ECON 404 - Homework 1.pdf

# G iq 100 eg g 2g it 100 gie 9 i 9 i 9 i 29 i 98 noo

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g - Iq = ( 100 - Eg ) g - 2g it = ( 100 - g.IE , 9 i - 9 i ) 9 i - 29 i 98 ( noo - Iq ; ) - 2g i - 2 = O Q = Nt , o N 98 - CN 1) g - 2g = O q = Iffy p = too - . N * = ( 98 - IIe . N ) When N is large with lningaaf , p = 100 - nodes , N is approximately I so as N gets bigger I larger the cournot equilibrium reaches the competitive equilibrium .

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Firm 2 cost function is two time that of firm 1 , so firm I can charge at a price that maximizes its profit at price point less than firm 2 . Firm I can capture the entire market and basically works as a monopoly so it could charge less than firm I for the same product . It's the Ber tant Nash equilibrium as firm I 's best choice is to charge at the price lower than 2 that maximize its profit Firm I profit is 1.75 and firm I ' s option is to charge as close to firm I 's price as possible and that is their MCC g) = 2 . Firm 1 monopoly function is LI - p . Q - 91 t 9 a = Ia - of TCC a) = q McCoy ) = I . TCC ga ) = Iq McCrea ) =L TR Cq ) = p . 9 = ¥ q ) 9 = Eq q 'd MRC g) = Es - Lg MRC q ) = Mc Cq , I E - 29=1 Bertrand Nash equilibrium . .
(h) (6 points) Explain why a Bertrand competition in di ff erentiated product markets with identical firm (identical cost functions) does not achieve the p = MC condition. A Bertrand competition reaches p = MC when the products are homogeneous because firms will try to undercut each other 's prices until I goes down to the marginal cost of making the product . When firms produce differentiated products it is a different story because people do have different preferences 1 different tastes , they care about stay loyal to certain products they like . or care about the quantity of the products Ee here fore , if firms try to undercut each other is prices it may not help them increase their sales or get more customers from each other 's businesses . Apple products are an example . They are expensive , however people would still buy apple products and choose Apple products over other ( similar I differentiated ) products from other companies . It's because people using apple products get used to using Apple products , like the specific features / services it offers and decide to stick with Apple product despite the price .

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# Pt = 3 - Ige - qg P2 =3 - 91 - 292 FOC : Itt = ( B - Igy ga )qe FOC :q= (3-91-292) 92 take the derivative of htt we have : Take the derivative gets we have 0 = 3 - 491 - 92 0 = 3 - 91 - 492 ÷÷÷÷÷ :* .
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