Heikkila Lin

8/12/2019 Heikkila Lin

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An Integrated Model of Formaland Informal Housing Sectors

Eric J. Heikkila

Professor & Director of International InitiativesPrice School of Public Policy

University of Southern CaliforniaLos Angeles, CA 90089-0626 USA

[email protected]

Michael C.Y. LinPh.D. Candidate

Price School of Public PolicyUniversity of Southern California

Los Angeles, CA 90089-0626 USA

[email protected]

February 2013


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ABSTRACT

Many cities in developing countries are characterized by a striking juxtaposition of

formal and informal housing, where these sectors co-exist in close proximity. This paper

develops a model of urban land markets where both the formal and informal sectors are

endogenously and mutually determined. More specifically, the informal market arises as

a kind of residual effect of decisions made in the formal sector. The model posits a fixed

number of rich and of poor households, all of whom are competing in the marketplace for

a place to live. Rich households enact formal land use regulations in the form of

minimum lot size requirements that directly reflect their preferences. The impacts of

these regulations on the informal sector depend upon relative incomes and populations of poor and rich households, as well as on housing preferences. In order to assess these

impacts empirically, the paper formulates a set of stylized case studies. The model

results illustrate that the formal and informal sectors do not exist independently from one

another but are instead dual aspects of a single market phenomenon. In particular, an

insufficient absorptive capacity of the formal sector results directly in informality.


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I. INTRODUCTION

Recent theoretical and empirical work on the role of institutions in development hasemphasized the importance of land titling and other formal institutional mechanisms for

ensuring property rights claims. This paper challenges this approach, arguing that it

overlooks a fundamental constraint on the supply side of the market. Because everyone

lives somewhere , and because the supply of land is fixed, allocation of land to formal

markets simultaneously and unavoidably creates a dual condition of informality. Acute

problems arise in many developing countries when the ability of the formal sector to

accommodate the resident population is small relative to the whole, thereby creating a

large informal sector which almost by definition lies outside the purview of formal

institutions. These conditions are all too common in contemporary urban spaces. In

Manila, Ballesteros (2010) reports that 37% of the total population residing in slums in

2010. According to UN-HABITAT (2003), Manilas Slums are now scattered usually

along rivers, near garbage dumps, along railroad tracks, under bridges and beside

industrial establishments. (p. 215) The Municipal Corporation of Greater Mumbai

(2002) advises us that, slum dwellers comprise more than 55% of the citys

population of 11.9 million, (p. 5) and this corroborates a similar percentage reported for

Nairobi. 1

This paper argues that the key to addressing this problem is the absorptive capacity of the

formal sector. Merely creating formal property rights is not sufficient, and may in fact be

counterproductive if the absorptive capacity is small relative to the population. This

shifts the policy focus to one of designing land use regulations that have suitable

absorptive capacities. In what follows we introduce a simple generic model of a land

1 See, variously, UN Habitat 2003. The Challenge of Slums: Global Report on Human Settlements, 2003 .

London: Earthscan, Part IV: Summary of City Case Studies, pp. 193-228; and Municipal Corporation of

Greater Mumbai 2002. Environmental Status Report of Mumbai: Executive Summary , accessed on 28

November 2011 from http://www.archidev.org/article.php3?id_article=384 ; and (for Nairobi) Sheehan

2005. Treating People and Communities as Assets. Global Urban Development Magazine (1) 1,

http://www.globalurban.org/Issue1PIMag05/Sheehan%20article.htm .


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market in a city characterized by a sharp duality in terms of economic wealth. As a

reference point, the model is framed initially in terms of a single unified formal market

for land with all households participating, rich and poor alike. Next, minimum lot size

land use restrictions are imposed based on circumstances suitable to the wealthier

households, and those restrictions make it untenable for some poor households to remain

within the formal sector.

