This paper presents an alternative view to the cause and size of market failures. The work here suggest that the size of the market failure is not man made per se but rather given a full set of initial conditions it is endogenous to the dynamical forces at play. It is shown that the level and variance of market failures is tied to the location of the steady state (i.e. level of development). The paper finds that only changes to the location of the steady state produces changes to the potential level of the market failure. This paper adds to the increasing body of literature the notion that institutional change is not a sufficient condition to sustained economic development.
Corruption and corruption abatement are an important string in economic theory because corruption is seen as a major source of economic instability and a leading cause of poverty among the worlds poor countries ([
The empirical literature on corruption has shown that there exist positive levels of some form of corruption in both rich and poor countries alike ([
The economic policy is to reform the institutions that allow for information asymmetries and weak legal enforcement environments to exist as a means of tackling market failures. However, [
For the most part, the corruption literature tells us that poor countries are more likely to suffer from market failures. The literature further describes its qualitative form as risk of expropriation, property rights, contract enforcement, institutions, efficiency of markets, institutional stability, etc ([
Clearly, institutions matter as do market failures at explaining development. However, this paper takes the position that the mechanism that creates market failures is also the mechanism that generates the existing institutional properties and an economies level of development. That is, the mechanism that determines level of development also determines the size of the market failure.
The source of market failures is not central to this paper. However, the fact that it occurs is. Here it is assumed that some degree of market failures exists everywhere. Again, making reference to [
This is a little controversial in that it claims that the size of the market failure is neither a factor of poverty nor poverty a factor of market failure. Rather, market failures and poverty are no more interrelated than ice-cream consumption and crime ([
Economists face a number of shortcomings when analyzing market failures or corruption primarily due to how it is measured (degree of institutional transparency, information asymmetries, cronyism, etc.)4. This paper employs a much more general measure of market failures. Market failure is assumed captured as the difference between that which is taken by the state (confiscation or taxation) and what is given back to society as a whole. To this end market failure in this paper is a measure, as suggested by [
This paper argues that the existing models on corruption, while descriptively correct (see [
The paper is organized as follows. The next section presents the basic model and economic participants. Section 3 derives the full dynamics of the model. Section 4 derives the various levels of corruption. Finally, Section 5 provides a brief summary and concluding remarks.
To simplify the various stages of development this paper assumes that there exists a finite set of closed economies that are distinguished by the
Government taxes workers income and use tax-generated income to consume public-goods from a public-goods producer and invest in public education. To simplify the exposition, the tax rate
Without any loss to generality it is assumed that total tax revenues is spent on public education
Output is composed of two goods, each produced in one of two sectors. Each sector produces either a consumer good
where
where,
The public-goods producer is small relative to the consumer goods market and hence it must pay market prices for both inputs. In addition, public goods operate under an imperfectly competitive framework where only a few (for simplicity, one) firm produces public goods. This profit maximizing firm is an input price taker and pays for both labor and capital at the rates determined by Equations (2) and (3) respectively. For simplicity, it is assumed that the public good producer earns zero economic profits. The imperfectly competitive public-goods producer maximizes the following profit function:
where,
across the two sectors. The public-good producer’s output is
capital rental rates based on Equations (2) and (3) respectively and the firm owner extracts
Via the current literature the value of
The economy is composed of
The household lifetime utility is maximized by its level of consumption and the child’s own level of human capital.
Subject to:
Rather than formalizing a functional form for taxation, here, a progressive tax scheme will satisfy the assumption that higher income,
From Equations (5) through (8) the optimal household choice of
As expected, increases in after tax income leads to higher investment in own-child human capital and retirement savings.
This section explores the dynamic mapping of the economy under two assumptions.
Under Assumption 1 returns of human capital investment maintain the assumption of diminishing returns while still generating a sizable impact on human capital accumulation. Assumption 2 assumes that investment in human capital has a low impact on human capital accumulation. It is also the corner solution and is included here for completeness. However, the central analysis of this paper is based on Assumption 1.
Under assumption, all households within a given economy (defined by its
To simplify notation let the systems map for both physical and human capital be defined by Equation (13).
