Question

I just need part 1 answered!!

1. Two firms compete in price in a market for infinite periods. In this market, there are N consumers; each buys one unit per period if the price does not exceed $10 and nothing otherwise. Consumers buy from the firm selling at a lower price. In case both firms charge the same price, assume consumers buy from each firm. Assume zero production cost for both firms. A possible strategy that may support the collusive equilibrium is: Announce a price $10 if the equilibrium price has always been $10; otherwise, announce the price as in the one-shot Bertrand game. 1.a. (3 points) Let 8 be the discount factor. Find the condition on 8 such that the above strategy can indeed support the collusive equilibrium. Now suppose that Firm 2's marginal cost is $4, but Firm l's marginal cost remains zero. 1.b. (3 points) Find the condition on d under which Firm 2 will not deviate from the collusive equilibrium. 1.c. (3 points) Find the condition on d under which Firm 1 will not deviate from the collusive equilibrium. 1.d. (4 points Knowing that both firms discount factor is 0.6, how should Firm 2 set its capacity constraint so that the collusive equilibrium can still be supported? (Hint: The idea here is that, by limiting its own output, Firm 2 lets Firm 1 have a greater market share. As a result, Firm l's gain of deviating from the collusive agreement is smaller.) 2. (4 points) In 1986, the U.S. Congress enacted a regulation (PL99-509) requiring railroads to disclose contractual terms with grain shippers. Following the passing of the regulation, rates increased on corridors with no direct competition from barge traffic, while rates decreased on corridors with substantial direct competition. How do you interpret these events?

Answer 1

1 a)

In infinite repeated bertrand game, both the firms will follow Grim trigger strategy: Set P=10 in initial period. Then set P=10, as long as other firm has set P=10 in all previous periods. Else, set P= 0 (Marginal cost) if other firm has ever set price other than 10.  

Answer: For all discount factors less than 50%, collusion is sustainable.

Working below:

Q-N if palo Go if polo If both firms conclude, they all behave as manote, pm = 10, Q =N ܡܘܐܫܝܢܘܠܘܢ ܠܢܟܢܟ ܓܝܓ݁ܶܢܐ Lone period : 7 collude SN Infinite period I couwde - 5 N t SN + SN tanni (its) Cits)? T collude - sx S N fragit fram defe ding One period π defect = 10x = to S Infinite period & defect - Lonto totaan defect -10 N So conclusion is possible if ☺ » (2) Scanned with CamScanner

e SN ZION Isso s ie so % equal to So for all discount factor less than 50% Callusive equilibrium is sustainable

1 b)

Furm a marginal cast z4 Furm a pragul from collusion - prm am 12- (2012 One period: T2 dit Carklude = 10XN -4X ON - SN-2N 3N a collunde = 3NT 3N +3 N + Infinite period. To its (AS) de = 3N -- Fuim a progut from deviatung One period π dogled = 10X N-UN Inginile pervad: To defect = 6NT o totam to defect -6N) -- 3 For collusiam = 3N GN - Is < 0.5 me 50% as I is less than I scanned with will collude CamScanner to so % as long or OS-

1 c)

classmate Date Page Form I marginal cast zo Form I profil from collusion one boriod. I Callusion a 10XN -o Ingenite period. I callesiana SNTSN + SN ta its (ts)² Callus iam a SN la fum I profit from defect One period: π defect = 10 N Infinite korrad: Ti defed =10 N+ 1 4,0 * 7 2/ 19 zlontan tant Lituad (175) ? >8 NtaNTaN tant tas I, defect SNT QN For Callusion - 8 N + 2 N SN Z AS 378 / 38 s Scanned with CamScanner

classmate Date Page Isco.375 ie 37.5% for all above Fim I will collyde values of S.

1 d)

classmate Date Page s = 0.6 Now furm 2 has to set Q2, such that it is not profitable. for fuim I to deviate form I propit from collusion - T one period. Collide - 10(N-Qz - zlos (N-Q2) - Infinite beriad: T Collide 10 (N-Q2) + 8 (N-Q2 CHS 10(N-Q2) -- +8 (0-82)+ --- (its) ♡ Form I profit from callusion one period: π defect =1ON Infinite period : π dege az IONT UN-Q) + 4 (N-Q2). Lits (48)² 2 IONA UN-Q2) Cit Its . - IONt u (N-Q2) I defect - ANT " (N-Q2) Slits) Cs Scanned with CamScanner

Form I will collaude if 0 2 10 (N-Q2) > LON+ 4 (N-Q2) 16.6 (N-Q2 7 IONt u (N-02) 166 N-16.6 Q2 7 ION + y.16N-4.160, 16 86 N- 16. B Q 2 7, 14.16 N- 4.16 2.44 N 2, 12:44 Q2 - 2.44 N Z Q2 12.44 ah < or 19 N aN/6 So fuim 2 should of approx one- le N/S doesn't deviate Scanned with CamScanner set its constraint fifth of N 7 0 201 that fim L , so CS