The analysis uncovers three distinct types of outcomes that are delineated on the basis of

relative incomes and prices. In the first case, a subset of the poor households remains in

the formal sector after the imposition of land use controls. There is no welfare impact onrich households in this case as land prices remain unchanged, whereas poor households

who do remain in the formal sector suffer a welfare loss because they are compelled to

consume more land than they would otherwise prefer. But even these households are

better off than their disenfranchised brethren whose only recourse to the imposition of

minimum lot size restrictions is to reside in the informal sector. In the second case all of

the poor households are disenfranchised, and so only wealthy households remain in the

formal sector as land prices fall to a lower equilibrium value. Rich households actually

experience a welfare gain here because they are in effect subsidized by the resultant

lower land prices. The third case is a hybrid of the two, where a subset of poor

households is just able to return to the formal sector, but only after land prices have

fallen. The analytical framework developed here enables one to calculate the welfare

gains and losses for each type of household in these three distinct cases. An important

but discouraging finding is that the welfare gain of wealthy households is higher in more

polarized settings. The reason for this is that as more poor households find themselves in

the informal sector, aggregate demand for land in the formal sector diminishes and thisleads to an effective price subsidy to those residing within the formal sector.

The paper begins the next section by placing this work in the context of two distinct

strands of the literature. One is the urban economics literature, primarily in a U.S.

context, that examines the efficiency and welfare implications of minimum lot size

restrictions and other forms of urban land use regulations. The other is the broader


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development literature that explores the causal dynamics of informal housing and land

markets. As explained below, the third section of this paper combines elements of both

by introducing a formal neoclassical model of an urban land market that includes an

informal sector. This enables us to model explicitly the interactive effects between the

formal and informal sectors. We then generates these interactive effects by introducing

minimum lot size restrictions based on the preferences of the wealthier (and presumably,

more politically influential) households. As explained above, three distinct cases emerge,

and these are explored empirically in the fourth section using notional data that enable us

to get a handle on the magnitudes involved. A concluding section reconsiders the

significance of our findings and points to promising avenues for further research. Weconclude that extending the realm of land use titles and other forms of property rights,

while perhaps worthwhile, is not a panacea. Instead, the results of our paper suggest that

greater focus should be placed on ensuring that land use regulations provide sufficient

absorptive capacity to accommodate all urban dwellers, rich and poor alike. The

informal sector is not a problem in and of itself; it is an expression of failures within the

formal sector.

II. INFORMAL LAND MARKETS IN THE CONTEXT OF THE LITERATURE

This paper builds upon two rather distinct sets of literature. One branch, beginning with

Fischel (1985; 1990) and extending more recently through Quigley and Rosenthal (2005),

Glaeser and Ward (2009) and Zabel and Dalton (2011), examines the efficiency and/or

price implications of land use regulation, primarily in the United States context. A

typical finding by works of this sort is that land use regulations result in an increase in

land and/or housing prices. Individual works vary in terms of methods used for treatingthe endogeneity of land use regulations, with some authors (Malpezzi et al , 1998;

Ihlanfeldt, 2007) employing two-stage least squares and others (Zabel and Dalton, 2011)

using a difference-in-difference approach. The general consensus that emerges from

these articles is that regulation-induced price increases are more attributable to supply

side restrictions rather than to any amenities that might accrue on the demand side of the

market.


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A second branch of the literature focuses more specifically on slum dwellings and

informal housing in the developing country context. There are several variants of this

literature. As noted in the introduction, much attention has been paid to land titling, an

issue widely associated with the work of Hernando de Soto (1989; 2000), but addressed

also by Feder and Nishio (1998), Cities Alliance (2004), Deninger and Feder (2009),

Durand-Lasserve and Selod (2009) and Payne et al (2009). The basic argument is that

even poor households do have financial capital, but the lack of land titling in the informal

sector deprives them of productive investment opportunities that would also help meet

local housing needs. From this perspective a policy priority is to formalize the informalsector through more extensive land titling. Other authors such as Jimenez (1984) and

Friedman et al (1988), and more recently Lanjou and Levy (2002) and Galiani and

Schargrodsky (2010), bolster this basic argument through empirical estimation of the

premium attributable to land title. Although we acknowledge the reasonableness of this

approach, we argue in this paper that land titling alone is not sufficient to resolve some of

the underlying causes of, and problems associated with, informal housing.

