Economics for Public Policy - Essay Example

? Economics for Public Policy Economics for Public Policy Response to question Part a. Considering the application of the prisoner’s game in economics, during the advertisement, the advertisement effectiveness of Firm A is determined by Firm B’s advertisement. On the other hand, the profits obtained from Firm B would be affected by the Firm A’s advertisement. Whenever the two firms decide to advertise in a certain period, the advertisement will cancel out, the cost of advertisement will increase the expenses, and the number of customers would remain constant (Becker and Ann, 2009). In this case, the two firms would benefit from a reduction in the advertisement. In this regard, the legal system is the legal advertisement by the two companies. The anarchy is a situation where both the two firms fail to take part in advertisement. This situation would be beneficial for both the two firms. On the other hand, if Firm B fails to advertise where as Firm A advertise, the advertisement would significantly benefit Firm A. However, the maximum level of advertisement by a single firm is depended on the degree of advertisement undertaken by the other firm (Axelrod, 2004). This means that there is an equal outcome whenever different companies pursue advertisement to a level below the equilibrium. This principle can be applied to different areas such as rational environments. It explains why the presidential candidates in two different parties are actually similar. Whenever the candidates are confirmed in the preliminaries, they would be created inside their camps of partisan. The electorate who are undecided would be categorised in the central political spectrum. The candidates may tend to rash to the middle group so as to appeal to the group. In this case, the assumption is that voters would select the close option thus many votes could be acquired whenever one is in the center. Part b. The benefits of welfare are an efficiency-enhancing insurance scheme, which may insure against incoming risks. Those individuals who hold the illustrations of the prisoner's dilemma believe that the game highlights morality in challenges that are faced by large groups or welfare. Similar to the game of two players, the game with many players pays the cooperating players R, and defecting players P. In welfare, when some individual defect while some cooperate the cooperating players would get an S while the defecting players will get a T. A good example is illustrated in the commons tragedy. All The members of a certain welfare prefer to graze their animals on the commons instead of maintaining the animals on his own land (Axelrod and William, 2006). The common resource will become unsuitable for grazing whenever it is used by a number above the threshold. In this case, there is a derived benefit B that each welfare member can achieve whenever he or she pays a cost C sufficiently. Above n choose C Below n choose C C C+ B C D B 0 Above n choose C Below n choose C C C+ B C D B 0 From the table, there is an assumption that cost C is negative. The dilemma in this case, is to obtain a benefit with no cost incurred. In a situation, that is ideal the benefit is always a be given reward together with the cost. The challenging situation is to incur a cost but no benefit. This means that a payoff is ordered as B>(B+C)>0>C. In this respect, whenever one chooses C he obtains C+B hence the benefits of welfare are an efficiency-enhancing insurance scheme. Response to question 2. Part a. The two categories of voters will include the rich the middle and the poor persons. R M P Gross income $13 $4 $3 Willingness to pay $4.5 $1.5 $0.5 . This cannot be said to be a pay off matrix since all the willingness to pay, being penalties needs to be identified as negative numbers. T= [] If we add $4 to each element we get T= ] T=] The first step involves checking for saddle points (Bendor, 2007). This is a point where the unstable and stable manifold has a dimension that fails to be a zero (Axelrod, 2007). In a matrix, it is an element that can be the smallest, in its own raw, and the largest, in its own column. In this respect, the matrix has no saddle point. Additionally, there are no column or rows that are dominant. The next step involves making the elements be non negatives. In this respect, we add 17 to all the elements taking K = 17. The new matrix would be given as; T=] The next step involves the use of linear programming. That is to say that Maximise T= x + y+ z subject to 0x + 17y + 10z 1 17x + 11y + 12z 1 X0, y0, z0. This inequality can be solved using the following method. X y z 0 17 10 17 11 12 17R3-11R2 X y z 0 17 10 289 0 34 X y z 0 1 10/17 17 0 2 10/17R3-2R2 X y z 0 1 10/17 10 0 0 [X Y Z]T = [1/10, 1/17,1]= [10,17] T= 17/10= 1.7 This implies that the appropriate tax rate would be $ 1.7. Part b. R M P Gross income $6 $3 $2. Willingness to pay $4.5 $1.5 $0.5 In this example of an income distribution, the gross income is