is diagonal with bii > 0 for all i and bij = 0 for i j, then the new approach collapses to the traditional approach with s one-to-one relationship between zi and qj.

One important insight of the new approach to consumer theory is that changes in relative prices may result in a switch from one bundle of commodities to another because the former becomes an inefficient way to attain the desired attributes. Lancaster called this the efficiency substitution effect, which is different from, but reinforces the personal substitution effect in the traditional theory of consumption.

The efficiency substitution effect may be operative in substitution between public and private goods. Because of the nature of collective goods, which will be discussed more thoroughly in the next section, individual voters may desire more or less of the public service, i.e., under the new approach more or less of the public good's attributes. This dissatisfaction with public provision leaves the consumer with basically four options. The consumer can form a lower-level government, migrate from the locality, seek help from voluntary organizations as extra-governmental providers of collective goods, or resort to private market alternatives. The first three options imply high transaction costs, but the last option has relatively low transaction costs associated with the search for an acceptable substitute.

Even though private market alternatives exist, they are often far from perfect substitutes for public provision. In fact, as the following examples supplied by Weisbrod indicate, these goods are generally different in form from public goods (1975). If the provision of clean air is inadequate one can substitute air filters and purifiers in the home or work place. Consumers or firms can also substitute sprinkler systems for public fire protection; and locks, alarms, guns, watchdogs, or guards for public police protection.

Public police protection is an interesting example of a good with several attributes. Consumers desire crime prevention, protection activity, and a feeling of security. If the public sector does not provide the desired amount of these attributes, citizen-consumers can purchase various goods in the private market to increase protection and provide a better sense of security. These private market alternatives nay be poor substitutes for policemen when it comes to apprehending a criminal, but a watchdog or burglar alarm enhances the sense of security. The private-good substitutes may be costly, but they give the consumer a degree of personal control, which is lacking in most public goods. The purchaser directly controls the watchdog or alarm for his own personal well-being. Collective goods by their non-excludable nature cannot provide this sense of individual ownership and control. In general, there are few private goods that are perfect substitutes for public goods, but the range of substitutability is wide and many private goods possess the same attributes found in public goods.


Public goods are distinct conceptually from private goods because public goods have a non-excludable and a non-exhaustible nature. A private country club, for instance, can exclude consumers from enjoying its recreational facilities, but a public park is shared by all citizens who desire to use it. The recent influx of Cuban refugees into Florida certainly caused a temporary strain on many private goods like food and clothing as suppliers' inventory became exhausted, but additional consumers cannot exhaust the supply of a "pure" public good, like national defense.

Most local public goods, however, have both private and public good characteristics. The use of a road is shared with other drivers, and due to congestion, a certain rivalryness in consumption occurs. A public fire department does not exclude homeowners from protection, but it cannot simultaneously extinguish fires in separate locations because its resources are constrained. Thus studies of the demand for local public goods must incorporate this aspect of congestion into the analysis. The way Borcherding & Deacon (1972), Bergstrom & Goodman (1973), and others did this was to use a median voter demand model specifying the public good in terms of a crowding function.

Consider the total physical quantity of any local public good, q*, which is subject to a certain degree of crowding due to the size of the population, N. Specify the crowding function as

q = q*N-a       0 < a < 1.   (3)

If a = 0, q* is a Samuelsonian pure public good where every individual consumes the total quantity available. As a approaches 1 individuals are not able to enjoy the full amount, but must share q* with others. When a = 1, the individual receives the fraction 1/N of the total provision. Estimates of the crowding parameter for most local public goods have been closer to one than zero, indicating a low degree of "publicness." [However, there is some reason to believe that these estimates of "publicness" might be biased (King 1977).]

These estimates of crowding are consistent with another type of substitution, which is mentioned here but not pursued at length. Increasingly, the private sector is directly providing local public services. Some local governments have found it appropriate to contract out to the private sector for services like fire protection or garbage collection. The usual argument, most recently confirmed by Bennett and Johnson, is that private delivery of public services lowers costs, since the private sector operates under incentives that encourage cost effective provision (1979). Although the growth in "privatization" of public goods is an important occurrence, the substitution here is not in consumption but in the production process, which is beyond the scope of this paper.

