In this problem we will derive a party posi- tion equilibrium with partisan politics and probabilistic...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
In this problem we will derive a "party posi- tion" equilibrium with partisan politics and probabilistic voting. The math involved is a little complicated, so we aren't going to do it all explicitly. Instead, we're going to do an example in Excel. That said, I wouldn't be Professor Keaton Miller if I didn't at least expose you to the math, so here we go. There are a continuum of voters that each occupy a position along the real number line that represents their policy preferences. There are two parties, denoted by i = {1, 2}. Each party chooses a position along the real line pi R. The median voter has position 0. Without loss of generality, we will assume that Party 1 is the "left" party and Party 2 is the "right" party, or in other words p P2. The parties each are comprised of partisans who have preferences over the position that the party takes. The partisans for party i are described by a mean preference, and a "preference width" o. The expected payoff for party i is given by (Pi; i, Oi, P-i) = P(Win pi, p-i). V(Pi; i, oi) where P() gives the probability of winning the election and V() gives the value of winning the election to the partisans comprising the party. Define u = 1-p. Then P(Party 1 wins P, P2) We can define P(Party 2 wins P, P2) = 1 - P(Party 1 wins/p, p2). The value of win- ning V() is V (Pij Mi, Oi) = = exp(u) exp(u) + exp(u) 1 O2 Pi Hi exp P(-1/2 (-=-^^)^). These equations are already entered into hw3-parties.xlsx for you. In the top-left of the "Equilibrium calculations" sheet, the ; and o, for each party can be entered. In cells G1 and G2, the position p; taken by each party can be entered. Column I reports the probability of winning as a function of both positions, column J reports the value of winning, and column K reports the expected payoff. We can solve this equilibrium by solving the first order conditions for each party si- multaneously. This a bit challenging to do by hand, so instead we'll take advantage of Excel's Solver utility. To do so, we first must calculate the first order conditions for each party as a function of their positions. I do this in rows 6-8 by taking a nu- meric derivative. That is, I define some d > 0 that is small and calculate the payoff T(pi+d;). The derivative can then be approximated by (pi+8;-)-(Pi). These approximate first order conditions are reported in cells L7 and L8. OTT Opi In this problem we will derive a "party posi- tion" equilibrium with partisan politics and probabilistic voting. The math involved is a little complicated, so we aren't going to do it all explicitly. Instead, we're going to do an example in Excel. That said, I wouldn't be Professor Keaton Miller if I didn't at least expose you to the math, so here we go. There are a continuum of voters that each occupy a position along the real number line that represents their policy preferences. There are two parties, denoted by i = {1, 2}. Each party chooses a position along the real line pi R. The median voter has position 0. Without loss of generality, we will assume that Party 1 is the "left" party and Party 2 is the "right" party, or in other words p P2. The parties each are comprised of partisans who have preferences over the position that the party takes. The partisans for party i are described by a mean preference, and a "preference width" o. The expected payoff for party i is given by (Pi; i, Oi, P-i) = P(Win pi, p-i). V(Pi; i, oi) where P() gives the probability of winning the election and V() gives the value of winning the election to the partisans comprising the party. Define u = 1-p. Then P(Party 1 wins P, P2) We can define P(Party 2 wins P, P2) = 1 - P(Party 1 wins/p, p2). The value of win- ning V() is V (Pij Mi, Oi) = = exp(u) exp(u) + exp(u) 1 O2 Pi Hi exp P(-1/2 (-=-^^)^). These equations are already entered into hw3-parties.xlsx for you. In the top-left of the "Equilibrium calculations" sheet, the ; and o, for each party can be entered. In cells G1 and G2, the position p; taken by each party can be entered. Column I reports the probability of winning as a function of both positions, column J reports the value of winning, and column K reports the expected payoff. We can solve this equilibrium by solving the first order conditions for each party si- multaneously. This a bit challenging to do by hand, so instead we'll take advantage of Excel's Solver utility. To do so, we first must calculate the first order conditions for each party as a function of their positions. I do this in rows 6-8 by taking a nu- meric derivative. That is, I define some d > 0 that is small and calculate the payoff T(pi+d;). The derivative can then be approximated by (pi+8;-)-(Pi). These approximate first order conditions are reported in cells L7 and L8. OTT Opi
Expert Answer:
Answer rating: 100% (QA)
a The correct answer is The equilibrium positions are p1 05 and p2 05 The expected position of the w... View the full answer
Related Book For
Financial Accounting and Reporting a Global Perspective
ISBN: 978-1408076866
4th edition
Authors: Michel Lebas, Herve Stolowy, Yuan Ding
Posted Date:
Students also viewed these economics questions
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
If the sum of the first 7 terms of an A.P. is 119 and that of the first 17 terms is 714, find the sum of its first n terms.
