Consider Two Firms That Produce Complementary Goods For Example Each Firm Could Be Producing Hot Dogs And Hot Dog Buns 1 (114.33 KiB) Viewed 13 times
Consider two firms that produce complementary goods. For example, each firm could be producing hot dogs and hot dog buns or printers and ink cartridges. Therefore, each firm's inverse demand function is decreasing in its own production and increasing in the production of the other firm. In particular, if q₁ and q2 are the firms' production levels, then their per-period profits are given by v₁(91, 92) = (10-9₁ +292)91 - 2q and v₂(91, 92) = (10 + 91-92)92 - 292.
(c) (4 points) Suppose both firms play the infinitely repeated version of this game with discount factors 8₁,82 € [0, 1]. Consider both firms are using grim-trigger strategies that reverse to the Nash equilibrium levels of production after deviation. What are the smallest discount factors that support the pair of production levels (91, 92) = (3,) in the infinitely repeated game? (d) (1 points) Suppose both firms share the same discount factor & € [0, 1]. What is the smallest discount factor that support the pair of production levels (9₁, 92) = (3,) in the infinitely repeated game? (e) (2 points) Is there a discount factor that would support the pair of production levels (91, 92) = (4,3) in the infinitely repeated game? If yes, compute the discount factor. If not, explain why not.
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