«Bribes For Faster Delivery Amal Sanyal Lincoln University, New Zealand and Instituto de Analisis Economico, UAB, Barcelona Abstract: The paper models ...»
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Bribes For Faster Delivery
Lincoln University, New Zealand
Instituto de Analisis Economico, UAB, Barcelona
The paper models the practice of charging bribes for faster delivery of essential services in third world
countries. It then examines the possibility of curbing corruption by supervision, and secondly, by
introducing competition among delivery agents. It is argued that a supervisory solution eludes the
problem because no hard evidence of the reduction of corruption can be established for this type of offenses. It is also shown that using more than one supplier cannot eliminate the practice, and the bribe paying part of the market attains a determinate proportion as the number of suppliers increases. However the bribe rate and average waiting time come down at a diminishing rate with increase in the number of suppliers, and this property can be used to determine an optimal number of suppliers.
JEL Classification: H8, D45 Key words: third world; queues; corruption; bribes; optimal mechanism.
Bribes For Faster Delivery
1. Introduction This paper analyzes the practice of charging bribes for faster delivery of publicly provided goods and services, a practice widely encountered in the third world. Typically the phenomenon arises where the principal uses a supplier to deliver a good or service at a publicly announced price. Unit delivery takes a finite time, so that customers wait to be served. They dislike waiting, and some are willing to pay to avoid it. The supplier then discretely announces that they can get faster delivery for an extra payment.
Those willing to pay are serviced ahead of the existing queue. The supplier’s payoff is revenue in excess of the announced price.
The problem would not be worth attention if the bribe sped up delivery for some leaving others unaffected; that would improve efficiency. However placing a subset of buyers ahead increases the average waiting time for others. Examples of this practice are ubiquitous in many developing and file:///A|/Workshop.htm (1 de 10) [15/12/2000 13:18:11] q1 = q0 + (n-y) transitional economies. They are found in the provision of essential services like connection to power, water, telephone and gas. Services to repair these amenities have similar features: sped up by a bribe, they otherwise remain slow. Other examples are at queues for railway reservation, getting appointments with public authorities, getting a date for a court hearing, waiting to get a passport issued or even in queues for various statutory registrations.
Customer queues originate from two different reasons. One that has been widely studied reflects the excess demand for the good or service at the announced price. Our paper focuses on a different reason.
Even when there is no excess demand for the product, queues appear as a result of the time taken for delivery. To put it differently, delivery as a distinct service may be in short supply compared to the flow demand for the product in any given period. These queues and the resulting bribes are worth analysis for at least two reasons. The first is that this problem, often seen as petty corruption, is widespread, and hence it is useful to understand the structure of these markets. The second reason is that bribes in a supply queue are in a class apart from problems analyzed in the enforcement literature. That literature analyzes situations where a fall in the level of the activity that reduces a principal’s pay off is verifiable.
For example in the case of evasion of income or commodity tax, a fall in evasion is evidenced by increase of tax revenue. In cases of work shirking, increase of labor productivity is an indicator of the reduction of work shirking. By contrast, in a supply queue, a fall of corruption can not be verified with an indicator or evidence. If the principal hires a supervisor and the latter reports a fall in the level of corruption, the report has to be accepted without evidence. As a consequence, supply queue corruption may not be eliminated unless supervisors are honest. But the problem is more prevalent in countries where collusion between agents and supervisors is also widespread. Thus this so-called petty corruption presents a tough problem for third world countries.
In this paper we first develop a model of markets with supply queue bribes. It is shown that in equilibrium the supplier partitions the market at a determinate point on the willingness-to-pay scale of buyers, places willing buyers ahead of the existing queue and serves the rest of the market residually.
The partition point, the bribe rate and the average waiting time for residual buyers are shown to be independent of the price of the product, so that a deterrent pricing policy is unavailable. We then examine two commonly encountered suggestions for these markets: to employ supervisors and to introduce competition. Regarding supervision, it is noted that the usual procedure of setting expected penalty costs equal to potential bribe earnings is likely to be undermined by collusion. We then argue that no acceptable evidence or indicator can generally establish a fall in corruption in these market situations, and this makes it impossible to design a contract ensuring bribe-free equilibrium. We then examine the effects of introducing competition. It is shown that competition does not introduce any strategic difference in the behavior of suppliers; so that bribe taking persists. However there is a scale effect: the bribe rate and the average waiting time for residual buyers fall as the number of suppliers increases. Two results are worth mentioning here. The first is that even if the number of suppliers were to increase indefinitely, the bribe paying part of the market would not fall below a determinate proportion. This highlights the stubborn nature of the problem. The second is that due to the scale effect the average waiting time of residual buyers falls with the introduction of more supply agents. An optimal number of suppliers can be established by balancing the additional cost of hiring suppliers with the gains in average waiting time for residual buyers.