The dynamic systems at steady state explicit form are given by Equations (14) and (15) and the phase diagram of these are shown in
where,
The arrows of motion under Assumptions 1 and 2 are attracting toward point A and attracting to point B in the area between the two curves and are respectively shown in
The phase diagram is constructed based on parameter values
Under Assumption 1, an interior solution for human and physical capital, point A in
where,
Based on parameter values outlined in
where,
The steady state point under Assumption 2 is a sink. By assumption human capital accumulation, Equation (8), has at minimum one unit of human capital for all insufficient levels of both human capital,
Before exploring the size of the market failure the establishment of the behavior in the neighborhood of the steady state
In what follows the existence of a periodic orbit around the steady state point and the steady state undergoing a bifurcation maintaining its orbit will be shown. To simplify the analysis it is assumed that there are two types of households, poor and rich households (as defined by
Let there be two types of households whose existence is based on Assumption 1 and whose level of development is subject to the household type value of parameters. To this it is said that there is a family of parameter values whose type is defined in
Assumption 3 At equilibrium, (that is, at point A in
human capital
Assumption 3 states that around or at
Given Assumption 3 the nonlinear Equation can be rewritten as:
where,
Given the use of a discrete dynamic system it is clear that any orbit in some local region
0.34 0.32
(a) (b)
distance from
The statement of distance is quite reasonable since under bifurcations undertaken by
Proposition 1 The positive and negative periodic point in the region around
The analysis of the size of the market failure is subject to the following definition:
Definition 1 (Market Failure) At the saddle point
The public-goods producer will generate output
Therefore,
This simply states that the size of the market failure is the difference between what the government and the public-goods producer agreed were the costs of production and what it ultimately cost to produce at the time of delivery. Under a perfect markets scenario this difference would be internalized and no system of bureaucrats be necessary (i.e.
Poor and rich households have already been defined over the parameter value set
Proposition 2 (a) The size of the market failure is larger in Poor households than rich ones.
(b) Poor households have higher variance in market failure than do rich ones.
Proof. The proof to Proposition 2 is easier found my numerical computation. For instance, Proposition 2(a) is
found by showing that
in its outer range from center in
In addition, the spread between
The theoretical model presented above provides a number of specific findings.
Implication 1 Poor households will have higher levels of corruption relative to more developed households.
Implication 2 Poor households will have higher variance in corruption levels than developed households.
Implication 3 Corruption abatement can only take place if the household moves to a higher steady state.
Implication 4 Corruption is a map and not a point.
Implication 5 Higher levels of human capital are present in more developed households and hence higher levels of human capital are associated with less corruption.
In addition, in [
Implication 3 is what this paper terms the [
[
Implication 5 is consistent with the findings in [
This paper has presented an alternative theoretical interpretation of market failures. It has been shown that the size of the market failure is produced naturally by the dynamics of an economy. The findings of the model showed that levels and dispersion of market failure and hence corruption at any given level of development can be found independent of a model that incorporates a system of bureaucrats.
Using a two-period OLG model the paper developed a full set of dynamical implications and showed that theoretically corruption is associated with a given level of development. Most importantly, it was not development per se that led to market failure rather it was the full set of priors that determined both the level of development and the size of the market failure. This has important implications to the development literature. As the present theory suggests, corruption abatement policies that ignore the dynamic forces of an economic system will not work.
The findings of the theoretical model are consistent with a large body of the corruption empirical and theoretical literature. This paper provided an alternative approach to view the cause of the observed corruption findings in the literature.
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4 uses a more direct way to capture corruption as the difference between government allotted rice to villages and household reported rice consumption.
5Work by further claims that top down institutional change policies are highly unlikely to succeed. The work by provides at least one case where top down monitoring reduces observed corruption. However, does not tie decreased corruption with long-term development.
6
7In what follows the special case of Assumption 2 and its dynamics are ignored. This case can be taught as a failed state (e.g., Somalia) and it is hard to justify theoretically that there exists a neighborhood of the poverty trap that will generate positive levels of growth even with small perturbations.
8This assumption states that rich households are expected to have slight differences in preferences. For instance, one can argue to poorer households relative to rich households are likely to have a higher first period consumption discount preference.
9See for a discussion on consumption time preferences and its effect to the level of development. Note that in the present model there is no population heterogeneity. That is, the heterogeneity exists across economies and the current analysis of rich and poor household are meant to capture rich and poor economies.
10Alternatively, one can think of government and the public-goods producer agreeing on the price level for public goods given the information acquired by the average physical capital level