Question

Section 2: Short Answer and Show your work (5 points) In this section, please complete the work below and then go to answer "Short answer" questions in the google form. Then show your work. Your work will be graded and partial credits will be given if you make mistakes in the calculation. For your work, you can write in a piece of paper and take photo, snapshot of ipad screed, pdf files from ipad or word. You can also just type your work in the provided space at Google form. (e.g.d^2+(x)/dx^2 + 2x^2+2) Any method that I can clearly read is ok. Firms A and B are competitors in the same industry. Each firm observes from the past record that the profits of the firms depend on the advertisement budget of her company and the other firm. Let A and B are advertisement budget of Firms A and B respectively. The profit functions of both firms are as follows and both firms know both functions. Profit of Firm A - ProfitA(A,B) = 497- 888 + (118-24)A-4A^2 Profit of Firm B. ProfitB(A,B) = 514 - 56A+ (7A-40)8 - 18^2 Note that A^2 - A and B^2 = 32 16) Find the Nash Equilibrium. What is the optimal advertisement budget of Firm A? (Go to Google Form to fill in the number of the optimal budget of Firm A and then upload your work and it will be graded for partial credits if you make mistakes)

Answer 1

Hence, at the nash equilibrium,

от Е83 р т (в - 24 А. | |Р - 24 ЗА о ОЛ : Б. Ед 1| 24 3 514 56A 4 ( 11 - 20 р НА - 40 - Рес 40 1A П Nain equilibrium Best seepouse Of A (BRA) But f«роции | ( BE ). А - ТА - 4 | | О. А - 17А ЧЧО 3. 16 16 Чууд ҮҮД 16 AX 488 6. 34 11. 24 yas шу-220 - 1 24 2.18 TL 6 th = 497 8% (218) 4 1 (218) - (6-3y) - (4-34) 1 ч. 2 50% 514 - 56 (69) +7 (63 (18) - 40 (28) - (28) 16. 766 4,505 2 - Та 1 = ALUS

the optimal advertisements budget of firm A = 6.34

the optimal advertisements budget of firm B = 2.18

profit of firm A = 144.2508

profit of firm B = 163.756

the difference in the optimal profit = 19.5052