ECON 2016 -Political Economics Questionnaire-ECON 2016 The University of Nottingham Political Economics Questionnaire

ECON2016-R1 The University of Nottingham SCHOOL OF ECONOMICS TAKE-HOME EXAM SPRING SEMESTER AUGUST EXAM, 2019-2020 ECON2016 POLITICAL ECONOMY Answer the Question in Section A Answer ONE Question from Section B The maximum word limit for this exam is 1500 words Specific Instructions: Sections A and B are given the same weight Typed Equations: Any equations in your answer should be typed either with the Word Equation Editor (or similar) or just with normal text (e.g. using subscripts etc.). Any mathematical notation used must be defined within your answer. Any diagrams in your answer should either be constructed directly within Word (e.g. using the Insert and Shapes menus, to obtain lines, curves etc.) or constructed separately and then imported (e.g. using Insert-Picture or Insert-Object). In all cases, your submission must be a single .pdf file and it is your responsibility to insure it contains and reliably displays all desired components. Academic Misconduct: Please Read the THE submission instructions fully regarding academic misconduct rules and regulations. SUBMISSION INSTRUCTIONS: • All submissions should be uploaded into the designated box on the deadline date shown on the Moodle page by 3pm (BST). • Please upload in PDF format only. • Exam start and return times are based on UK clocks (British Summer Time), so if you are based out of the country, please ensure this is considered in your workload planning. • University lateness regulations will apply. Unless you have been formally granted an extension to the above deadline, a take-home exam submitted after 3pm on the day of the deadline will incur a lateness penalty of 5%; an exam submitted after 3pm on the following working day will incur a 10% penalty; and so on. • This rubric should be read in conjunction with the previously released THE submission instructions which provides more detailed information about formatting and referencing. Submission of your work to the Moodle box constitutes an acceptance of the above procedures and that you have read and understood them. ECON2016-R1 2 ECON2016-R1 SECTION A Answer the question below 1. Consider an economy with seven voters and one policy issue, the tax rate. Each of the voters has an ideal tax rate. The ideal tax rates are t1 = 0.05, t2 = 0.15, t3 = 0.35, t4 = 0.60, t5 = 0.65, t6 = 0.70 and t7 = 0.85, where ti is the ideal tax rate of voter i. Suppose each of the voters simultaneously decides whether to run for office. Voters can only run on a policy platform equal to their ideal tax rate. Each of the voters then votes for the candidate that offers a tax rate closest to their ideal. If two or more tax rates are equally desirable, the voter votes for one of them at random. The winner is the candidate with the most votes; ties are resolved at random. Any candidate that runs for office incurs a utility loss of 0.15. Furthermore, if the actual tax rate is t, each voter experiences a utility loss equal to the distance between the actual tax rate and their ideal, |t – ti|. When deciding whether to run for office, a voter aims to minimize the total utility loss incurred. Discuss the set of equilibria of this game. Hint: Find as many equilibria as you can, commenting on their properties and explaining why they are equilibria. You may also want to discuss why some particular strategy combinations that look promising are not equilibria, or what modifications of the data in the exercise would produce more (or fewer) equilibria. SECTION B Answer ONE of the following questions 2. Suppose there are five voters and four alternative policies (a, b, c and d). The voters rank the alternative policies as follows: Voter 1 (15 votes): a, c, d, b Voter 2 (12 votes): b, a, c, d Voter 3 (8 votes): c, b, d, a Voter 4 (6 votes): d, c, b, a Voter 5 (3 votes): d, b, a, c Note that each voter is given a different number of votes (voter 1 has 15 votes, voter 3 has 12 votes etc). Voters cannot split their votes between several alternatives, but must cast all their votes for the same alternative. The final policy is decided in the following way (elimination voting procedure). Initially all four alternatives are available. Voters vote simultaneously between the alternatives. The alternative with the fewest votes is eliminated (if two alternatives have the fewest votes, one is eliminated at random) and the rest go into the next round of voting until there is only one alternative left. Discuss the set of equilibria of this game. Hint. Is there an equilibrium in which each of the five voters votes sincerely in every round? Is there more than one equilibrium? You may also want to comment on ECON2016-R1 3 ECON2016-R1 whether your answer would change if preferences were slightly different. How does your answer relate to the Gibbard-Satterthwaite theorem? 3. Consider an economy where individuals have utility function 𝑢(𝑐, 𝑙) = 𝑐 + 5ln⁡(𝑙), where 𝑐⁡is consumption and 𝑙 is leisure. Each individual has 1 unit of time that can be divided between 𝑛 (work) and 𝑙 (leisure), hence 𝑙 + 𝑛 = 1. Individuals differ in their productivity 𝑥 ≥ 0. If an individual spends n time units on work, he produces 𝑥𝑛 units of income. This income is taxed at a rate 𝑡, and each individual also receives a lump-sum tax 𝑟, hence disposable income is 𝑦 = (1 − 𝑡)𝑥𝑛 + 𝑟. All disposable income is consumed (there are no savings), hence 𝑐 = 𝑦. When deciding on their labour supply, individuals maximize their utility taking the tax rate t and the lump-sum transfer 𝑟 as given. The government budget constraint requires that tax revenue is spent on the lump-sum tax 𝑟 (there can be no surplus or deficit). There are five individuals in the economy, with productivities equal to 3, 6, 8, 15, and 25 respectively. Suppose the tax rate and lump-sum transfer are determined as follows. In the first stage, the median voter decides on t and r. After t and r are decided, each of the five individuals decides on their labour supply. Income is then taxed and redistribution then takes place. What are the values of t and r set by the median voter? Compare this situation with one in which the productivities are the same but the utility function is 𝑢(𝑐, 𝑙) = 2𝑐 + ln⁡(𝑙). Hint. Set up the maximization problem for the median voter, and find the values of t and r for each of the two utility functions provided. Discuss what considerations arise from the point of view of the median voter in deciding the tax rate. What features of the distribution of the productivities lead to higher or lower taxes? What features of the utility function lead to higher or lower taxes? 4. Consider the following Parliament Seats Lib Left Con Green SD 43 29 29 14 9 Initially the threshold required for a majority is 72. The parties can be ordered in terms of ideology from left to right in the following way: Left, Green, SD, Lib, Con. Suppose the Con party’s seats are reduced from 29 to 26, while the threshold remains at 72. Discuss how this change affects the predictions of the minimal connected winning coalition theory and the homogeneous representation. Which parties gain and which parties lose from this change? Hint. Outline the predictions of the minimal connected winning coalition theory and the homogeneous representation. Explicitly state which parties gain and which parties lose and motivate your answer. Do the theories agree on the effect of reducing the Con party’s weight? END ECON2016-R1
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