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Within any economic set-up, the pursuit of efficiency is an inherent objective. Thus, it is not surprising that models depicting how to achieve optimal resource allocation are dominant within the discipline of economics. One of the models that outline how to attain optimum resource use is the Pareto framework of efficiency. Developed by Vilfredo Pareto, the Pareto efficiency model posits that the allocation of resources is efficient when an action leads to individuals becoming in a better position, without others appearing in a worse one (Kanbur 2005). The model is based on the aspect of satisfaction. In essence, the works of Vilfredo on the model helped establish discipline of welfare economics. It is argued that there is a relationship between Pareto efficiency and inequality.

**General Efficiency Assumptions **

Under the general conceptualization of efficiency, the allocation of resources is effective if a number of assumptions hold. The first assumption is that input and output markets remain perfectly competitive (Kanbur 2005). The second assumption is that households have access to perfect information about the quality and prices of all available products. Thirdly, firms need to be perfectly knowledgeable about input prices and technologies. Fourthly, decision makers need to consider all costs and benefits attributable to their decisions. The latter assumption posits that external costs do not exist. In an event that the assumptions are not met, the general efficiency is not attainable. Given that market imperfections are common, the probability of obtaining general equilibrium or efficiency is low(Stiglitz 2013).

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**Pareto Efficiency **

Applying the Pareto efficiency model requires an observer to assess whether it is possible to improve someones position without worsening anybodys. From the introduction, it is held that whenever it is possible that changing a certain aspect can lead to improving somebodys condition without jeopardizing other parties, then Pareto optimality is lacking.

An allocation is deemed Pareto efficient or optimal when there is no possibility for further improvements. However, the concept takes a minimal assessment of efficiency, since other important attributes, such as the social aspect, is not considered in the allocation of resources (Klass, Biham, Levy, Malcai & Soloman 2006). While developing the concept, Pareto quashed the notion of cardinal utility, as well as its additive approach. In effect, the economist separated welfare economics from interpersonal association of utilities(Feiwel 1985). The Pareto concept draws on ordinal utility besides distancing itself from value judgments.

Reed (2001) observed that for Pareto efficiency to be secured, the following marginal conditions must be satisfied:

Every person has a unique utility function and enjoys a given amount of each good and factor.

For every firm, the production function and state of technology remain unchanged.

Products are perfectly divisible.

Each producer attempts to produce a specified level of output using the smallest possible cost.

Every person is interested in maximizing his/her satisfaction.

Each individual buys a given volume of all products.

All production factors are perfectly mobile.

After meeting the assumptions, the first order conditions of optimality are listed. There must be optimum distribution of goods amongst consumers (known as efficiency in exchange) (Rushton, Oxley & Croucher 2000). Secondly, the marginal rate of substitution between goods should be equal to the extent that the amount of a good being substituted can compensate for the marginal unit of the other goods without sacrificing the levels of satisfaction. Thirdly, the marginal rate of substitution (MRS) between products has to be the same for each person who uses both of them.

In the fourth place, the MRS between products should not be equal for two consumers in a way that when they seek an exchange, an increase in the level of satisfaction for one does not undermine the satisfaction of the other (Rushton, Oxley & Croucher 2000). The fifth assumption posits that all production factors should be used in manufacturing different goods. In such scenario, it is impractical to increase the production of one good without lowering the production of another. Besides, it is not possible to alter the levels of production without undermining the production of a given product.

Attaining the Pareto optimality would also require that the MRS between a given pair of production factors is the same among the firms that produce different products, while using the two factors in the process (Okun 1975). The other assumption is that efficiency in the production process is connected to technical conditions and customers preferences. It is also a requirement that fulfilling the Pareto efficiency position determines the maximal quantities for different commodities processed given the available factors.

In order to attain optimality, satisfying consumer preferences is central to the realization of maximum economic or social efficiency (Berg & Ostry 2011a). Another condition is that the optimum level of specialization is a necessary requirement in determination of the maximal outputs by all firms. However, the marginal rate of transformation between products must be constant for any entity. Another condition is that the marginal product arising from any factor must also be the same for all organizations.

