problem+set+8+solutions

problem+set+8+solutions - Econ 1 Fall 2010 University of...

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Econ 1, Fall 2010 Problem Set 8 Solutions University of California, Berkeley Page 1 of 15 Problem Set #8 Solutions 1. Economic Theory of Politics: Suppose that voters’ preferences as to the size of federal government spending are uniformly distributed between a lower value of 10% of GDP and a higher value of 40% of GDP. Suppose also that each political party announces a single number as its platform for the federal government share of GDP, and assume that each voter votes for the party whose platform is closest to her preference on this sole issue. a. Suppose that the Republicans announce a platform of 15% of GDP and the Democrats announce a platform of 30% of GDP. What share of the vote do the Republicans get? The midpoint between 15% of GDP and 30% of GDP is 22.5% of GDP. Everyone who has a preference for federal government spending that is less than 22.5% of GDP will be attracted by the closer Republican platform, and everyone who has a preference for federal government spending that is more than 22.5% of GDP will be attracted by the closer Democratic platform. Since the voter preferences are uniformly distributed between 10% of GDP and 40% of GDP the Republicans will get g2779g2779 . g2782 g2778g2777 g2781g2777 g2778g2777 = g2778g2779 . g2782 g2780g2777 ≈g2781g2778 . g2783g2784 % of the vote. b. Suppose that the Republicans announce a platform of 25% of GDP and the Democrats announce a platform of 30% of GDP. What share of the vote do the Republicans get? The midpoint between 25% of GDP and 30% of GDP is 27.5% of GDP. Everyone who has a preference for federal government spending that is less than 27.5% of GDP will be attracted by the closer Republican platform, and everyone who has a preference for federal government spending that is more than 27.5% of GDP will be attracted by the closer Democratic platform. Since the voter preferences are uniformly distributed between 10% of GDP and 40% of GDP the Republicans will get g2779g2784 . g2782 g2778g2777 g2781g2777 g2778g2777 = g2778g2784 . g2782 g2780g2777 ≈g2782g2785 . g2780g2780 % of the vote. c. Suppose that the Republicans announce a platform of 24.99% of GDP and the Democrats announce a platform of 25.01% of GDP. What share of the vote do the Republicans get? The midpoint between 24.99% of GDP and 25.01% of GDP is 25% of GDP. Everyone who has a preference for federal government spending that is less than 25% of GDP will be attracted by the closer Republican platform, and everyone who has a preference for federal government spending that is more than 25% of GDP will be attracted by the closer Democratic platform. Since the voter preferences are uniformly distributed between 10% of GDP and 40% of GDP the Republicans will get g2779g2782 g2778g2777 g2781g2777 g2778g2777 = g2778g2782 g2780g2777 =g2782g2777 % of the vote. d. Economists Anthony Downs and James Buchanan and political scientist Gordon Tullock have argued that a two-party system where politicians are most interested not in maintaining ideological purity but in getting elected and reelected does a good job in producing a government that governs according to the will of the people. What bearing do you think this problem has on this issue? Does it strengthen or weaken your assessment of the Downs, Buchanan, Tullock position?
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