Illustrating Finance Policy with Mathematica
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Illustrating Finance Policy with Mathematica

Nicholas L. Georgakopoulos

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eBook - ePub

Illustrating Finance Policy with Mathematica

Nicholas L. Georgakopoulos

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Students in various disciplines—from law and government to business and health policy—need to understand several quantitative aspects of finance (such as the capital asset pricing model or financial options) and policy analysis (e.g., assessing the weight of probabilistic evidence) but often have little quantitative background. This book illustrates those phenomena and explains how to illustrate them using the powerful visuals that computing can produce. Of particular interest to graduate students and scholars in need of sharper quantitative methods, this book introduces the reader to Mathematica, enables readers to use Mathematica to produce their own illustrations, and places specific emphasis on finance and policy as well as the foundations of probability theory.

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Informazioni

Anno
2018
ISBN
9783319953724
Argomento
Économie
Categoria
Économétrie
© The Author(s) 2018
Nicholas L. GeorgakopoulosIllustrating Finance Policy with MathematicaQuantitative Perspectives on Behavioral Economics and Financehttps://doi.org/10.1007/978-3-319-95372-4_1
Begin Abstract

1. The Non-graphical Foundation: Coase and The Law’s Irrelevance

Nicholas L. Georgakopoulos1
(1)
Indiana University, Indianapolis, IN, USA
Nicholas L. Georgakopoulos
End Abstract
The foundation of all policy analysis springs from the thought of the late Ronald Coase that individuals bargain around rules to achieve the best that they can for themselves. According to economic principles, individuals pursue the course of action that maximizes their welfare (not limited to their monetary welfare). Everybody does that in the context of a market economy, and economic forces push individual action toward greater productivity. Injecting in this system a law that impedes a preferred activity will only result in people bargaining around this law, this suboptimal allocation of rights by the legal system. As long as people can do so with no costs, then suboptimal laws are no impediment to the economy functioning well; people just bargain around the suboptimal rules and the economy returns to the optimal. Thus, in a world where bargaining around rules faces no obstacles, distortions, or impediments, the law does not matter. The outcomes are identical regardless of the law.
This notion, that in a perfect world the law is irrelevant, is often called the Coase theorem. Coase did not express it as a theorem. Rather, Coase focused on transaction costs as an important impediment to people bargaining around the rules. If reaching an agreement to reallocate rights is costly, then individuals do not enter into the agreements that cancel any misallocations. Then, the legal rule needs to be correct. Thus, Coase justified some rules by building the much more important foundation that every rule needs to be justified. Each rule must help people overcome an impediment against allocating rights and obligations freely and, therefore, optimally.
A lot more analysis has dealt with this issue since Coase’s article. Coase earned the 1991 Nobel Memorial Prize in Economics for his contribution and proceeded to lament the focus on his foundation—that the law is irrelevant—rather than that transaction costs justify laws, and to also lament the mathematization of economic analysis.1 This chapter visits a couple of paradigmatic examples of Coasean irrelevance and its failures, which make the law relevant again. Readers who seek a fuller analysis may turn to an earlier book of mine.2