The paper is structured as follows. In section 2 we model the structure of a market with supply queue corruption, and show that there is no solution to bribe taking based on appropriate pricing of the product, nor does enforcing a minimum number of sales per period help. In section 3, we explore the effect of
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employing a supervisor. It is shown that if the supervisor is honest, a mechanism is easily designed to eliminate supply line bribes. But if supervisors are potentially corrupt, bribe taking can be eliminated only in one-shot encounters between the supplier and the supervisor. Preventing collusion in repeated game situations, when possible, is costly. In section 4, we analyze the effect of introducing more agents rather than a supervisor. A model with two supervisors is first developed and then generalized to produce a number of results. We conclude in section 5 by putting the theoretical results in the perspective of the social and political environment in which supply queue corruption is commonly encountered.
2. A Model of Bribes for Faster Delivery
1. Consumers are arranged in the ascending order of income in the continuous and closed interval (m, n), m, n ε ; m, n 0. The distribution of consumers over income is uniform with density 1.
2. Consumers' dislike for waiting is modeled by assuming that besides from the product itself, they derive utility from a perceived quality q, negatively related to the average waiting time. If d is the average waiting time, then the perceived quality is q = Q – d, where Q is the quality corresponding to instant delivery. All buyers facing the same average waiting time perceive the same quality.
3. A consumer with income y, gets a surplus, S = y.q - p, where p is the price and q the quality. A consumer buys the product only if S ≥ 0. If more than one quality are available, one with the highest surplus is purchased. Indifference leads to purchasing the higher quality. A consumer buys only one unit of the product, if at all.
4. Each unit takes T units of time for delivery. Total waiting time for all buyers is then Consider a supplier who has been employed at a fixed wage to deliver the product at price p, and remit the sales revenue to the principal. Suppose the supplier separates out [y, n], my n, for priority delivery at a bribe. The bribe rate B must be such that consumers with income y will choose not to pay it, while file:///A|/Workshop.htm (3 de 10) [15/12/2000 13:18:11] q1 = q0 + (n-y) others will pay the bribe to buy priority. The consumer at the margin is indifferent between the two
qualities. The indifference of the marginal consumer is given by:
For simplifying the presentation we now convert [m,n] into a normalized range [0,1]. On this new scale (2) can be rewritten by substituting n =1, m=0 and replacing y by a new variable Y = (y-m)/(n-m). Revenue on the new scale is given by R = (1-Y)Y[(1-Y)2 +2Y-1] = (1-Y)Y3, (3) while bribe rate b is Y[(1-Y)2 +2Y-1] = Y3. (4) This revenue function is maximized at Y*=3/4, implying that the supplier will take a bribe from the top 25 per cent of buyers on the income scale, and serve the rest of the market residually. Equilibrium bribe rate, given by (4) is 0.4219 in normalized income units. As the supplier increases the cut off Y for taking bribes, the bribe rate increases [equation (4)] but the number of buyers from whom bribe is taken falls.
These opposing tendencies produce the interior maximum.
Average wait time for residual buyers in equilibrium is given by dn = (1-Y*)2 +Y*, while a group [0,Y*) should have average waiting time Y* in a bribe-free situation. The expression (dn/Y*) -1 = C, can be used as a measure of the time cost of corruption imposed on each person in the group [0,Y*]. For Y*=0.75, C works out as 0.0833 on the normalized scale.
Since in (3) R is independent of p, setting a different price does not influence the supplier’s behavior.
Secondly the common suggestion that the supplier be forced to sell a specified number of units per period does not achieve anything. It is easy to check that the average waiting time for the market as a whole does not change under bribes. Bribe taking only alters the average waiting time for the two parts of the market. Bribe payers get served before others, and as a group enjoy a smaller average waiting period. Others wait out through this whole period and their average waiting period as a group increases.
Since only the average waiting time for the market is observable through sales flow, but that for its separate parts are not, potential monitoring is rendered difficult. For the same reason, enforcing a maximum permissible delay for individual buyers also does not achieve anything. The waiting time for the buyer last serviced is the same whether bribes are taken or not. We summarize these observations in the following proposition.
Proposition 1: (i) The supplier sets a determinate separation point on the willingness-to-pay scale, and charges bribes from those willing to pay.
(ii) The equilibrium can not be altered by a price policy.
(iii) Insisting on a specified number of sales per period or a maximum permissible waiting time for individual buyers does not alter the equilibrium.
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The next two sections explore the possible effects of supervision and competition on the equilibrium characterized in this section.
3. Supervision and the nature of evidence The normal supervisory solution of setting a fine for the supplier with expected value no less than his gains from queue manipulation generally fails because of collusion between the supervisor and the supplier. The standard method of weaning away the supervisor from collusion is to pay him a reward for reporting, large enough to ensure that the supplier can not pay him this amount and yet retain some gains.
This method too is likely to fail in repeated encounters between the supervisor and the supplier as the following argument shows.