not enough to pay for the tax and the project. This is an unstable condition since the individuals may not be able to pay for whatever they were willing. In this situation, the individuals have a will to pay, but mat lack the potential to pay for the project and the tax (Aumann, 2008). This distribution of income would be rejected at the poll because the participants have insufficient funds to pay both the tax and the project. Such a situation may exist in many situations in which an individual may have a willingness to purchase a product, but lack the money to make the purchase. Part c. No. A project will gain a majority whenever such a project receives the most votes and the project are financed by all the voters. This enables the project to avoid the prisoner’s dilemma. Financing a project with a lump sum tax does not necessarily mean that the lump-sum tax is given out by all voters. Lump-sum tax is normally collected from voters with a majority of votes. This means that the other voters are non cooperative in contributing. This means that a lump-sum tax is normally collected from the voters who vote for the project, but not those who those who vote against the project. In this respect, the project will not gain a majority through being financed by a lump-sum tax due to the prisoner’s dilemma. A majority gain will be obtained if the tax to finance the project is contributed by everyone hence efficiency. Part d. Policies that are efficient are enabling policies for which both the voters avoids the prisoner’s dilemma. This may also occur whenever the voters avoid the possibilities for a failure in the market. Aspects such as public goods, market power, externalities, and asymmetric information should be considered keenly. Failure in the market occurs whenever the public good is inefficient as justified for the intervention of the government (Mueller, 2003). Voting may lead to efficient policies because it gives a chance for both parties to take the cost hence a maximum benefit. In this respect, voting enhanced efficient policies in part a. In part c, voting did not enhance efficiency because the project was financed by a lump sum tax and not the majority of the voters. This is so because the cooperation of the voters in voting enhances efficiency. Part e. When the voters vote for the proportion tax in part a and the lump sum tax in part c, the proportional tax in part a will obtain a majority of gain. This is because, in part a, all the participants or voters for the project will undertake the cost of paying the required tax. In this case, there is cooperation among the voters. Cooperation among participants will reduce the chances of market failure and also do away with the prisoner’s dilemma. In this case, the voting would enhance efficiency. On the other hand, in part c the lump some tax is contributed by the non-cooperative voters only. This option is not efficient because it leads to the prisoner’s dilemma and the least majority.Response to question 3. Part a. Median voter theorem. This theory argues out that a voting system of majority rule picks an outcome that is the median voter most preferred outcome. In each model of economy, the middle voter could come up with a number of assumptions. This theorem has an assumption that the voters can give all the alternatives of an election in a political spectrum that is one dimensional. It is interesting that different voters can do this whenever they are voting for a policy that is single. Problems may come up whenever they are multiple policies that are considered for the referendum hence coming up with a continuum multidimensional (Axelrod and William, 2006). This theory has an assumption that the preferences of voters are normally single-peaked meaning that the voters select the alternatives that are closest towards their outcome. This means that as the outcome moves away from the voter, the voter chances to vote for that outcome reduces. Additionally, this theorem strictly argues out that the voters would vote for their real preferences. However, from the research this may not be true since voters may not vote for their preferences. Part b. Public goods have a number of properties. The first property is known as non-excludability. This property argues outlines that the rewards obtained out of the available public good may not be kept for those individuals who really paid for them. This means that even the non cooperative payers may equally enjoy the consumption benefits having no financial cost for themselves. Another property of public goods is the no rival consumption. This property argues out that the public good consumption by an individual fails to reduce the existence of the good to every other individual. In this case, all individuals in the society consume an equal amount of public good besides the many different preferences and tests for the goods. Public good is provided through finding the quantity for which individuals would be willing to purchase at each