In addition to crowding, the median voter's demand for a local public good is dependent upon income, y, the tax price or tax share, pt, the prices of related goods (substitutes and complements), pk, and tastes, T,

q = f(ptNa, y, pk, T).   (4)

Although many local public good demand studies recognized the conceptual importance of private-good substitutes, empirical estimation of the degree of substitutability was not usually undertaken due to data unavailability. Research to shore up this empirical gap has just begun. The next section reviews recent studies that attempted to quantify the degree of substitutability.


Police Protection

Ann Bartel analyzed the demand for private protection by firms (1975). The main purpose of her study was to answer the following three questions. One, how is firm demand for protection related to business losses from crime and the probability of crime? Two, are public and private expenditures substitutes or complements? Three, does a firm choose self-protection as a substitute for market insurance, or will it spend more on protection if it has insurance?

She developed an extensive theoretical model that took into account expected losses and risk aversion, but was unable to test all of the model's implications due to data limitations. However, she was able to answer the three main questions through the use of logit analysis. A survey conducted by the SBA provided data on whether or not private firms hired guards. These data became the dependent variable in the logit analysis.

She found that firms do respond rationally to economic forces in making their protection decisions. Firms placed relatively more weight on the probability of loss than the size of anticipated losses. Also firms were willing to reduce their demand for private protection when public police protection was increased, so the two types of protection are substitutable. It appears that firms have a target level of desired protection, which is a mix between public and private protection services. Insurance, however, was not a substitute for private protection because firms could purchase insurance at a lower price if they hired private guards or protective services.

Lancaster's new approach to consumer theory is helpful in understanding Barrel's results. The attribute that firms desire is a certain level of protection at the lowest cost. So firms combine public services and private services until they obtain their desired level of protection, while at the same time judiciously choosing the mix of private protection services to minimize costs.

Clotfelter employed a conceptual approach similar to Lancaster's, except he viewed the attribute as the final output and commodities as intermediate goods (1977). This approach allowed Clotfelter to formulate the private-public choice issue in terms of a production function

z = f(q*N1-a , q')   (5)


z - the ultimate output or attribute

q*N1-a = the total amount of the public good adjusted for crowding

q' = the total amount of the private good.

Within the production framework, output can be maximized by equating the marginal rate of technical substitution between public and private inputs to the ratio of their marginal costs. This type of model indicated that the question of substitution depended on the relative costs of inputs, the state of technology, the public good characteristics of the public input, and the public institutions that decide how to raise revenue and distribute benefits.

Clotfelter's next step was to develop an empirical test that would measure the degree of substitutability between a public and private good. He chose protection against crime as the final output, z, with employment in public and private protection as the inputs. Using a CES production function, he estimated the elasticity of substitution under two assumptions. First, he assumed that the wage rates for public and private policemen were exogenous and found, through ordinary least squares on cross-sectional state data, that the elasticity of substitution was positive, .58, implying a low degree of substitutability. Then he assumed that the wage rates were endogenous and used the instrumental variable estimation technique. Under this assumption the elasticity of substitution was much larger, 2.47, suggesting considerable latitude for substitution when input prices change. An elasticity of substitution above one implies the demand for private substitutes will increase proportionately more than public wage increases, thus decreasing the relative share of public spending on a given activity. Clotfelter's estimate, 2.47, was significantly greater than zero, but the standard error was too large to confirm that the estimate was also greater than one. He concluded by suggesting that other forms of private protection besides protective employment merit consideration if we are to understand how the consumer achieves a desired level of protection.

Consumer use of various means of private security measures like locks, alarms, handguns, etc. was examined in a more recent article by Clotfelter (1978). Here he analyzed various effects from increased consumption of private protection devices. One obvious effect from increases in private protection activity is the deterrence of crime. Criminals will have to search longer and their expected returns will be smaller because of private protection activity. This gross deterrence effect, however, may be partially offset by what is termed as the isolation effect. Increases in private protection activity may erode the citizen's social responsibility for routine surveillance and reporting of suspicious activity. In addition to the gross deterrence and isolation effects, private protection activity by some could simply divert crimes to other unprotected households. This is termed the displacement effect.