In particular, we agree with those authors who argue that land use regulations in

developing countries are in fact a root cause of informality. As stated by Buckley and

Kalarickal (2006), in many ways, and in many places, urban land markets remain the

most pervasive binding constraint on the provision of shelter for the urban poor. (p. xiii)

Zoning and other land use regulations may artificially increase the cost of housing in the

formal sector and thereby induce squatting (Brueckner and Selod, 2009). A specific

example is offered by a minimum lot size regulation enacted by Buenos Aires in 1977.

Goytia and Lanfranchi (2009) assert that because of this law, low-income householdshave been forced to rely on informal mechanisms to access housing, such as purchasing

land in illegal subdivisions or squatting on public land and building their dwellings

incrementally. (p. 163) Enabling housing markets in developing countries to work

efficiently, as Arnott (2008) argues, requires the removal of unnecessary land use and

housing restrictions.


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Finally, there are a few authors who apply a neoclassical framework to analyze aspects of

informal housing in developing countries. Our paper follows in this same tradition and

thus shares some similarities with these works. For example, Bruekner (1996) examines

the effects of changing land use regulations in post-Apartheid South Africa. His model

contains two types of households, poor blacks and relatively wealthy whites, with

correspondingly different bid rent gradients. We also introduce two classes of

households, rich and poor, but we do not include a commuting dimension. Instead, we

focus in more detail on the interaction between the formal and informal sectors.

Duranton (2008) uses wage and living cost curves to illustrate the effect of exclusionary

zoning on the size of squatter settlements in developing countries. Like him, we use adiagrammatic analysis to explicate our model of the interaction between the formal and

informal housing sectors, but with several notable differences. First, Durantons focus is

on the labor market with an ancillary focus on housing, while we focus exclusively on the

interactions between the formal and informal housing sectors. A related point is that

Durantons model features an open city with the labor market shaping the equilibrium

size of the city. Ours is a closed model wherein welfare impacts of land use regulation

are modeled explicitly. Finally, we supplement our analytical framework with an

empirical analysis based on a set of pseudo case studies as explained below.

In several respects, our paper bears most in common with that of Brueckner and Selod

(2009). Like them, we begin with a fixed supply of undifferentiated urban land that must

accommodate formal and informal housing sectors, linked primarily to rich and poor

households, respectively. Based on their explicit analyses of the interaction between the

formal and informal housing sectors, both models are able to assess the relative welfare

impacts associated with the emergence of an informal housing sector. Moreover, bothmodels address the distinct challenge of modeling demand for land in the informal sector

which, almost by definition, lies outside the regular land market. It is how we respond to

this challenge that chiefly differentiates our model from that of Brueckner and Selod.

They take an interesting game-theoretic approach, whereby a community organizer in the

informal sector occupies land strategically, while also engaging in defensive tactics to

avoid eviction. Our approach is different. Taking the view that everyone lives


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somewhere, we employ a linear expenditure system (LES) specification of demand for

housing and other goods that builds in minimum basic needs for livelihood. An

advantage of the LES over a Cobb-Douglas specification within the context of our model

is that when poor households are compelled to leave the formal housing market, their

existence is still accounted for. It also enables us to side-step an outcome that Brueckner

and Selod (2009) encounter whereby the formal and informal sectors occupy precisely

half of the total urban land area regardless of the numbers of households in either sector,

the strength of their preferences for land over other goods, or their respective income

levels. As noted above, our paper also includes an empirical analysis based on quasi-case

studies. Finally, and quite significantly, our model includes an explicit minimum lot sizeregulation (imposed, in effect, by wealthy households) that gives rise to the informal

sector. This feature links our work to the literature, described above, that examines the

inefficiencies arising from distortionary land use regulations.

III. The model

An urban land use market witho ut land use restrict ions

We introduce here a model of a highly dualistic economy where the total population of n

households comprises n0 poor households having incomes of y0 and n1 (= n n0)

wealthier households with incomes of y1, where y1 > y0. Each household, rich or poor,

has a common utility function with two arguments: land l and other consumption items x.

