One strategy that rms often strive for is what is called "product drlferentiation", where a rm, either through advertismg or other means, convinces consumers that its product is different than what other rms are offering. One question is whether or not differentiating one's product translated into increased protability, which would explain such behavior by rms. To investigate this question, note that if two rms 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 P1=1UU_Q1_)GQQ P22100[301-Qg respectively, where the term ,8 represents how much the other rm's production a'ects the demand for my product. Notice that when = U , the demand for each rm does not depend on the output of the other rm at all, so that each rm is in essence a monopoly. On the other hand, if is very large, then the demand for each rm can increase or decrease by large amounts depending on what the other rm does. Therefore, we may interpret this as follows: The more a rm can di'erentiate it's product, the smaller the ,8 term, and the more it has monopoly power. Let us investigate whether di'lferentiating our product is a protable venture. To that end, given the demand curves above, it follows that for each rm that we have MR1=1UD2Q1-02 M92 =1ooQi202 Also, ifwe assume that TC(Q1) : Q21 TCtOQ) : Q22 it follows that MC(01) = 201 MCtCJg) = 202 Solve for each rm's best response function given the information above. 05:?1 scumgo; 3.92 02:1OD%O1 03.91 (mas02 Ba2 mas01 @391 Gemgag as2 02:25 01 0 DD . ='lil_ (Product Differentiation Problem) In the case when / = 6, solve for Nash equilibrium and profits. O Q"1= 100, Firm 1 profits = 2800 Q"2 =100, Firm 2 profits = 2800 O Q*1 = 10, Firm 1 profits = 200 Q 2 = 10, Firm 2 profits = 200 O Q*1 = 28, Firm 1 profits = 100 Q 2= 28, Firm 2 profits = 100 O Q*1 =280, Firm 1 profits = 10 Q 2= 280, Firm 2 profits = 10 QUESTION 10 (Product Differentiation Problem) In the case when / = 1, solve for Nash equilibrium, and calculate profits. Compare this to what you found in the case when S = 6 . What can we conclude? We can not conclude anything with the information given. One firm was able to increase profits, but the other wasn't. Therefore, differentiating one's product may or may not be beneficial. Both firms exhibited lower profits after differentiating their products. Therefore, it is better to make your product as similar to your competitor's as possible. We can conclude that when firms are able to differentiate their products, they are able to make more profits