Lack of appropriate data restricted Clotfelter's empirical analysis of the various effects of private protection on crime levels. Also he was unable to obtain any data regarding market interaction between private protection activity and public protection.

Fire Protection

Vehorn extended the median voter approach (Equation 4) to the demand for public goods by examining market interaction between publicly-provided and privately-provided goods for the case of fire protection (1979). The long standing difficulty, as mentioned previously, has been lack of data. In the case of fire protection, however, it was possible to obtain private good price data for homeowners insurance and fireproofing materials in different SMSAs, allowing for a cross-sectional analysis. Since public fire protection is a shared good, each consumer must make his own personal choice about whether publicly provided fire protection is his optimal amount of fire protection. Hirsch hypothesized that a substitute for public protection, to a certain degree, is the private market good insurance (1970). Vehorn conducted an empirical test of Hirsch's conjecture by estimating cross-price elasticities between public and private services in the fire protection market using a simultaneous equations framework. A simultaneous equation model was appropriate because the price of insurance along with the firemen's wages are endogenous factors.

In order to test for the existence of market interaction, the signs and statistical significance of the cross-price elasticity estimates had to be considered. If these elasticity estimates were positive, then it could be concluded that increases in private-good prices lead to increases in the demand for public fire protection, ceteras paribus. Vehorn found that the cross-price elasticity estimates for both insurance and fireproofing materials were positive and in most cases significant. The range for insurance was from .44 to .81 depending on how the tax share was measured and whether the observations were for SMSAs or central cities. The range for fireproofing materials was from 1.48 to 1.82.

The evidence that Vehorn presented showed price changes in private markets do indeed effect the voter's demand for public goods. His general conclusion was that in areas where the prices of private market alternatives were high the demand for public fire protection was also high.


Erekson also used a median voter model to examine the interrelationship between public and private education (1978). In 1976-77, 16.8 percent of all elementary and secondary schools were non-public, so private education does provide a viable market alternative to consumers. The question remains, what is the effect of private education on the provision of public education?

One expected effect in public schools is an increase in per pupil expenditures as non-public schools attract more students. Offsetting this effect, however, is the taxpayer's decreased support for public education as more students switch to non-public education. Erekson's empirical results support the former effect, but he could not confirm the existence of the latter effect for his sample of 671 school districts in the state of New York. He also estimated a cross-price elasticity between the demand for public education and non-public tuition rates. This estimate was positive and significant in most cases indicating that private education was indeed a substitute for public education. The magnitude of the estimate, however, was small suggesting that public and private education are far from perfect substitutes. Perhaps the vast difference in the quality dimension restricts the degree of substitutability. Erekson concluded by noting that any attempt to model the demand for public education must take into account the market for private education.


The purpose of this paper was to present an overview of consumer substitution between public and private goods. Initially, one might think that such substitution is impossible due to the unique nature of collective goods. However, if one views the consumer as a utility maximizer who chooses between attributes rather than physical commodities, it becomes apparent that a wide range of substitution possibilities exist.

Literature in the area of public-private substitution is sparse, but growing. In general, these studies have been able to observe a moderate degree of substitution occurring. Thus citizen-consumers do have other alternatives to public provision, and some do make use of these alternatives whenever they feel that the public provision does not meet their own personal needs. However, more detailed research on specific private markets is needed to further our understanding of exactly how these markets spring up to meet consumer preferences.

Local public officials who recognize the existence of private market alternatives, instead of assuming that the public sector is s monopoly provider, can use these private markets to their advantage. Encouraging the growth of private markets to help meet the needs of citizens with diverse preferences can reduce the pressure to increase public services without expanding the budget. Budgetary pressures, in part, have been the impetus in the move towards "privatization" of public goods, and tight budgets could be the stimulus for an effort to expand the use of private market alternatives. Public sector resources could be allocated more efficiently if research provided local officials with estimates of consumer responses to such an effort.


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