1 The Farmer–Rancher Example

The farmer–rancher example illustrates that the law is not relevant by considering a rancher who would save by having the cattle traverse a farm whereas the farmer would suffer from the cattle trampling the crops. The law at issue is whether the farmer is entitled to fences preventing the cattle from crossing compared to an “open range” rule prohibiting fences. If the farmer and the rancher can bargain without impediments, then the optimal outcome arises regardless of the rule.
The setting may be that the farm sits between a watering hole and the ranch. Driving the cattle around the farm to the watering hole costs an extra amount to the rancher, −w. Crossing the farm means that the rancher does not incur that cost but the farmer incurs the cost of trampling, −t. The optimal result is what would obtain if a single person both farmed the farm and ranched at the ranch. This single owner would compare the cost of trampling to the cost of driving the cattle to the water the long way, and choose the least costly. Namely, the single owner would drive the cattle the long way if −w > −t and would have the cattle cross and trample if −t > −w. For example, if the long drive costs $50 and the trample costs $100, the single owner would choose the long drive.
Suppose that the law imposes the wrong rule. The rule is that ranchers are entitled to an open range whereas the long drive costs less than trampling. Is the farmer condemned to suffer trampling? Coase argues that the farmer would bargain with the rancher and have the rancher take the long drive. If the farmer suffers $100 from trampling and the rancher suffers $50 from the long drive, the farmer is willing to pay any amount up to $100 to avoid trampling and the rancher is willing to accept any amount over $50 for taking the long drive. The two sides have room to reach an agreement for the rancher to not cross the farm.
Vice versa, suppose the rule is that the farmer has the right to fence the land but only suffers $25 from trampling while the long drive still costs $50 to the rancher. Will the rancher take the wasteful long drive? Again, Coase’s analysis says no. The rancher is willing to pay up to $50 to avoid the long drive. The farmer should accept anything over $25 to suffer the trampling. The two sides have room to reach an agreement for the rancher to cross the farm, avoiding the long drive.
The point is that the parties circumvent the suboptimal allocation of the right by the law. The private initiative of the two sides leads them to bargain. The bargain leads to the optimal outcome, what a single owner of both the farm and the ranch would have done. The false law is irrelevant in the sense that the law has not changed the actual conduct.

2 The Polluter–Neighbor Example

The polluter–neighbor example takes us to a setting where the polluter sets up a factory that produces a harmful emission and a single neighbor suffers all the harm from that emission. Again, Coase argues that the sides will bargain depending on the cost of avoiding the emission and the harm to the neighbor. Whether the law requires the factory to have a filter that eliminates the emissions or allows the factory to pollute will not change conduct compared to what would occur with a single owner of both the factory and the neighboring property. Analytically, the setting is identical to the farmer–rancher example.
Suppose the filter costs $50 per month and the neighbor suffers $100 per month. A single owner of both would install the filter. Even if the law did not require the filter, the two sides would reach the same outcome. The neighbor would be willing to pay up to $100 to avoid the harm from the unfiltered emissions. The factory should be willing to install the filter if it were to receive anything over $50. The two sides have room for an agreement that would circumvent the suboptimal allocation of the right by the law.
Vice versa, if the neighbor’s harm were only $25 per month, then a single owner of both would not install the filter. Even if the law did require the filter, the owner of the factory would offer up to $50 for the neighbor to suffer the harm without asking for a filter. The neighbor should accept offers above $25 to bear the damage. The two sides have room for an agreement that would circumvent the suboptimal allocation of the right by the law.

3 Impediments to Irrelevance: Transaction Costs and Others

The polluter–neighbor example also serves as an illustration of the importance of transaction costs. A transaction cost is a cost that impedes the reaching of an agreement (as opposed to the costs of fulfilling the agreement). Thus, the cost of traveling to the market, for example, is a transaction cost. The cost of providing a service to customers once at the market is not a transaction cost. Rather, one may call it a fulfillment cost, the cost of fulfilling the bargain to provide them with that service.
To see the importance of transaction costs, suppose that instead of a single neighbor, the polluter has 1000 neighbors who suffer from the pollution. Each suffers a thousandth of the harm but faces some cost in communicating with their neighbors. Suppose that one of the neighbors needs to mail the agreement to each one to sign at the cost of a postage stamp, rounded to $0.50. One thousand mailings produce a cost of $500. Using the numbers of the example, the agreement is not worth the mailing costs. That the mailing costs are greater than the gains of the agreement means that the parties will not enter in the agreement. Any false allocation of the right by the legal system will persist. Transaction costs can cause the failure of Coasean irrelevance.
Any impediment to reaching agreements can cause the failure of irrelevance. Transaction costs are not the only possible impediment to reaching an agreement.
The combination of the irrelevance of the law when agreements have no impediments and the existence of impediments is crucial for policy analysis. Once policy analysis accepts these premises, then the desirability of a certain outcome, such as environmental cleanliness, alone, is not grounds for regulation. Rather, for regulation to be justified, one must also identify an impediment to the private resolution of the matter or regulatory interest. In this way, the adoption of Coase’s premise has made legal analysis much more rigorous and difficult. No longer is the desirability of an outcome a sufficient justification for law. For regulation to be justified, one must also show that the private initiative cannot reach that outcome despite its desirability. Sometimes this second step is trivially easy, as in the case of environmental regulation. Very often, however, establishing that an impediment to private solutions exists is the more difficult step of the analysis.
Returning to the impediments against private resolution of the allocation of rights, scholarship seems to have settled into accepting a few broad categories besides transaction costs: distribution of wealth, systematic errors, negotiation holdouts, and aversion to risk. These are not closed categories. Settings may exist with unique impediments and additional categories may emerge.