Motivated by a basic needs approach, our model assumes that each household occupies

some minimum amount ( l ) of land and likewise consumes some minimum quantity ( x)

of other goods to ensure its survival. For this purpose it is convenient to adopt a linear

expenditure system (LES) which is in effect a Cobb-Douglas system with the origin point

translated to the minimum consumption pair ( l , x).2 This gives us the following form

for the utility function:

2 For more information on the LES specification the interested reader may refer to Deaton and Muellbauer

(1980), Phlips (1983), Johnson et al (1984), and Pollak and Wales (1992).


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(1) 1)()(),( xl xl xl U u

where is a parameter lying within the unit interval. Households maximize this utility

expression subject to a budget constraint

(2) iii y x pl

where p is the price of land and where i = 0 or 1, depending on whether the household is

poor or rich, respectively. We let )( l l l , )( x x x , and )( xl p y y

represent the discretionary land occupation, goods consumption and income levels,

respectively, after adjusting each quantity by its corresponding subsistence requirement.

After doing so, the individual household demand curves derived from this formulation

resemble their Cobb-Douglas counterparts:

(3) p yl ii /*

i=0,1

(4)ii

y x )1(* i=0,1

where and (1- ) are the shares of household income allocated to land and other

consumables, respectively. For our purposes it will be useful to derive the inverse

aggregate demand curves for land for rich and poor:

(5)l ii

xiii n L

nY p

)1()( i=0,1

where iii ynY and iii l n L are the aggregate discretionary incomes and land

consumption quantities, respectively.


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Figure 1

Aggregate demand for and supply of urban land by the poor (i=0) and by the rich (i=1)

p * p *

l n 0 l n 1

p 1 p 1

l

x

n LnY

p

00

000 )1(

)(

l

x

n LnY

p

11

111 )1(

)(

*0

L

*0 L

*1

L

*1 L

These aggregate demand curves are juxtaposed in figure 1 where the demand for land bythe poor is downward sloping to the right as usual. Its counterpart for the rich, in contrast,

is read from right-to-left and so is downward sloping to the left. In both cases, the

quantity demanded falls asymptotically towards the minimum aggregate quantity ni l ,

where again i = 0 or 1, to indicate the poor or rich populations, respectively. Presenting

the two demand curves together this way on a single graph allows both to be depicted

readily within the context of a fixed supply of land, L. The quantity L is represented in

figure 1 by the length of the horizontal axis so that any point along that axis indicates acomplete allocation by the formal land market between rich and poor households. 3

It is evident from figure 1 that there is a unique market clearing price p* for this land

market, and from equation 5 we know that this occurs when aggregate discretionary land

3 See chapter 2 of Heikkila, E.J. 2000, The Economics of Planning , New Brunswick: CUPR Press, for a

textbook treatment of this basic diagram.


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consumption by the poor and rich populations is in the same proportion as their

respective aggregate discretionary incomes.

(6)1

0

1

0

Y Y

L L

Although we know that y0 < y1, we cannot say in general whether more land is allocated

to rich or poor households without knowing their relative population sizes.

Introducing zoning restrictions

In the scenario described above there are no planning interventions. We introduce these

now in the form of minimum lot size restrictions. In order to simplify the analysis we

assume that the minimum lot size restriction replicates and thereby consolidates the

conditions that apply to the wealthy class under pure market conditions. This might be

expected to occur, for example, where wealthy neighborhoods feel under siege by

lower income households and so are prompted to use their political influence to impose

standards for land use befitting their own expectations and preferences. Thus, by planning

decree we set

(7) l min =*1 L / n 1 = (

*1

L + n 1 l ) / n 1 =*

1l + l

where, as indicated in figure 1, *1 L corresponds to the total amount of land allocated to the

rich household sector under pure market conditions, and this is then divided by the

number of wealthy households n1 to yield the new standard that defines the norm for the

formal land sector. This restriction is illustrated in figure 2, where point A indicates the

initial budget allocation ( *0l ,*0 x ) for a poor household in response to the original

equilibrium price p* . Once the minimum lot size restriction is imposed, this budget

allocation will no longer be tenable. Three cases emerge, as discussed below.


