Question

(15) 1. Suppose the advertising decisions of two firms are inter-related. Firm I always spends $2 million plus what firm 2 spends on advertising. And firm 2 always spends $7 million plus 12.5% of what firm I spends advertising of ! i) Draw the reaction functions for the firms in this problem label each curve and the axes in the same diagram Best Use the inverse matrix method to find the Nash equilibrium in this problem Now use Cramer's rule to verify your answer input in

qn 1

Answer 1

Solution: (15) Given advertising decisions of a fims are inter related. from spends $2million plus 33/31 of what firma spends on Advertising . firma spende $7 million plus 12.51. of what form I spends on advertising. (i) Reaction, funestions graph: - Reaction function is also known as best response function, shows the optimal output que as a function of S = 2000 ++ ) Sy = 7000 + ŚⓇU where si is the spending of fim i Ci =1,2) in millim dollars. Graphi

/ Sz=7+ spending of firmi 31=2+53 function firmy beaction Ja Reaction Reaction fonction of fima. 02 4 7 spending of finna W using inverse matrix method to find Nash Equilibrium: → S1 - 22 sa-st=7 Now read/anging the si, sa terms : Si-S2-2 - S1 + S2 at This linear equation can be written in matrix form:

Thus The (0) - 47 8 1 inverse of 2023 " @ -690 512 loul 23 - $9.522 million and 52 = 174123 ? $7.565 million. (ii) using oramer's gole to verify these we have si, sz in part)

using craness sole: 51. - Są 2 + S2 =7 is written af 0= 1 * * (23/24) A = 125 13/3) 17 !! 62 = Het = (2016) · SI = e = 1813 (235y = (109/03) S2 = = 21/4/23/24 = (194/13) ::Siz $47522 million and. S2 = 87.565 millim (Same of in partin) - O- SUCCESS