3.1 Distribution of Wealth

The most obvious impediment is distributional concerns. To whom a right is allocated determines who will receive compensation for parting with that right, in the cases when the right is not allocated optimally, and who will avoid expenditure, in the cases where the right is correctly allocated. Before celebrating the ease with which distribution may justify rules, however, one must be attentive to the analysis that rules that have distributional consequences distort incentives. The outcome for society is that redistributing through rules is usually inferior to redistributing through an optimal tax regime and letting the rules be optimal.3

3.2 Systematic Errors

One of the most popular sources of failures of Coasean irrelevance is systematic errors. In the economic literature, it appears under the rubric behavioral economics. The 2002 Nobel Memorial Prize in Economics as well as the 2017 prize decorated leaders in behavioral economics, Daniel Kahneman in 2002 and Richard Thaler in 2017. The relevance of systematic errors for failures of Coasean irrelevance is straightforward. If individuals tend to make certain mistakes, then their related decisions to bargain around rules will also tend to be erroneous. Therefore, those decisions may not promote social welfare. Intervention by the legal system may be, then, justified. The caveat in this category is that a strong reaction by the legal system, in the form of a mandatory rule, could end up hurting the very people who do not make the mistake. Professors Sunstein and Thaler have promoted, as a response, the principle of libertarian paternalism: rules designed to overcome the biases that individuals tend to display but also designed so that individuals can elect not to be bound by these rules.4 A new and little understood concern, about the discount rates for evaluating present costs against distant-in-time gains, also seems as a systematic error. Using falsely low discount rate...

Indice dei contenuti

  1. Cover
  2. Front Matter
  3. 1. The Non-graphical Foundation: Coase and The Law’s Irrelevance
  4. 2. Introduction to Mathematica: Hello World in Text and Graphics
  5. 3. The Mathematical Frontier: Trigonometry, Derivatives, Optima, Differential Equations
  6. 4. Money and Time
  7. 5. The Capital Asset Pricing Model
  8. 6. Options
  9. 7. Illustrating Statistical Data
  10. 8. Probability Theory: Imperfect Observations
  11. 9. Financial Statements and Mergers
  12. 10. Aversion to Risk
  13. 11. Financial Crisis Contagion
  14. Back Matter
Stili delle citazioni per Illustrating Finance Policy with Mathematica

APA 6 Citation

Georgakopoulos, N. (2018). Illustrating Finance Policy with Mathematica ([edition unavailable]). Springer International Publishing. Retrieved from https://www.perlego.com/book/3491058/illustrating-finance-policy-with-mathematica-pdf (Original work published 2018)

Chicago Citation

Georgakopoulos, Nicholas. (2018) 2018. Illustrating Finance Policy with Mathematica. [Edition unavailable]. Springer International Publishing. https://www.perlego.com/book/3491058/illustrating-finance-policy-with-mathematica-pdf.

Harvard Citation

Georgakopoulos, N. (2018) Illustrating Finance Policy with Mathematica. [edition unavailable]. Springer International Publishing. Available at: https://www.perlego.com/book/3491058/illustrating-finance-policy-with-mathematica-pdf (Accessed: 15 October 2022).

MLA 7 Citation

Georgakopoulos, Nicholas. Illustrating Finance Policy with Mathematica. [edition unavailable]. Springer International Publishing, 2018. Web. 15 Oct. 2022.