price. Part c. Whenever the median voter votes for the preferred candidate, it means that the median voter will be the only cooperative voter in the game. This is not efficient as it creates about the existence of the prisoner’s dilemma. If only few individual contribute for the cost of maintaining the public good, it will be extremely inefficient for the cooperative individuals. This is so because overutilization of the public good would make the public good be overexploited. If some people fail to participate in the contribution of the cost, the whole resource would not be well managed hence will be depleted. This will be inefficient to all the voters. In this respect, the voting in part a will lead to under-provision of the public good. Response to question 4. Part a. Condorcet rule. Condorcet rule involves a method of election that selects a certain candidate who would win through a majority rule of all the pairings over the other different candidates especially if one candidate has keeps that property. A Condorcet winner is that the candidate who has a property win. In many situations a Condorcet winner never always exists due to the existence of a majority of preferences. In a case of each candidate, there must be a different one who is the preference of a majority hence a Condorcet paradox. In this respect, the methods of voting which normally elects Condorcet winner are those that are satisfied by the criterion of Condorcet. This method has a single voting round, where by the voters rank different candidates in a top-bottom hierarchy. This is the order of preference for the ranking voter. This is because voters are always free to vote and could specific reasons of ranking in a certain manner. The winner is found through conducting a number of comparisons that are pair wise by use of the basic procedures. For instance, N candidates, will need 1/2N (N-1) hypothetical pair wise elections. For this problem, there are three options to be voted for by nine voters. This means that there would be 1/2x 3(3-1) = 3 pair wise comparisons that would be made. The winning project of each pairing would be the preferred vote. C1: F > S > T C2: F > S > T C3: S > F > T C4: S > T > F C5: T > F > S C6: T > F > S C7: F > T > S C8: F > T > S C9: S > T > F The first step involves counting the number of voters who gave each project the highest vote. F= C1,C2,C7,C8 S= C3,C4,C9 T=C5,C6 In this case the football stadium project is the Condorcet winner. Borda rule. Border rule involves the border count system of voting. In this system, points are normally provided for a candidate’s position in the rank order of a voter. The winning candidate is one with most votes. For the case of this problem, the winning project will be one with most points. The border rule awards the first choice two points, second choice one and a zero for the third choice. C1: F > S > T C2: F > S > T C3: S > F > T C4: S > T > F C5: T > F > S C6: T > F > S C7: F > T > S C8: F > T > S C9: S > T > F In this respect, F receives 2 points from C1,C2,C7,C8, hence a total of (2x4) which is 8, 1 point from C3,C5,C6, hence a total of (1x3) which is 3, and 0 points the rest of the voters. The total points for F will be 8+3+0=11. For the case of S, 2 points are obtained from C3, C4,C9 totalling to (2x3) 6 points, 1 point from C1,C2,totalling to (1x2) 2, and 0 points from the rest of the voters. The total points for S will be 6+ 2 = 8. Considering project T, it receives 2 points from C5,C6 totalling to 4 points, 1 point from C4,C7, C8,C9 totalling to 4 points. The total points for t would be 4+4=8. The Borda winning project will be project for the football stadium since it obtained 11 points, which is 3 points higher than the points for other projects. Plurality rule. Plurality rule involves plurality voting system whereby the preference of the voter is not considered on the ballot. In a tactical voting assumption, it can be simple to come up with an example that fails the criterion of Condorcet. C1: F > S > T C2: F > S > T C3: S > F > T C4: S > T > F C5: T > F > S C6: T > F > S C7: F > T > S C8: F > T > S C9: S > T > F In this problem the voters preferring project F to S to T, F to T to S and vote F is 44.4%. Those who prefer project S to F to T, S to T to F and vote S is 33.3%. Those who prefer project T to F to S, T and vote for T is 22.2%. The winner would be project F with 44.4%. Two-round elimination rule. This involves the two-round voting system that may be used in electing a single winner. In this system a voter casts a unit vote for their choice project. Whenever no project gets the needed vote number, then the project with votes less than the required proportion is eliminated and another voting round happens. Round 1. F:4 S: 3 T: 2 Round 2 No project has an absolute number of votes hence the two projects having thigh votes: F and S move to the second round where as T is eliminated. The supporters of project T must now vote for either F or S since their preferred project