-
The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...
-
Help on this. thanks 2022SP CS234 Computer Science II 1. (Based on P6.11) A supermarket wants to reward its best customer of each day, showing the customer's name on a screen in the supermarket. For...
-
Suppose someone offered to sell you a note calling for the payment of $1,000 15 months from today. They offer to sell it to you for $850. You have $850 in a bank time deposit which pays a 6.76649...
-
Transfer-pricing problem (continuation of 22-25). Refer to Exercise 22-25. Assume that Division A can sell the 1,000 units to other customers at $155 per unit with variable marketing cost of $5 per...
-
Sherman Lawn Service, Inc., began operations and completed the following transactions during August: Aug 1 Received \($1,000\) and issued 100 shares of common stock. Deposited this amount in bank...
-
The bookstore at State University purchases from a vendor sweatshirts emblazoned with the school name and logo. The vendor sells the sweatshirts to the store for $38 apiece. The cost to the bookstore...
-
The comparative financial statements of Lomax Cosmetic Supply for 2024, 2023, and 2022 include the data shown here: (Click the icon to view the comparative financial data.) Read the requirements....
-
Del Conte Construction Company has experienced generally steady growth since its inception in 1976. Management is proud of its record of having maintained or increased its earnings per share in each...
-
For this discussion, focus on a healthcare organization. This can be an organization that you currently work for or an entity that exists within your community. Conduct and present a SWOT analysis of...
-
At year-end 2018, Wallace Landscapings total assets were $2.17 million, and its accounts payable were $560,000. Sales, which in 2018 were $3.5 million, are expected to increase by 35% in 2019. Total...
-
Start with the partial model in the file Ch09 P10 Build a Model.xlsx on the textbooks Web site, which contains the 2018 financial statements of Zieber Corporation. Forecast Ziebers 2019 income...
-
Marti, the owner of an expensive sports car, agreed in writing to sell the car to Berini. Because both parties recognized that some necessary engine repairs were needed, their contract did not...
-
Weintraub wished to donate a music rehearsal room to Northern College, from which she had graduated. She hired Hazelton, an architect who specialized in acoustics, to design the room. Shortly after...
-
A company has outstanding long-term bonds with a face value of $1,000, a 10% coupon rate, 25 years remaining until maturity, and a current market value of $1,214.82. If it pays interest semiannually,...
-
b) Find the apparent depth of the diver's head below water as seen by the instructor. Note, the bending of the light only changes the apparent vertical position of the diver, not its horizontal...
-
A copper wire (density = 8.96 g/cm 3 ) has a diameter of 0.25 mm. If a sample of this copper wire has a mass of 22 g, how long is the wire?
-
Repsol is a Spanish group involved in the oil and gas sector. From the financial statements (annual reports 2010 and 2011), which are prepared in accordance with IFRS, we extracted the following...
-
Multiple Choice Question Select the right answer (only one possible answer unless otherwise stated). 1 The most appropriate method of depreciation of land is (a) The straight-line method (b) The...
-
A company has the following shareholders equity section: Ordinary shares: par = 2 CU; 250,000 shares authorized; 100,000 shares issued and outstanding .. 200,000 Share premium . 30,000 Retained...
-
Sales discounts should appear in the financial statements a. as an addition to inventory. b. as an addition to sales. c. as an operating expense. d. as a deduction from sales.
-
What is the effect of Rice Corporation's 2020 inventory error on net income for 2021? a. No effect b. Understate c. Overstate
-
An error understated Rice Corporation's December 31 , (2020, ending inventory by \(\$ 40,000\). What effect will this error have on total assets and net income for 2020? Assets a. No effect b. No...
Study smarter with the SolutionInn App