###### A country which decides to join a Monetary Union expects a decreased ability to stabilize its output around the full employment level and keep
September 3, 2020
###### Price Discrimination There are two types of consumers with inverse demands P1= 202Q1 and P2= 162Q2. Assume for now that N1=N2 = 1. There is a…
September 3, 2020

Looking for help with this market entry problem from an economics class but is very closely related to statistics!

Problem 1. Market Entry (65 points) Setup For this problem, you will need to read the paper by Camerer and Lovallo (1999) posted on NYU Courses.We will consider a slightly simpliﬁed version in our theoretical analysis below. The setup is as follows: 1. N players privately and simultaneously choose whether to enter a market with some known capacity,c, and proﬁt, 1;. 2. The (N ~— E) players who stay out earn a payment of l].3. The E players who enter are randomly assigned an integer-valued ranking, r, ranging from 1 to E. 4. If the number of entrants, E, does not exceed the industry capacity, c, all entrants earn an equal shareof the proﬁt, v/E. 5. If the number of entrants exceeds capacity, then the c highest-rammed entrants (ranked 3* S c) earn v/c.The remaining (E —» :2) players (ranked r &gt; :2) each suffer a loss of K . Formally, we can denote the strategy space of player 3′ E {1, 2, …,N} by 5′, =6 {0,1}, where 0 denotesnon-entry and 1 denotes entry. Throughout this problem, we assume that players maximize their expectedmonetary payoffs. (a) [10 pts] Explain why player i’s expected payoff can be written as: l] Si=01T5= E s,=1,E5c gxg—Kx(%) s,=1,E&gt;c (b) [5 pts] Show that there are no pure-strategy Nash equilibrium in which the number of entrants isstrictly smaller than c. [Hintz use the payoff functions from (a) to show that in such a scenario, there isalways a proﬁtable deviation for nonentrants.]