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Case 1: Some poor households remain in the formal sector

In the first case we consider the formal sector remains within reach of poor household

budgets, but any poor household remaining in the formal sector must reallocate its

household budget away from A to the point B, which corresponds to a higher degree of

land consumption ( l min) than the poor household would otherwise have preferred, as it

leaves only an amount ( y0-p*l min) < x* 0 left over for consumption of other goods. The

welfare impact on such households is designated by an amount WB given implicitly by

(8) ),(),( min*

0min0* l p yl U W y pV B

where V(p, y) is the indirect utility function indicating the maximum utility that a

household could attain with price p and income y. The right hand side of equation 8

corresponds to the direct utility at point B in figure 2. Thus, WB is the hypothetical loss

in income that just corresponds to the welfare loss that poor households in the formal

sector experience because of the imposition of the minimum lot size restriction. One can

solve for WB explicitly, yielding:

(9) 11min*

0min*

0 )1(/)()]([ xl B l p yl p yW

Not all poor households are able now to remain in the formal sector. Because the

minimum lot size is given by equation 7 above, we can specify the upper bound, nz, on

the number of households in the formal sector after a minimum lot size restriction is

imposed.

(10) )/()( min l l z l n Ln

The differential ( n nz) therefore represents the number of households who are now left

to fend for themselves outside the formal land market. Although there is nothing in the

model thus far to indicate it must be so, we may reasonably assume that this displaced


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population comes entirely from the ranks of the poor households, and so all n1 rich

households remain within the formal sector after minimum lot sizes are imposed. From

this, we may infer that the number of poor households in the formal sector will now be

(11) 10 nnn z z

Figure 2

Impact on poor households of minimum lot size restrictions in the formal sector

l min

Land

Other goods

y0

A

B

IC for richhousehold

IC for poorhousehold

For p = p*

For p = pmax

y0 p* l min x*0

l* 0

? X

?l

The remaining )( 00 z nn households those who are left stranded in the informal sector

are unable to meet the minimum lot size requirement in the formal sector and so the landconsumption for any such household is simply l , the minimum subsistence level. These

households then have no other recourse but to spend their remaining income )( *0 l p y

on other goods. 4

4 Because of the LES specification, any income spent by poor households in the informal sector on other

goods is futile because l l 0 ensures that household utility is zero.


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The impact of the minimum lot size restriction on these unfortunate households is all too

easy to calculate using the same compensating variation approach used earlier

(12) 0),(),( *000*

l l p yU W y pV

It follows immediately that the welfare impact for poor disenfranchised households is

given by

(13) xl p y yW *000

Stated simply, these disenfranchised households now have zero utility because they are

only able to consume the minimum subsistence land allocation l . In effect, therefore,

they can no longer derive any positive utility from any extra income they might have had

above and beyond the minimum subsistence level, and so their welfare loss is equivalent

to that lost discretionary income.

Case 2: No poor households remain in the formal sector

As illustrated in figure 2, a land price above min0max /)( l y p x would leave any poor

household unable to attain land in the formal sector because

(14) x pl y p p )( min0max

Equation 14 shows that if a poor household were to adhere to the minimum lot size

regulation given such a high price for land, it would not have sufficient income left over

to meet the subsistence requirement for other goods.

In this case the entire set of n0 poor households experiences the welfare impact 00 yW ,

which is the cost of total disenfranchisement from the formal sector, as set out in equation


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13. Rich households, however, are actually better off because they are the only ones

remaining in the formal sector, and so any rich household will now occupy a lot size of

10 /)( nn L l , which is larger than l min. With reference to equation 5, we know that the

equilibrium price for land in the formal sector in this case will be given by

(15)l

x

n LnY

p

11

111 )1(

)(

where l n L L 01 .

The shaded area in figure 1 denotes the welfare gain experienced by rich households in

this case. The rectangular portion is in effect a straight subsidy of 1* p p that applies to

the original consumption amount. Added to that is the consumer surplus from extra

consumption of land induced by the lower price, and that extra portion can be

approximated by the triangular amount 2/)( 1**

0 p p L , and so a close measure of the

aggregate welfare gain to the rich in this case is given by

0)]2/()[( *0*11

*1 L L p pW

Case 3: Hybrid case

In case 2 just discussed, the equilibrium price fell in order to clear the formal sector land

market after the poor households had dropped out. If in doing so the price falls to the

critical value pmax, then some poor households will once again be able to enter the formal

land market. At the price pmax, poor households will be indifferent between their formal

or informal land market options, because either way their utility remains equal to zero. Of

course, the moment the price actually falls below pmax, poor households will queue up to

enter the formal sector, so it follows that pmax will be the equilibrium value in this hybrid

case. Again with reference to equation 5, we can solve for the aggregate quantity of land

occupied by rich households, H L1 , given the hybrid equilibrium price of pmax.