In equality economics, Pareto efficiency has been reviewed based on the connection between wealth and the population (Shubham & Ravallion 2007). In the observations of Pareto, eighty percent of the land in Italy was owned by twenty percent of people (Koch 2001). Upon carrying surveys in other countries, Pareto discovered the same aspect within many other countries. The results were then graphed using the champagne glass effect that demonstrated the unequal distribution of wealth. Overall, twenty percent of the worlds population was in control of over eighty percent of all resources. The same inequality is visible within companies where 80% of companies are owned by 20% of customers. Similarly, 80% of complaints emanate from 20% of the customers, 80% of sales come from 20% of a companys products and 80% of a companys performance is attributable to 20% of the staff. Thus, it is possible to have significant improvement by concentrating on the most profitable/relevant areas of business, while ignoring the less important.

The Pareto rule is based on 80-20 statistics. However, not every case that fits the rule is qualified as a Pareto scenario. Relying on the Pareto index, when ? is taken as one of the parameters that characterize a given distribution outlined as: ? = log45 ? 1.16, then if eighty percent effect is associated with twenty percent of the causes, it is deemed as a Pareto case (Koch 2004). Eighty percent of the top effect eighty percent must come from twenty percent of the highest causes twenty percent. Put differently, the 64-4 law must also hold, since 80% of 80% is 64, while 20% of 20% is 4 %. The Pareto cases apply in that order.

When assessing equality, two measures: the Gini coefficient and the Hoover index are commonly applied. Using X:Y notation to reflect a case of 8:2, where X+Y = 1, it is possible to compute the two measures.

H = G = |2X-1| = |1-2Y|

X : Y = 1+H : 1- 2Y

2 2

H = G = |2X-1| = |1-2Y|

X : Y = 1+H : 1- 2Y

2 2

The latter index, Theil, is useful in quantifying inequalities with a measure ranging from 0 for half split distributions. It reaches 1 at Pareto distributions having 82:18. Theil indices over 1 lead to high inequalities.

It is apparent that a certain connection exists between Pareto efficiency and equality or inequality. According to Berg and Ostry (2011), inequality does not augur well for long-term efficiency, although Pareto efficiency is hard to obtain without disadvantaging some sections of a society. Moreover, poorly developed efforts to address inequality might lead to negative results.

Lant (2000) noted that a Pareto efficient position could be highly inequitable. Mbaku and Takougang (2003) support the idea that pursuing Pareto efficiency protects the status quo which is largely unequal. As an example, an instance where one person has all products in a community is Pareto because there is no way to put another person in a better condition without negatively influencing the possessor. It also emerges that Pareto efficiency is a mere notion, since an allocation is either efficient or not.

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Taking the example of a market where bundles are traded, it is assumed that if the trader cares about the bundle he/she possesses, then Pareto efficiency is obtained, since a competitive equilibrium is attained. Given that Pareto efficiency has no link with equality, the implication is that a Pareto efficient scenario is equitable. It is also apparent that a Pareto efficient outcome does not imply the absence of Pareto improvements. Moreover, Hausmann, Pritchett and Rodrik (2005) observe that under such concept many efficient positions or scenarios are possible. It is also assumed that any outcome where buyers and sellers are the same as those trading within a competitive equilibrium is Pareto efficient irrespective of the transaction costs. The assumption that each player only cares about his/her bundle is fundamental. In an event that an individuals welfare varies based on what another person buys, the competitive equilibrium is not Pareto efficient.

Although Pareto efficiency is based on the pursuit of increasing satisfaction, the model supports inequality in many cases. Reallocation of resources affects some people negatively; hence, while making others prosper, some are left in a relatively bad position. However, the overall perception that societies need to avoid situations that are inefficient since they predispose some people to suffering underlies the significance of the Pareto model. It is concluded that attaining Pareto efficiency enhances inequality under current conditions.