has been eliminated. The two supporters of proposal T are game conscious hence, give their votes to proposal F. If the supporters of the remaining proposals in the first round maintain their vote, the new scores of the second round would be; F: 6 S: 3 The football proposal has a majority vote that is absolute hence the declared winner. Part b. Plurality voting does not ensure selection of the Condorcet winner. In a tactical voting assumption it can be simple to come up with an example that fails the criterion of Condorcet (Hillman, 2009). Consider the voting system shown. In this problem the preferences for councillors 4,7, and 9 were modified. The preference for councillor 4 was modified from S > F > T to S > T > F preference for councillor 7 was modified from S > F > T to F > T > S preference for councillor 9 was modified from S > F > T to S > T > F. C1: F > S > T C2: F > S > T C3: S > F > T C4: S > F > T C5: T > F > S C6: T > F > S C7: S > F > T C8: F > S > T C9: S > F > T In this example if 30% of the councillors prefer project F to project S to project T and vote for F, 30% of the voters prefer project T to F to S and vote for T, and 40% of the voters prefer project S to project F to project T and vote for project S. The project proposal B would win having 40% of the votes. In this case, the Condorcet winner would be F beating T 70% to 30% and S 60% to 40%. Part c. The system of two-round-elimination voting does not ensure selection of the Condorcet winner. Consider the voting system shown. In this problem the preferences for councilors4,7, and 9 were modified. The preference for councillor 4 was modified from S > F > T to S > T > F preference for councillor 7 was modified from S > F > T to F > T > S preference for councillor 9 was modified from S > F > T to S > T > F. C1: F > S > T C2: F > S > T C3: S > F > T C4: S > F > T C5: T > F > S C6: T > F > S C7: S > F > T C8: F > S > T C9: S > F > T In this voting system project F is the Condorcet winner since it has a majority of the preferred votes. However, using the two-round elimination voting, the result is different. Round 1. F:3 S: 4 T: 2 Round 2 No project has an absolute number of votes hence the two projects having thigh votes: F and S move to the second round where as T is eliminated (Aumann, 2005). The supporters of project T must now vote for either F or S since their preferred project has been eliminated. The two supporters of proposal T are school conscious hence, give their votes to proposal S. If the supporters of the remaining proposals in the first round maintain their vote, the new scores of the second round would be; F: 3 S: 6 The School building proposal (S) has a majority vote that is absolute hence the declared winner. Part d. Borda voting does not ensure selection of the Condorcet winner. Consider the voting system shown. In this voting system the preferences for councillor 1 and two were modified. This preferences were modified to F, T, S from F, S, T. In this system proposal F is the Condorcet winner. However, the result is different when using the Borda rule. C1: F > T> S C2: F > T > S C3: S > F > T C4: S > T > F C5: T > F > S C6: T > F > S C7: F > T > S C8: F > T > S C9: S > T > F In this respect, F receives 2 points from C1,C2,C7,C8, hence a total of (2x4) which is 8, 1 point from C3,C5,C6, hence a total of (1x3) which is 3, and 0 points the rest of the voters. The total points for F will be 8+3+0=11. For the case of S, 2 points are obtained from C3, C4,C9 totalling to (2x3) 6 points, and 0 points from the rest of the voters. The total points for S will be 6+ 0 = 6. Considering project T, it receives 2 points from C5,C6 totalling to 4 points, 1 point from C1,C2,C4,C7, C8,C9 totalling to 6 points. The total points for t would be 4+6=12. The Borda winning project will be project T since it obtained 12 points which is 1 points higher than the points for F and 6 points higher than the points for S. References. Aumann, R., 2005. Backward Induction and Common Knowledge of Rationality, Games and Economic Behavior, 8:97-105 Aumann, R., 2008. Note on the Centipede Game, Games and Economic Behavior, 23:97-105 Axelrod, R.,2007. The Emergences of Cooperation Among Egoist, J American Political Science Reviews, 75: 306-318. Axelrod, R., 2004. The Evolution of Cooperation , New York: Basic Books. Axelrod, R., and Douglas, D., 2008. The Further Evolution of Cooperation Science, 242: 1385-1390. Axelrod, R., and William, H., 2006. Evolutionary Cooperative Science, 211: 1390-1396. Becker, N., and Ann., 2009. Indefinitely Repeated Games: A Response to Carroll, Theory and Decision, 28: 189-195. Bendor, J., 2007. Good and Bad Times: Reciprocities in an Uncertain Worlds, American J of Political Science, 31: 531-558. Hillman, A.L., 2009., Public Financse and Public Policies. Responsibility and Limitation of Governments, Second Editions. Cambridge: Cambridge University Press. Mueller, D.C., 2003. Public Choice III, Cambridge. UK: Cambridge University Press. Read More