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(17) max1111 /)()1( pnY n L xl H

In a similar vein we define H H L L L 10 as the aggregate amount of land occupied by poor

households, and l H H n L L 000 as that aggregate quantity of land occupied by poor

households that is above and beyond the aggregate subsistence requirement for poor

households. This latter quantity, H L0 , is available only in the formal sector, so any poor

household that wishes to reside on more than the bare subsistence quantity of land is

obliged to increase its land holding by an amount l l min . Thus, the number of poor

households that can be accommodated in the formal sector is )/( min00 l H H l Ln . The

welfare gain for rich households is similar to the previous case, as set out in equation 16,

but with the pmax replacing p1.

IV. EMPIRICAL ILLUSTRATION

Table 1 summarizes the welfare impacts for the three cases described in the previous

discussion. Which one of these cases applies in any situation depends on the relationship between key price benchmarks. Of particular interest is pmax, defined above as the price at

which a poor households discretionary budget would be entirely exhausted just by

meeting the minimum lot size requirement. If this price exceeds the initial market

equilibrium price ( pmax > p* ), then case 1 applies and so some poor households do remain

in the formal sector after imposition of the land use restrictions there. At the other

extreme, if pmax falls below the market clearing price for land that applies when only the

rich remain in the formal sector ( p1 > pmax) , then case 2 applies and so all poor

households are completely disenfranchised from the formal sector. For intermediate

values ( p* > p max > p 1) the hybrid case 3 arises, where some poor households are

nominally in the formal sector but they are no better off than those who are excluded.

In this context table 1 does two things for each of the three cases and for each of three

categories of households (rich/formal, poor/formal and poor/informal). First, it shows the


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aggregate demand for land in the formal sector. 5 Secondly, table 1 summarizes the

welfare impacts for each type of household and for each of the three cases. Note that the

welfare impact of minimum lot size regulations on rich households is never negative, and

is positive whenever the equilibrium price falls below the original value of p* ,

corresponding to cases 2 and 3. As noted earlier, this welfare gain for rich households

arises from the reduced price of land resulting from the drop in aggregate demand for

land in the formal sector as poor households are forced out. In contrast, the welfare

impact of minimum lot size restrictions on poor households is always negative. The

reason is straightforward: the minimum lot size restriction compels any poor household in

the formal sector to occupy more land than its modest budget would otherwiseaccommodate. As a direct result, less income is left over for meeting other consumption

needs.

5 Note that aggregate demand for land in the formal sector by households residing in the informal sector is

uniformly zero, as shown in the corresponding row of table 1. Of course these poor households in the

informal sector do occupy the minimum subsistence quantity of land, l , but table 1 reports only on the

formal sector land allocations.


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There is a woeful paucity of detailed data regarding the population and conditions of the

informal housing sector. Indeed, the very definition of informal housing suggests that it

lies beyond the purview of official record keeping. As noted by Gulyani and Talukdar

(2009), Not surprisingly, in most developing countries there are no reliable estimates even

of basic indicators such as the number of people residing in slums and the proportion of

them who are poor. (p. 191) Table 2 therefore provides four numerical examples based

on stylized data to illustrate how and under what conditions these three different cases

might arise. The two cases on the left hand side of the table correspond to presumed annual

income levels of $2,000 for poor households, while those on the right hand side correspond

to presumed incomes of $4,000 for poor households.6

Likewise, the two cases on the toprow indicate incomes of $20,000 for rich households, in contrast to $10,000 on the bottom

row. In all cases here we assume that seventy (thirty) percent of the population is poor

(rich), and that the preferred share of household discretionary budgets spent on land is

twenty percent ( = 0.20).

