Amendment of Coase Theorem under Zero Transaction Cost

Song, Guiwu

Coase theorem states that if trade in an externality is possible and there are sufficiently low transaction costs, bargaining will lead to a Pareto efficient outcome regardless of the initial allocation of property. This is analyzed by an example of factory pollution issue, where both parties reached maximum mutual benefit through negotiation and installation agreement.

There is a case study in economics called ultimatum game which can be seen as a relocation of resource under zero transaction cost. However, its result does not follow Coase theorem.

The ultimatum game has a rule like this: one player, the proposer, is endowed with a sum of money. They are tasked with splitting it with another player, the responder. Once the proposer communicates their decision, the responder may accept it or reject it. If the responder accepts, the money is split per the proposal; if the responder rejects, both players receive nothing. The proposer should predict the reaction of the responder. For example, if proposer has $100 and proposed a split of 99% for himself and 1% for the responder. The responder would get only $1 by accepting it or nothing by rejecting it. A British game theory expert experimented that proposer tends to propose a 50:50 split and responder would most likely accept a split of more than 30% for them. Additionally, according to comparative culture studies done by American scholars, a similar result can be experimented in both developed culture and a primitive tribe of the Amazon basin.

Under ultimatum game theorem, both parties would not reach maximum collective gain or minimum transaction cost if responder reject the proposal. This outcome does not follow standard Coase Theorem.

In order to solve this contradiction, the author suggests that below two terms could be implemented in existing theorem.

Firstly, we should extend the concept of cost and benefit in Coase Theorem. Costs and benefits in Coase's theorem, mainly considering material costs and benefits without considering spiritual costs and benefits. In the ultimatum game, the actual consideration of the material is the sum of material cost, material income, spiritual cost and spiritual income. The resource allocation strategy is determined according to the material cost plus the spiritual cost and the sum of the material income and the spiritual income. In this case, for the proposers, some planners tend to split 50:50 instead of giving themselves more, and there is a spiritual benefit problem. Because proposer can treat responder fairly, and he can bring spiritual benefits to himself and let others have respect for him. On the contrary, let responder disrespect him and he will have spiritual loss. On the responders’ perspective, most responders would tend to reject when they get less than 30%. This is also factor in the spiritual gain and loss. When responders were given a proposal of less than 30%, the sum of material gain and spiritual loss would be negative and they will reject the offer.

Secondly, we should include the initial allocation of the property as a factor as to reach Pareto efficient outcome. It can be observed from ultimatum game theorem that under zero transaction cost, more people (responder) would likely to accept the offer under fairer distribution of the property. This would eventually help both parties to reach maximum material and spiritual gain as a whole. Furthermore, we could promote this theorem into the perspective of sociology which is under sufficiently low transaction cost, bargaining will lead to Pareto efficient outcome with the fair amount of initial allocation of property.

Finally, it may be concluded that the comprehensive statement of Coase theorem should be: from social’s perspective, if trade in an externality is possible, there are sufficiently low transaction costs and the initial allocation of property is fair at certain level, bargaining may lead to a Pareto efficient outcome (note: here it may lead to a Pareto efficient outcome but not guaranteed. There are many other factors affecting the outcome, like level of rationalization, moral standards, unequal distribution of information, etc.); from individual’s perspective, people consider maximum personal gain as a sum of material and spiritual gain instead of just material gain.

Above conclusion could also be implemented into scenarios where transaction cost is high. However, this may increase the complexity of initial property allocation thus the difficulty of reaching Pareto efficient outcome. After all the overall direction is that the fairer the initial allocation of the property is, the more likely the state will reach maximum collective gain.

Lanzhou, Gansu, China

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