One strategy that firms often strive for is what is called "product differentiation", where a firm, either through advertising or other means, convinces consumers that it's product is different than what other firms are offering. One question is whether or not differentiating one's product translated into increased profitability, which would explain such behavior by firms. To investigate this question, note that if two firms in the same industry have differentiated products, then each will demand a possibly different price in the market. Hence, let us describe Firm 1 and Firm 2's demand curves as P = 100- 21- Be2 P, =100-BQ - 22 respectively, where the term @ represents how much the other firm's production affects the demand for my product. Notice that when = 0 , the demand for each firm does not depend on the output of the other firm at all, so that each firm is in essence a monopoly. On the other hand, if / is very large, then the demand for each firm can increase or decrease by large amounts depending on what the other firm does. Therefore, we may interpret this as follows: The more a firm can differentiate it's product, the smaller the / term, and the more it has monopoly power. Let us investigate whether differentiating our product is a profitable venture. To that end, given the demand curves above, it follows that for each firm that we have MR = 100-20 - Be MR = 100- BQ - 202 Also, if we assume that TC(Q ) =02 TC(Q,) = 02 it follows that MC(Q) =20 MC(Q,) = 20 2 Solve for each firm's best response function given the information above. BR : Q, = 100- -Q, BR : Q, = 100- - Q O BR : Q, = 25 - - 2 2 BR: Q, =25- - 2 O BR : Q, =25 - - BR : Q, =25 - -0, BR : Q, = 100- - 2 2 BR : Q, = 100--Q,QUESTION 12 (Product Differentiation Problem) Comparing the cases of when [3 = 6 and ,3 = 2 above, what can we conclude? We can conclude that when rms are able to differentiate their products, they are able to make more profits. C) One firm was able to increase prots, but the other wasn't. Therefore, differentiating one's product may or may not be beneficial. C) 0 Both firms exhibited lower prots after differentiating their products. Therefore, it is better to make your product as similar to your competitor's as possible. 0 We can not conclude anything with the information given. QUESTION 10 (Product Differentiation Problem) In the case when = 6, solve for Nash equilibrium and profits (Round each answer to two decimal places, for example 10.32. Also, do not use dollar signs in the profit calculation). 2 = 10 2, = 10 Firm 1 Profit= 200 Firm 2 Profit= 200QUESTION 11 (Product Differentiation Problem) In the case when = 2, solve for Nash equilibrium and profits (Round each answer to two decimal places, for example 10.32. Also, do not use dollar signs in the profit calculation). 2 = 9.63 2, = 9.63 Firm 1 Profit= 431.20 Firm 2 Profit= 431.20