The results are rather interesting. We can see that case 1 arises in the bottom right

quadrant, where the income gap between rich and poor households is least pronounced, and

so some poor households are able to remain in the formal sector. Notice that rich

households do not gain at all in this scenario because they occupy the same amount of land

and consume the same quantity of other goods as before. In this case only thirty-seven

percent of the poor remain in the formal sector while sixty-three percent of the poor are

disenfranchised. This occurs of course because the minimum lot size implicitly (but

directly) places a restriction on the number of households that can be accommodated

within the formal sector. As explained earlier, even the poor who do remain in the formal

sector suffer a welfare loss relative to the initial market equilibrium because they are

6 The 2000 annual poverty threshold income for a five-member household in Metro Manila is 78,390

Philippine Pesos (Ballesteros, 2004: 6). This is equivalent to 1,797 US Dollars based on the exchange rate as

of November 29, 2011. Low-income households [in India] are defined as households with monthly incomes

of Rs7,000 (about $165) or less (Asian Development Bank, 2000: 9). That is to say the annual household

income for the low-income household is $1,980. We determine the income level for the poor households in

reference to these data.


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compelled to purchase more land than they would prefer. In this numerical example the

welfare loss for each such household is equivalent to $771, compared to an initial income

of $4000. That is to say, poor households remaining in the formal sector would be just as

well off with an income of $3,229 if they were able to choose freely, rather than being

compelled to adhere to the minimum lot size regulation. Households in the informal sector

are even worse off, because they can only occupy the minimum subsistence land quantity,

l , and so their utility drops to zero. This welfare loss is thus equivalent to the entire loss

of a poor households discretionary income of $3,483 (which is $4,000 less the $517

needed to acquire the subsistence amounts of land and other goods). The weighted average

of these two types of poor households translates into a loss of $2,487 per household.

Diagonally opposite of that, in the upper left quadrant, one finds an example of case 2

where all poor households are disenfranchised from the formal sector. In this numerical

example, the income gap between rich and poor households is at a maximum and that has

two consequences. First, it means that poor households are unable to meet the new

minimum land requirements for the formal sector even if they were to devote their entire

discretionary income to that end. Secondly, the relative wealth of the rich class ensures

that the price of land still remains out of reach of poor households even when the market

price falls as only rich households occupy the formal sector. The conjunction of these two

effects gives rise to case 2, whereby p1 > pmax . In this numerical example the welfare loss

of each poor household is $1,448; this is less than in the previous example because the

initial income for poor households is less. As the saying goes: When ya aint got nothing,

ya got nothing to lose. The story is different here for rich households who are clearly

better off as a result of the land use restriction to the extent of $622 per rich household.

Of course, there are many more poor households than rich households, so the aggregate

loss in welfare is even more pronounced. Moreover, the welfare loss indicated here is

strictly an efficiency loss, and does not factor in adverse equity considerations.


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Table 2

Four numerical examples

Outcome type:Case 2

IncomesPoor household income:Rich household income:

Land pricesEquilibrium land price:

Land price; rich only:Limiting price for poor:

Percentage of poor after regulationPoor households (formal)

Poor households (informal)Land use before & after

Rich households before:Poor households before:

Rich households after:Poor households (formal) after:

Poor households (informal) after:Welfare impacts

Per capita welfare loss; poor:Per capita welfare gain; rich:

All poordisenfranchised

y0 = $2,000y1 = $20,000

p* = $1,522 p1 = $1,298 pmax = $602

0100%

L1* =79.7L0* =20.3L1R =93.0

L0f R =0L0iR =7.0

w0 = ($1,448)w1 = $622

Outcome type:Case 3










Hybrid: Pooreffectively out

y0 = $4,000y1 = $20,000

p* = $1,826 p1 = $1,298

pmax = $1,617

12%88%

L1* =66.8L0* =33.2L1R =75.1L0f R =18.7

L0iR =6.2

w0 = ($3,417)w1 = $474

Outcome type:Case 3










Hybrid: Pooreffectively out

y0 = $2,000

y1 = $10,000

p* = $870 p1 = $636

pmax = $699

5%95%

L1* =68.6L0* =31.4L1

R =84.8L0f R =8.6L0iR =6.6

w0 = ($1,513)w1 = $418

Outcome type:Case 1








Poor households (informal) after:Welfare impactsPer capita welfare loss; poor (formal):


Some poorremain

y0 = $4,000

y1 = $10,000

p* = $1,174 p1 = $636

pmax = $2,098

37%63%

L1* =51.5L0* =48.5L1

R =51.5L0f R =44.1

L0iR =4.4

wB = ($771)w0 = ($2,487)

w1 = $0

Note: 1. Seventy percent of the households are poor and thirty percent of the households are rich.

