Which one of the following statements about the 2-stage linear city model in topic 4 is correct? (topic 4 is in the images attached) A.In the first stage, the firms simultaneously choose locations. In the second stage the firms simultaneously choose prices. B.In the first stage, the firms simultaneously choose capacities. In the second stage the firms simultaneously choose prices. C.In the first stage, the firms simultaneously choose locations. In the second stage the firms simultaneously choose quantities. D.None of the other three statements is correct. 1. Consider a linear city model with unit length of the city and linear trans-portation cost td, where d is consumer's distance to his selected shop. Thelocation of the two firms are at the two ends of the city.(a) Show that when 5 > c+3t , a firm i's best response to any price ofits rival p; always results in all consumers purchasing from one of thetwo firms (i.e., the market is covered).(b) Derive both firms' best response functions, show that prices of thetwo firms are strategic complements.(c) Derive the Nash equilibrium prices and profits of the game.2. Show that if transportation costs are td?, where d is consumer's distance tohis selected shop, Salop's circular city model yields p= c+t/n², and that(t/f)/3 > n* = [t/ (6f)]³ (suppose 3 is sufficiently|1/3with free entry, n° =high so that the market is covered in equilibrium).3. Consider the linear city model in which the two firms may have differentpositive constant unit costs ci < c2. The city has unit length and thetransportation cost is linear, i.e., td. Suppose s is sufficiently high so thatthe market is covered in equilibrium.(a) Determine the Nash equilibrium prices and sales levels for equilibriain which both firms make strictly positive sales. How do local changesin c1 affect the equilibrium prices and profits of firms 1 and 2?(b) For what values of c1 and c2 does the equilibrium involve one firmmaking no sales? 1. Solution:(a) First consider firm i's best response when firm j's price is too highto provide any positive net surplus for any consumer, i.e., p; 2 5.In this case firm i is a monopoly, and a marginal consumer who isdifferent between buying its product and not doing so is r units ofdistance away, that 5-p;-tx = 0, giving rise to the demand function:D; (p;) =equals e, and entails the monopoly output: D; (p")=. When§ >c+2t (which is satisfied given that 5> c+3t), D; (p") > 1, i.e.,the market is covered.Pi. The monopoly price p" maximises (p; – c) -PiNow consider firm i's best response when p; < 5. Suppose that themarket is not covered, then firm i must be a local monopoly; theabove analysis suggests that when s >c+ 2t it is not optimal for afirm to leave any consumer in his (local) monopoly market unserved,this gives rise to a contradiction. Hence, in firm i's best response,the market must be covered.(b) Equation: 5 – p1 – tx = 5 – p1 – t (1 – x) determines the location ofa marginal consumer who is indifferent between buying from eithershop, hence, the demands (if both firms have positive market shares):D1 (p1, p2) = x = P2-Pi+t and D2 (p1, P2) = 1 – x = P1-P2+t.Firm 1 maximises its profit: (pi – c) P²¬P1+, the FOC entails pi =P2+c+t, which is the best reaction function for firm 1. Similarly, thebest reaction by firm 2 is p2 = Ptett. Given that P = > 0, we2tdp;conclude that prices of the two firms are strategic complements.(Extra: To ensure that the above reaction functions do not makeany firm react suboptimally, we need to impose a condition: pi 2Pj – t, since pi = Pj – t already allows firm i to take over theentire market and makes a lower price unnecessary and undesir-able. Hence, Pi =Pj+c+t> Pj – t which entails p; < c + 3t.Overall, given that s > c+ 3t, a firm's best response should be:Pj 5Pi+c+t2ifR (p;) =Pj – t5 - tif(c) N.E.: pi = p = c+t, q† = q = and II = II; = .2. The analysis is similar to the lecture note except that the transportationcost takes a quadratic form. To locate the marginal consumers, use thep-Pi+equation: tx + Pi =t ( - x) + p, which gives rise to x =and the demand function: D¡ (pi,p) = 2x =P-Pit Using the FOCp-Pi+for maximising (Pi – c) _2 and then imposing pi = p, the symmetric

In the first period, firms choose location and in the second period, the firms compete in prices,…

Answered: Which one of the following statements…

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter16: Bargaining

Section: Chapter Questions

Problem 16.1IP

	A.	In the first stage, the firms simultaneously choose locations. In the second stage the firms simultaneously choose prices.
	B.	In the first stage, the firms simultaneously choose capacities. In the second stage the firms simultaneously choose prices.
	C.	In the first stage, the firms simultaneously choose locations. In the second stage the firms simultaneously choose quantities.
	D.	None of the other three statements is correct.