2. The minimum subsistence quantity of land ( l ) is 0.1, while that of other goods ( x) is 400.3. Numbers in parentheses are negative.


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Both of the remaining numerical examples in table 2 (lower left and upper right hand

quadrants, respectively) correspond to the hybrid case 3. In both examples, the income of

a rich household is five times that of a poor household. Were it not for the subsistence

quantities l and x, these two examples would be virtually identical and any remaining

differences between them would be purely nominal as though all prices and incomes

were merely denominated in different currencies. With our LES specification, however,

the specified subsistence requirements are more onerous for the $2000 households than

they are for the $4000 households, and this explains why the land use allocations and other

outcomes differ between these two examples.

In either event case 3 arises, which as discussed earlier is a kind of hybrid of cases 1 and 2.

Poor households are unable to afford the minimum lot size requirement at the initial market

equilibrium price, but as they exit the formal land market the price eventually drops to a

level that does just permit them to enter, but only by exhausting their entire budget. This

corresponds to the condition that ( p* > pmax > p1). Although some poor households do

remain nominally in the formal land market they are no better off than their

disenfranchised brethren, and so the per capita welfare loss for the poor is equal to theirentire discretionary incomes. The welfare gain for rich households in both examples is a

relatively small proportion of their initial incomes, and is less than the welfare gain they

enjoy in case 2.

The principal message emerging from these four numerical examples is that while the

welfare gains to the rich are relatively modest, especially in comparison to their initial

incomes, the welfare losses for the poor are considerably larger, especially with reference

to their meager initial incomes. Poor households comprise a large share of the total

population, and so in all of these examples the aggregate welfare loss is substantial, and

this efficiency loss is further compounded by the strikingly adverse equity implications.

This gross inefficiency of land use regulations in our examples does of course suggest the

potential for Pareto-improving measures, at least in principle. One would no doubt want to

devise any such measure to avoid the unseemly prospect of poor households having to

compensate rich households in order to dissuade the latter from imposing minimum lot size


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restrictions. 7 This model does not address the political process directly, but that may be

where the crux of the issue lies.

V. CONCLUSIONS

The model introduced in this paper integrates the informal and formal housing sectors

within a single unified framework. It does so by drawing on two distinct subsets of the

literature on urban housing markets. One subset, undertaken primarily in a U.S. or western

context, applies a neoclassical perspective to analyze the efficiency implications of land

use regulations. Another subset is aligned more closely to the economic development

literature that seeks to explain the dynamics of developmental processes and their attendant

outcomes, especially the phenomenon of persistent poverty as embodied in many squatter

settlements. The work presented here combines these approaches by introducing a

neoclassical model of urban land use where informal settlements emerge as an endogenous

outcome from market and regulatory interactions within the formal sector.

Several implications flow from this approach. One is that land titling, while perhaps useful

in its own right, may not be sufficient to address the underlying causes of informality.

Instead, the results presented here suggest that informality may arise as a direct result of

market interactions in the formal sector. In particular, the imposition of (in this case)

minimum lot size restrictions may not provide for a sufficient absorptive capacity of

urban land, and so some poor households are left out in the cold, both literally and

figuratively. This suggests that local planning agencies should be more pro-active in

ensuring that restrictions on the supply side of the housing market are consistent with the

number of households requiring shelter on the demand side. It is futile to stipulate thateveryone should have a quarter piece of pie if there are ten hungry people with only one

pie to feed them.

7 Recall that in our model minimum lot size restrictions were presumed to conform to the preferences of the

wealthy class.


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